WAR DEPARTMENT

OFFICE OF THE CHIEF SIGNAL OFFICER

WASHINGTON

MILITARY CRYPTANALYSIS

Pa:r.t I

MONOALPHABETIC SUBSTITUTION SYSTEMS

By

WILLIAM 'F. FRIEDMAN

Principal Cryptanalyst

Chief of Signal Intelligence Section

War Plam and Training Divi.ion

PREPARBD UNDER THE DIRECTION 01' THE

CHIBP SIGNAL OJ'li'ICER

trNI'l'ED STA.'t1S

GOVERNMENT PRINTING OPFICE

WASIIINGTON I 1918
MILITARY CRYPTANALYSIS, PART I. -MONOALPHABETIC SUBSTITUTION

SYSTEMS

B1lction Paragraphs Pages

I. Introductory remark8..___________________________________________________________________________________ 1- 3 1- 6

II. Fundamental principles__________________________________________________________________________________ 4- 8 7-10

III. Frequency distributions______________________________________________________________________________________ 9-11 11-17

IV. Fundamental uses of the uniliteral frequency distribution 12-16 18-26

V. Uniliteral substitution with standard cipher alphabets 17-22 27-39

VI. Uniliteral substitution with mixed cipher alphabets 23-34 40-58

VII. Multiliteral substitution with single-equivalent cipher alphabets 35-36 59-62

VIII. Multiliteral substitution with multiple-equivalent cipher alphabets.. 37-40 63-69

IX. Polygraphic substitution systems, ,________________ 41-46 70-98

X. Concluding remarks__________________________________________________________________________________ 47-50 99-104

XI. Appendix 105-120

(ID)
r

SECTION I

INTRODUCTORY REMARKS

PlII'lIg!'llph Scopeof this ten .. .. .________________________________________ 1

Mental equipment neceB8&1'Y for cryptanalytio work. .. ••_ 2

V&1ldity of reSults of crypt&nAlysia. • •__• ._ 3

1. Scope of this text.-a. It is assumed that the student has studied the two preceding

texts written by the same author and forming part of this series, viz, Elementary Military Cryptography, and Adronced Military Oryptography. These texts deal exclusively with cryptography

as defined therein; that is, with the various types of ciphers and codes, their principles of construction, and their employment in cryptographing and decryptographing messages. Particular

emphasis was placed upon such means and methods as are practicable for military usage. It is

also assumed that the student has firmly in mind the technically precise, special nomenclature

employed in those texts, for the terms and definitions therein will all be used in the present text,

with essentially the same significances. If thisis not the case, itis recommended that the student

review his preceding work, in order to regain a familiarity with the specific meanings assigned

to the terms used therein. There will be no opportunity herein to repeat this information and

unless he understands clearly the significance of the terms employed, his progress will be retarded.

b. This text constitutes the first of a series of texts on cryptanalysis. Although most of the

information contained herein is applicable to cryptograms of various types and sources, special

emphasis will be laid upon the principles and methods of solving military cryptograms. Except

for an introductory discussion of fundamental principles underlying the science of cryptanalyties,

this first text in the series will deal solely with the principles and methods for the analysis of

monoalphabetic substitution ciphers. Even with this limitation it will be possible to discuss

only a few of the many variations of this one type; but with a firm grasp upon the general principles no difficulties should be experienced with any variations that may be encountered.

c. This and some of the succeeding texts will deal only with elementary types of cipher

systems not because they may be encountered in military operations but because their study is

essential to an understanding of the principles underlying the solution of the modern, very much

more complex types of ciphers and codes that are likely to be employed by the larger governments today in the conduct of their military affairs in time of war.

d. All of this series of texts will deal only with the solution of visible secret writing. At

some future date, texts dealing with the solution of invisible secret writing, and with secret

signalling systems, may be prepared.

2. Mental equipment necessary for cryptanalytic work.-a. Captain Parker Bitt, in the

first United States Army manual ' dealing with cryptography, opens the first chapter of his

valuable treatise with the following sentence:

Bueeessin dealing with unknown ciphers is measured by these four things in the order named: perseverance,

careful methods of analysis. intuition. luck. (\ Q., h I, •

1 Hitt. Capt. Parker, Manual/or the Solution oj Mt'litary Ciphers. Army Servioe Schools Press, Fort Leavenworth, Kansas, 1916. 2d Edition. 1918. (Both out of print.)

(1)
2

These words are as true today as they were then. There is no royal road to success in the

solution of cryptograms. Hitt goes on to say:

Cipher work will have little permanent attraction for one who expects results at once, without labor, for

there is a vast amount of purely routine labor in the preparation of frequency tables, the rearrangement of

ciphers for examination, and the trial and fitting of letter to letter before the message begins to appear.

The present author deems it advisable to add that the kind of work involved in solving

cryptograms is not at all similar to that involved in solving "cross-word puzzles", for example.

The wide vogue the latter have had and continue to have is due to the appeal they make to the

quite common instinct for mysteries of one sort or another; but in solving a cross-word puzzle

there is usually no necessity for performing any preliminary labor, and palpable results become

evident after the first minute or two of attention. This successful start spurs the cross-word

"addict" on to complete the solution, which rarely requires more than an hour's time. Furthermore, cross-word puzzles are all alike in basic principle and once understood, there is no more to

learn. Skill comes largely from the embellishment of one's vocabulary, though, to be sure, constant practice and exercise of the imagination contribute to the ease and rapidity with which

solutions are generally reached. In solving cryptograms, however, many principles must be

learned, for there are many different systems of varying degrees of complexity. Even some of

the simpler varieties require the preparation of tabulations of one sort or another, which many

people find irksome; moreover, it is only toward the very close of the solution that results in the

form of intelligible text become evident. Often, indeed, the student will not even known whether

he is on the right track until he has performed a large amount of preliminary "spade work"

involving many hours of labor. Thus, without at least a willingness to pursue a fair amount of

theoretical study, and a more than average amount oj patience and perseverance, little skill and

experience can be gained in the rather difficult art of cryptanalysis. General Givierge, the author

of an excellent treatise on cryptanalysis, remarks in this connection: 2

The cryptanalyst's attitude must be that of William the Silent: No need to hope in order to undertake, nor

to succeed in order to persevere.

b. As regards Hitt's reference to careful methods of analysis, before one can be said to be a

cryptanalyst worthy of the name it is necessary that one should have firstly a sound knowledge

of the basic principles of cryptanalysis, and secondly, a long, varied, and active practical experience in the successful application of those principles. It is not sufficient to have read treatises

on this subject. One month's actual practice in solution is worth a whole year's mere reading

of theoretical principles. An exceedingly important element of success in solving the more

intricate ciphers is the possession of the rather unusual mental faculty designated in general

terms as the power of inductive and deductive reasoning. Probably this is an inherited rather

than an acquired faculty; the best sort of training for its emergence, if latent in the individual,

and for its development is the study of the natural sciences, such as chemistry, physics, biology,

geology, and the like. Other sciences such as linguistics and philology are also excellent. Aptitude in mathematics is quite important, more especially in the solution of ciphers than of codes.

c. An active imagination, or perhaps what Bitt and other writers call intuition, is essential,

but mere imagination uncontrolled by a judicious spirit will more often be a hindrance than a

help. In practical cryptanalysis the imaginative or intuitive faculties must, in other words, be

guided by good judgment, by practical experience, and by as thorough a knowledge of the general

situation or extraneous circumstances that led to the sending of the cryptogram as is possible

to obtain. In this respect the many cryptograms exchanged between correspondents whose

identities and general affairs, commercial, social, or political, are known are far more readily

2 Givierge, CMn~ral Marcel, Oour« de Cryptographie, Paris, 1925, p. 301.

"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"1 I

3

solved than are isolated cryptograms exchanged between unknown correspondents, dealing with

unknown subjects. It is obvious that in the former case there are good data upon which the

intuitive powers of the cryptamalyst can be brought to bear, whereas in the latter case'no such

data are available. Consequently, in the absence of such data, no matter how good the imagination and intuition of the cryptanalyst, these powers are of no particular service to him. Some

writers, however, regard the intuitive spirit as valuable from still another viewpoint, as may be

noted in the following: 3

Intuition, like a flash of lightning, lasts only for a second. It generally comes when one is tormented by .

a difficult decipherment and when one reviews in his mind the fruitless experiments already tried. Suddenly

the light breaks through and one finds after a few minutes what previous days of labor were unable to reveal.

This, too, is true, but unfortunately there is no way in which the intuition may be sumtnoned at will, when it is most needed! There are certain authors who regard as indispensable

the possession of a somewhat rare, rather mysterious facu1ty that they designate by the word

"flair", or by the expression "cipher brains." Even so excellent an authority as General

Givierge," in referring to this mental facility, uses the following words: "Over and above perseverance and this aptitude of mind which some authors consider a special gift, and which they

call intuition, or even, in its highest manifestation, clairvoyance, cryptographic studies will

continue more and more to demand the qualities of orderliness and memory." Although the

present author believes a special aptitude for the work is essential to cryptanalytic success, he is

sure there is nothing mysterious about the matter at all. Special aptitude is prerequisite to

success in all fields of endeavor. There are, for example, thousands of physicists, hundreds of

excellent ones, but only a. handful of world-wide fame. Shou1dit be said, then, that a physicist

I Lange et Soudsrt, TraiU de Cryptographie, LlbrairieFelix Alcan, Paris, 1925, p. 104.

C The following extracts are of interest in this connection: .

The fact that the scientific investigator works 50 per cent of his time by non-rational means is, it seems, quite

insufficiently recognized. There is without the least doubt an instinct fOfresearch, and often the most successful

investigators of nature are quite unable to give an account of thek reesona for doing such and such an experiment, or for placing side by side two apparently unrelated facts. Again, one of the most salient traits in the

character of the successful scientific worker is the capacity for knowing that a point is proved when it would not

appear to be proved to an outside intelligence functioning in a purely rational manner; thus the investigator

feels that some proposition is true, and proceeds at once to the next set of experiments without waiting and wasting

time in the elaboration of the formal proof of the point which heavier minds would need. Questioriless such a

scientific intuition may and does sometimes lead investigators astray, but it is quite certain that if they did

not widely make use of it, they would not get a quarter as far as they do. Experiments confirm each other, and a

false step is usually soon discovered. And not only by this partial replacement of reason by intuition does the

work of science go on, but also to the born scientific worker-and emphatically they cannot be made-the structure of the method of research is as it were given, 'he cannot explain it to you, though he may be brought to agree

a pOBtiori to a formal logical presentation of the way the method works.-Excerpt from Needham, Joseph,

The Sceptical Biolo(JiBt, London, 1929, p. 79.

The essence ofscientific method, quite simply, is to try to see how data arrange themselves into causal

configurations. Scientific problems are solved by collecting data and by "thinking about them all the time."

We need to look at strange things until, by the appearance of known configurations, they seem familiar, and to

look at familiar things until we see novel configurations which make them appear strange. We must look at

events until they become luminous. That is scientific method. .. Insight is the touchstone. •. The application of insight as the touchstone of method enables us to evaluate properly the role of imagination in scientific

1Jlethod. The scientific process is akin to the artistic process: it is a process of selecting out those elements of

experience which fit together and recombining them in the mind. Much of this kind of research is simply a ceaseless mulling over, and even the physical scientist has considerable need of an armchair. .• Our view of scientific method as a struggle to obtain insight forces the admission that science is half art . .• Insight is the

unknown quantity which has eluded students of scientific method.-Excerpts from an article entitled lmiqht anq

Scientific Method, by Willard Waller, in The Americ4n Journal of Sociology, VQ1, J(L, 1934,

lOp. cit., p. 302.
4

I 1"11111"11111"11111"11111"11111"11111"11111"11111"1111I"IIIII"IIIII"IIIII"IIIII"IIIII"IIIII"IIII~IIIII"IIIII"11111"11111"11111"11'1"

who has achieved very notable success in his field has done so because he is the fortunate poseeeser

of a mysterious faculty? That he is fortunate in possessing a special aptitude for his subject is

granted, but that there is anything mysterious about it, partaking of the nature of clairvoyance

(if, indeed, the latter is a reality) is not granted. While the ultimate nature of any mental

process seems to be as complete a mystery today as it has ever been, the present author would

like to see the superficial veil of mystery removed from a subject that has been shrouded in

mystery from even before the Middle Ages down to our own times. (The principal and easily

understandable reason for this is that governments have always closely guarded cryptographic

secrets and anything so guarded soon becomes "mysterious.") He would, rather, have the

student approach the subject as he might approach any other science that can stand on its own

merits with other sciences, because cryptanalytics, like other sciences, has a practical importance

in human affairs. It presents to the inquiring mind an interest in its own right as a branch of

knowledge; it, too, holds forth many difficulties and disappointments, and these are all the more

keenly felt when the nature of these difficulties is not understood by those unfamiliar with the

special circumstances that very often are the real factors that led to success in other cases.

Finally, just as in the other sciences wherein many men labor long and earnestly for the true

satisfaction and pleasure that comes from work well-done, so the mental pleasure that the

successful cryptanalyst derives from his accomplishments is very often the only reward for much

otthe drudgery that he must do in his daily work. General Givierge's words in this connection

are· well worth quoting:- .

Bome studies wDIlast for Yello1'8 before bearing fruit. In the case of others, cryptanalysts underta.king them

never get any result. But, for a cryptanalyst who likes the work, the joy of discoveries effacesthe memory of his

hours of doubt and impatience.

d. With his usual deft touch, Bitt says of the element of luck, as regards the role it plays in

analysis:

As to luck, there is the old miners' proverb: "Gold is where you find it."

The cryptanalyst is lucky when one of the correspondents whose ciphers he is studying

makes a blunder that gives the necessary clue; or when he finds two cryptograms identical in

text but in different keys in the same system; or when he finds two cryptograms identical in

text but in different systems, and so on. The element of luck is there, to be sure, but the cryptanalyst fflmt be on the alert if he is to profit by these lucky "breaks."

e. If the present author were asked to state, in view of the progress in the field since 1916,

what elements might be added to the four ingredients Bitt thought essential to cryptanalytic

success, he would be inclined to mention the following:

(1) A broad, general education, embodying interests covering as many fields of practical

knowledge as possible. This is useful because the cryptanalyst is often called upon to solve

messages dealing with the most varied of human activities, and the more he knows about these

activities, the easier his task.

(2) Access to a large library of current literature, and wide and direct contacts with sources

of collateral information. These often afford clues as to the contents of specific messages. For

example, to be able instantly to have at his disposal a newspaper report or a personal report of

events described or referred to in a message under investigation goes a long way toward simplifying or facilitating solution. Government cryptanalysts are sometimes fortunately situated in

this respect, especially where various agencies work in harmony.

(3) Proper coordination of effort. This includes the organization of cryptanalytic personnel

into harmonious, efficient teams of cooperating individuals.

• Op. cit., p. 301.

(4) Under mental equipment he would also include the faculty of being able to concentrate

on a problem for rather long periods of time, without distraction, nervous irritability, and

impatience. The strain under which cryptanalytie studies are necessarily conducted is quite

severe and too long-continued application has the effect of draining nervous energy to an

unwholesome degree, so that a word or two of caution may not here be out of place. One should

continue at work only so long as a peaceful, calm spirit prevails, whether the work is fruitful or

not..But just as soon as the mind becomes wearied with the exertion, or just as soon as a feeling

of hopelessness or mental fatigue intervenes, it is better to stop completely and turn to other

activities, rest, or play. It is essential to remark that systematization and orderliness of work

are aids in reducing nervous tension and irritability. On this account it is better to take the

time to prepare the data carefully, rewrite the text if necessary, and 80 on, rather than work

with slipshod, incomplete, or improperly arranged material.

(5) A retentive memory is an important asset to cryptanalytic skill, especially in the solution of codes. The ability to remember individual groups, their approximate locations in other

messages, the associations they form with other groups, their peculiarities and similarities, saves

much wear and tear of the mental machinery, as well.as much time in looking up these groups in

indexes.

J. It may be advisable to add a word or two at this point to prepare the student to expect

slight mental jars and tensions which will almost inevitably come to him in the conscientious

study of this and the subsequent texts. The present author is well aware of the complaint of

students that authors of texts on cryptanalysis base much of their explanation upon their foreknowledge of the "answer"-which the student does not know while he is attempting to follow

the solution with an unbiased mind. They complain too that these authors use such expressions

as "obviously", "naturally", "of course", "it is evident that", and so on, when the circumstances

seem not at all to warrant their use. There is no question but that this sort of treatment is apt

to discourage the student, especially when the point elucidated becomes clear to him only after

many hours' labor, whereas, according to the book, the author noted the weak spot at the first

moment's inspection. The present author can only promise to try to avoid making the steps

appear to be much more simple than they really are, and to suppress glaring instances of unjustiflable "jumping at conclusions." At the same time he must indicate that for pedagogical reasons

in many cases a message has been consciously "manipulated" so as to allow certain principles to

become more obvious in the illustrative examples than they ever are in practical work. During

.the course of some of the explanations attention will even be directed to cases of unjustified

inferences. Furthermore, of the student who is quick in observation and deduction, the author

will only ask that he bear in mind that if the elucidation of certain principles seems prolix and

occupies more space than necessary, this is occasioned by the author's desire to carry the

explanation forward in very short, easily-comprehended, and plainly-described steps, for the

benefit of students who are perhaps a bit slower to grasp but who, once they understand, are

able to retain and apply principles slowly learned just as well, if not better than the students

who learn more quickly.

3. Validity of results of cryptanalysis.-Valid, or authentic cryptanalytic solutions cannot

and do not represent "opinions" of the cryptanalyst. They are valid only so far as they are

wholly objective, and are susceptible of demonstration and proof, employing authentic, objective

methods. Itshould hardly be necessary (but an attitude frequently encountered among laymen

makes it advisable) to indicate that the validity of the results achieved by any serious cryptanalytic studies on authentic material rests upon the same sure foundations and are reached by

the same general steps as the results achieved by any other scientific studies; viz, observation,

hypothesis, deduction and induction, and confirmatory experiment. Implied in the latter is the

I

i

i

i

I

I

I

i

I

I

I
[:

;

I

I

I

I

i

I

i

I

i

I

6

possibility that two or more qualified investigators, each working independently upon the same

material, will achieve identical (or practically identical) results. Occasionall;y a ps.eudo-~ryptanalyst offers "solutions" which cannot withstand such tests; a second, unbiased, illvestlga~r

working independently either cannot consistently apply the methods alleged to ha~e been applied

by the pseudo-cryptanalyst, or else, if he can apply them ~t ~ll, the.results (pla~-t~xt translations) are far different in the two cases. The reason for this IS that ill such cases It IS generally

found that the "methods" are not clear-cut, straightforward or mathematical in charac.ter.

Instead, they often involve the making of judgments on matters t~o tenuou~ to measure,. we~gh,

or otherwise subject to careful scrutiny. In such cases, the conclusion to which the unprejudiced

observer is forced to come is that the alleged "solution" obtained by the first investigator, the

pseudo-cryptanalyst, is purely subjective. In nearly all co:ses wh~re this ~s happened (and they

occur from time to time) there has been uncovered nothing which can ill a~y war b~ used to

impugn the integrity of the pseudo-cryptanalyst. The wors~ that can be s~d of.him IS that he

has become a victim of a special or peculiar form of self-delusion, and that his desire to solve the

problem, usually in accord with some previously-formed opinion, or notion, has over-balanced,

or undermined, his judgment and good sense," ,

7 Specific reference can be made to the following typ~cal "ease histories":

Donnelly,lgnatiu!l, The Great Cryptogra.m. Chicago, 1888.

O;rim. Orville W. j Sir Fr(mCilt &con's Cipher Story. Detroit, 1895.

'Gallu~, Elizabeth Wells, Francis &COfl.'S Biliter4I.Cipher. Detroit, 1900.

lolqaliquth, ,D. 8.• The Homer 01 ArisWtle. Oxford, 1923.. . NewboldWUliam Romaine, The Cipher of Roger Bacon, Philadelphia, 1928. (For a scholarly and

, complete demolition of Professor Newbold's work, see an article entitled Roger BilCOfl. aM

the Voyntch MS, by John M. Manly, in Speculum, Vol. VI, No.3, July 1931.)

Arensberg, Walter Conrad, The Cryptography 01 Shakespeare. Los Angeles, 1922.

The Shakespearean My8tery. Pittsburgh, 1928.

The Baconian Keys. Pittsburgh, 1928.

Feely, Joseph Martin, The Shakespearean C71pher. Rochester, N. Y., 1931.

Deciphering Shake8peare. Rochester, N. Y., 1934.

SECTION II

FUNDAMENTAL PRINCIPLES

Paragraph

The four basic operations in cryptanalysis ._. ._.__________________________________________________________________ 4

The determination of the language employed • . • ,_________________________ 5

The determination of the general system • • 6

The reconstruction of the specific key • • •• 7

The reconstruction of the plain text__.• . ••••_., 8

4. The four basic operations in cryptanalysis.-a. The solution of practically every cryptogram involves four fundamental operations or steps:

(1) The determination of the language employed in the plain-text version.

(2) The determination of the general system of cryptography employed.

(3) The reconstruction of the specific key in the case of a cipher system, or the reconstruction, partial or complete, of the code book, in the case of a code system; or both, in the case of an

enciphered code system.

(4) The reconstruction or establishment of the plain text.

b. These operations will be taken up in the order in which they are given above and in which

they usually are performed in the solution of cryptograms, although occasionally the second

step may precede the first.

6. The determination of the language employed.-a. There is not much that need be said

with respect to this operation except that the determination of the language employed seldom.

comes into question in the case of studies made of the cryptograms of an organized enemy.

By this is meant that during wartime the enemy is of course known, and it follows, therefore,

that the language he employs in his messages will almost certainly be his native or mother tongue.

Only occasionally nowadays is this rule broken. Formerly it often happened, or it might have

indeed been the general rule, that the language used in diplomatic correspondence was not the

mother tongue, but French. In isolated instances during the World War, the Germans used

English when their own language could for one reason or another not be employed. For example,

for a year or two before the entry of the United States into that war, during the time America

was neutral and the German Government maintained its embassy in Washington, some of the

messages exchanged between the Foreign Office in Berlin and the Embassy in Washington were

cryptographed in English, and a copy of the code used was deposited with the Department of

State and our censor. Another instance is found in the case of certain Hindu conspirators who

were associated with and partially financed by the German Government in 1915 and 1916; they

employed English as the language of their cryptographic messages. Occasionally the cryptograms of enemy agents may be in a language different from that of the enemy. But in general

these are.. as has been said, isolated instances; as a rule, the language used in cryptograms exchanged between members of large organizations is the mother tongue of the correspondents.

Where this is not the case, that is, when cryptograms of unknown origin must be studied, the

cryptanalyst looks for any indications on the cryptograms themselves which may lead to a

conclusion as to the language employed. Address, signature, and plain-language words in the

preamble or in the body of the text all come under careful scrutiny, as well as all extraneous

circumstances connected with the manner in which the cryptograms were obtained, the person

on whom they were found, or the locale of their origin and destination.

(7)
"'"1111'"1111'"1111'"1111'"1111'"1111'"1111'"1111'"1111'"1111'""1111111111111111111111111111111111111111111111111111111111111111111111.11111111111111

8

b. In special cases, or under special circumstances a clue to the language employed is found

in the nature and composition of the cryptographic text itself. For example, if the letters Kand

Ware entirely absent or appear very rarely in messages, it may indicate that the language is

Spanish, for these letters are absent in the alphabet of that language and are used only to spell

foreign words or names. The presence of accented letters or letters marked with special signs of

one sort or another, peculiar to certain languages, will sometimes indicate the language used.

The Japanese Morse telegraph alphabet and the Russian Morse telegraph alphabet contain

combinations of dots and dashes which are peculiar to those alphabets and thus the interception

of messages containing these special Morse combinations at once indicates the language involved.

Finally, there are certain peculiarities of alphabetic languages which, in certain types of cryptograms, viz, pure transposition, give clues as to the language used. For example, the frequent

digraph CH, in German, leads to the presence, in cryptograms of the type mentioned, of many

isolated C's and H's; if this is noted, the cryptogram may be assumed to be in German.

c. In some cases it is perfectly possible to perform certain steps in cryptanalysis before

the language of the cryptogram has been definitely determined. Frequency studies, for example,

may be made and analytic processes performed without this knowledge, and by a cryptanalyst

wholly unfamiliar with the language even if it has been identified, or who knows only enough

about the language to enable him. to recognize valid combinations of letters, syllables, or a few

common words in that language. He may, after this, call to his assistance a translator who may

not be a cryptanalyst but who can materially aid in making necessary assumptions based upon

his special knowledge of the characteristics of the language in question. Thus, cooperation

between cryptanalyst and translator results in solution.'

6. The determination of the general system.-a. Except in the case of the more simple

types of cryptograms, the determination of the general system according to which a given cryptogram has been produced is usually a difficult, if not the most difficult,step in its solution. The

reason for this is not hard to find.

b. As will become apparent to the student as he proceeds with his study, in thefinal analysis,

the solution of every cryptogram involving a form of substitution depends upon its reduction to monoalphabetic terms,ifit is not originally in those terms. This is true not only of ordinary substitution

ciphers, but also of combined substitution-transposition ciphers, and of enciphered code. If the

cryptogram must be reduced to monoalphabetic terms, the manner of its accomplishment is

usually indicated by the cryptogram itself, by external or internal phenomena which become

apparent to the cryptanalyst as he studies the cryptogram. If this is impossible, or too difficult

the cryptanalyst must, by one means or another, discover how to accomplish this reduction,

by bringing to bear all the special or collateral information he can get from all the sources at his

command. If both these possibilities fail him, there is little left but the long, tedious, and often

fruitless process of elimination. In the case of transposition ciphers of the more complex type,

the discovery of the basic method is often simply a matter of long and tedious elimination of

possibilities. For cryptanalysis has unfortunately not yet attained, and may indeed never

attain, the precision found today in qualitative analysis in chemistry, for example, where the

analytic processis absolutely clear cut and exact in its dichotomy. A fewwords in explanation of

what is meant may not be amiss. When a chemist seeks to determine the identity of an unknown

I The writer has seen in print statements that "during the World War ... decoded messages in Japanese

and Russian without knowing a word of either language." The extent to which such statements are exaggerated

will soon become obvious to the student. Of course, there are occasional instances in which a mere clerk with

quite limited experience may be able to "solve" a message in an extremely simple system in a language of which

he has no knowledge at all; but such a "solution" calls for nothing more arduous than the ability to recognize

pronounceable combinations of vowels and consonants--an ability that hardly deserves to be rated as "cryptanalytic" in any real sense. To say that it is possible to solve a cryptogram in a foreign language "without

knowing a word of that language" is not quite the same as to say that it is possible to do so with only a slight

knowledge of the language; and it may be stated without cavil that the better the cryptanalyst's knowledge of

the language, the greater are the chances for his success and, in any case, the easier is his work.

9

substance, he applies certain specific reagents to the substance and in a specificsequence. The

first reagent tells him definitely into which of two primary classes the unknown substance falls.

He then applies a second test with another specific reagent, which tells him again quite definitely

into which of two secondary classes the unknown substance falls,and so on, until finally he has

reduced the unknown substance to its simplest terms and has found out what it is. In striking

contrast to this situation, cryptanalysis affords exceedinglyfew "reagents" or tests that may be

applied to determine positively that a given cipher belongs to one or the other of two systems

yielding externally similar results. And this is what makes the analysis of an isolated, complex

cryptogram so difficult. Note the limiting adjective "isolated" in the foregoing sentence, for it

is used advisedly. It is not often that the general system fails to disclose itself or cannot be

discovered by painstaking investigation when there is a great volume of text accumulating from

a regular traffic between numerous correspondents in a large organization. Sooner orlater the

system becomes known, either because of blunders and carelessness on the part of the personnel

entrusted with the cryptographing of the messages, or because the accumulation of text itself

makes possible the determination of the general system by cryptanalytic studies. But in the

case of a single or even a few isolated cryptograms concerning which little or no information can

be gained by the cryptanalyst, he is often unable, without a knowledgeof, or a shrewd guess as to

the general system employed, to decompose the heterogeneous text of the cryptogram into

homogeneous, monoalphabetic text, which is the ultimate and essential step in analysis. The

only knowledge that the cryptanalyst can bring to his aid in this most difficult step is that gained

by long experience and practice in the analysis of many different types of systems.

c. On account of the complexities surrounding this particular phase of cryptanalysis, and

because in any scheme of analysis based upon successive eliminations of alternatives the cryptanalyst can only progress so far as the extent of his own knowledgeof all the possible alternatives

will permit, it is necessary that detailed discussion of the eliminative process be postponed until

the student has covered most of the field. For example, the student will perhaps want to know

at once how he can distinguish between a cryptogram that is in code or enciphered code from one

that is in cipher. It is at this stage of his studies impracticable to give him. any helpful indications on his question. In return it may be asked of him. why he should expect to be able to do

this in the early stages of his studies when often the experienced expert cryptanalyst is baftled on

the SRIne scoret

d. Nevertheless, in lieu of more precise tests not yet discovered, a general guide that may be

useful in cryptanalysis will be built up, step by step as the student progresses, in the form of a

series of charts comprising what may be designated An Analytical Key For Oryptanalysis. (See

Par. 50.) It may be of assistance to the student if, as he proceeds, he will carefully study the

charts and note the place which the particular cipher he is solving occupies in the general cryptanalytic panorama. These charts admittedly constitute only very brief outlines, and can

therefore be of but little direct assistance to him. in the analysis of the more complex types of

ciphers he may encounter later on. So far as they go, however, they may be found to be quite

useful in the study of elementary cryptanalysis. For the experienced cryptanalyst they can

serve only as a means of assuring that no possible step or process is inadvertently overlooked in

attempts to solve a difficult cipher.

e. Much of the labor involved in cryptanalytic work, as referred to in Par. 2, is connected

with this determination of the general system. The preparation of the text, its rewriting in

different forms, sometimes being rewritten in a half dozen ways, the recording of letters, the

establishment of frequencies of occurrences of letters, comparisons and experiments made with

known material of similar character, and so on, constitute much labor that is most often indispensable, but which sometimes turns out to have been wholly unnecessary, or in vain. In a

lilll

IIt1

mm

11111
10

recent treatise 2 it is stated quite boldly that "this work once done, the determination of the

system is often relatively easy." This statement can certainly apply only to the simpler types of

ciphers; it is entirely misleading as regards the much more frequently encountered complex

cryptograms of modern times.

T. The reconstruction of the specific key.-a. Nearly all practical cryptographic methods

require the use of a specific key to guide, control, or modify the various steps under the general

system. Once the latter has been disclosed, discovered, or has otherwise come into the possession

of the cryptanalyst, the next step in solution is to determine, if necessary, and if possible, the

specific key that was employed to cryptograph the message or messages under examination.

This determination may not be in complete detail; it may go only so far as to lead to a knowledge

of the number of alphabets involved in a substitution cipher, or the number of columns involved

in a transposition cipher, or that a one-part code has been used, in the case of a code system.

But it is often desirable to determine the specific key in as complete a form and with as much

detail as possible, for this information will very frequently be useful in the solution of subsequent

cryptograms exchanged between the same correspondents, since the nature of the specific key

hi a solved case may be expected to give clues to the specific key in an unsolved case.

, b. Frequently, however, the reconstruction of the key is not a prerequisite to, and does not

cOnstitute an absolutely necessary preliminary step in, the fourth basic operation, viz, the reeonsti1,lction.()r est1tblOOunent of the plain text. In many cases, indeed, the two processes are

carried along aimultanoously, the one assisting the other, until in the final stages both have been

completed in their entireties. In still other cases the reconstruction of the specific key·may

succeed instead of precede the reconstruction of the plain text, and is accomplished purely as a

matter of academic interest; or the specific key may, in unusual cases, never be reconstructed.

8. The reconstruction of the plaintext.-a. Little need be said at this point on this phase

of cryptanalysis. The process usually consists, in the case of substitution ciphers, in the establishment of equivalency between specific letters of the cipher text and the plaintext, letter by

letter, pair by pair, and so on, depending upon the particular type of substitution system

involved. In the case of transposition ciphers, the process consists in rearranging the elements of

the 'cipher text, letter by letter, pair by pair, or occasionally word by word, depending upon the

particular type of transposition system involved, until the letters or words have been returned

to their original plain-text order. In the case of code, the process consists in determining the

meaning of each code group and inserting this meaning in the code text to reestablish the original

plain text.

b. The foregoing processes do not, as a rule, begin at the beginning of a message and

continue letter by letter, or group by group in sequence up to the very end of the message. The

establishment of values of cipher letters in substitution methods, or of the positions to which

cipher letters should be transferred to form the plain text in the case of transposition methods,

comes at very irregular intervals in the process. At first only one or two values scattered here

and there throughout the text may appear; these then form the "skeletons" of words, upon which

further work, by a continuation of the reconstruction process, is made possible; in the end the

complete or nearly complete 8 text is established.

c. In the case of cryptograms in a foreign language, the translation of the solved messages

is a final and necessary step, but is not to be considered as a cryptanalytic process. However,

it is commonly the case that the translation process will be carried on simultaneously with the

cryptanalytic, and will aid the latter, especially when there are lacunae which may be filled in

from the context. (See also Par. 5c in this connection.)

2 Lange et Soudan, op. cit., p. 106.

, Sometimesin the caseof code,the meaning of a few codegroups may be lacking, becausethere is insufficient

text to establish their meaning.

SECTION III

FREQUENCY DISTRIBUTIONS

The simple or uniliteral frequency distribution. Paragrapb

Important features of the normal uniliteralfreq:~;;~;-~rib~tk>~~~~~~~~~::~::::::::::::::::::::::::::::::::::::::::: 1~ Constancy of the standard or normal uniliteral frequency distribution. .••_._________ 11

. 9. The siJIlple or uniliteral frequency distribution.-a. It has long been known to cryptographers a~d typographers that the letters composing the words of any intelligible written text

compose~ In.anylanguage ~hich is alphabetic in construction are employed with greatly vaning

fre~~enCles. For ex~~le, o~ eross-secnon paper a simple tabulation, shown in Fig. 1, elilled a

unuiteraljrequ~nc.Y d~t1"tbutwn, 18 ~ade ~f .the letters composing the words of the preceding sentence, the variation ill frequency IS strikingly demonstrated. It is seen that whereas certain

letters, such as A, E, I, N, 0, R, S, and T, are employed very frequently, other letters, such as

C, G, P, and Ware employed not nearly so frequently, while still other letters such as F J Q V

all:dZ are employed either seldom or not at a.11. " , , ,

(Total=200 letters)

FIGURJll.

b. If.a similar ta~ulation is now made of the letters comprising the words of the second

.sentence In the preceding paragraph, the graph shown in Fig. 2 is obtained. Both sentences

have exactly the same number of letters (200).

::::: :::::

~.~ ~~~

~~~~ ~~~ ~~~

~:::::~~~~~~~-~~~~~:::::~~~~ -_::::: ABCDEFGHIJKLMNOPQRSTUVWXYZ

2 8 7 7 , G mOl g 6 U U 6 2 U UU 6 1 2 1 3 0

(Total=200 letters)

FIGt1BJl2.

. e. .A!tho~gh each of these two graphs exhibits great variation in the relative frequencies

WIth whi~h different lette~ ~re employed in the respective sentences to which they apply, no

marked differences are exhibited between the frequencies of the same letter in the two graphs.

~o~pare, for .example, the frequencies of A, B, C . . . Z in Fig. 1 with those of A, B, C, . • . Z

1Jl FIg.~ ". ~Slde from one or two exceptions, as in the case of the letter F, these two graphs agree rather strikingly.

(11)

==::

I::::::

1;11

I

II

lill

In

I
12 13

10: I~port~nt fea~ur~s of th.e normal uniliteral frequency distribution.-a. When the graph

shown m FIg. 3 IS studied in detail, the following features are apparent:

.(1) It is qu~te irreg.ular in ~ppearance. .This is because the letters are used with greatly

varyI~g frequenc~es, as discussed m the preceding paragraph. This irregular appearance is often

described by saying that the graph shows marked crests and troughs, that is, points of high frequency and low frequency.

i

.

i

I

766

780

231

967

49

V _

W _

X_. _

y._----

Z •__

TABLE 2-A.-Absolute jrequencies oj letters appearing in the combined five set8 oj me8sages totaling

50,000 letters, arranged alphabetwally

A 3,683 G ._ 819 L 1,821 Q...____ 175

B .__ 487 R 1,694 M__. 1 ,237 R._..._ 3,788

C 1,534 L . 3,676 N 3,975 S_..__. 3,058

D 2, 122 J . 82 0 3,764 T__• 4,595

E_. 6,498 K_____ 148 P .._ 1 ,335 U 1,300

F__.___ 1, 416

g. The frequencies noted in subperagraph j', when reduced to the basis of 1 000 letters and

~hen us~d. as a basis for.constructing simple chart that will exhibit the variati~ns in frequency

m a striking manner, yield the following graph which is hereafter designated as the normal or

standarduniliteraljrequency distribution for English telegraphic plain text: '

i?

i?

i? i?

g §§ -

~~ i?

i? i? ~i?

i? i?~ ~_i?

i?i? i?~i? i?~ i?i?~

i? i? ~~ ~~~ i? ~~ ~~ ~~~ ~~ _ i?~ ~~~

-~~ ~~ ~~ ~~i? ~~~~ ~~ ~~~ i?~~

i? ~~~~ ~~ ~~~~~ ~~~~

i? ~~~~_~i? ~i?~~~ ~i?i?i?

~i?i?i?i?i?i? ~~~i?i? i?i?~~~~ ~~~~~~~~~ ~~~~~ ~~~~~~

~~~i?~~i?~~~~~~~~~~~~~~~~~~ _

ABC D E F G H I J K L MN 0 P Q R STU V WX y Z

74 10 31 42 130 28 16 34 74 2 3 36 25 79 75 'n 3 76 61 92 26 15 16 5 19 1

FIGURE 3.

d. This agreement, or similarity, would be practically complete if the two texts were much

longer, for example, five times as long. In fact, when two texts of similar character, each containing more than 1,000 letters, are compared, it would be found that the respective frequencies

of the 26 letters composing the two graphs show only very slight differences. This means, in

other words, that in normal text each letter of the alphabet occurs with a rather constant or

characteriatw freq:uency which it tends to approximate, depending upon the length of the text

ana.lyzed. The longer the text (within certain limits), the closer will be the approximation,'

e. An experiment along these lines will be convincing. A series of 260 official telegrams J

passing through the War Department Message Center was examined statistically. The messages were divided into five sets, each totaling 10,000 letters, and the five diatributions shown

in Table I-A, were obtained.

J. H the five distributions in Table I-A are summed, the results are as shown in Table 2-A.

TABLE 1-A.-Ab8ol'l.4e freg:tUnCie8 of letter8 appearing in jive 8et8 of OOfJef'nmerdaJ, plain-tezl 16k.

gram8, each 8et containing10,000letter8, arranged aJ,phabeticaJly

I See footnote 5, page 16.

I These comprisedmessages from several departments in addition to the War Department and were all of

an administrative character.

K ....No.l K-eeNo.2 M-ae No. 8 :M-.e No. 4 M....No.6

Absolute AbIOlnte AbBolnte Ab80lute AbBolute

Letter I'nqIJelieJ Let... J'nItl1IIDClJ Letter FrequenClJ Letter J'req1WlC1 Letter FrequenClJ

A. 738 A 783 A 681 A.__ 740 A--__ 741

B_ 104 B_ 103 B.____ 98 B 83 B 99

C_ 319 C 300 C.___ 288 C 326 C 301 D_____ 387 D .u3 D 423 D 451 D 448 E..____ 1,367 E..___ 1,294 E 1,292 E 1,270 E 1,275 F__._ 253 F__.__ 287 F 308 F___ 287 F 281 G____ 166 G_____ 175 G____ 161 G 167 G____ 160 8.____..__ 310 8.-___ 361 H . 335 H...______ 349 H - 349 I._______ 742 I 760 I___.. 787 I_ - 700 I ___ 697

J 18 J._ 17 J___._ 10 J -- 21 J 16

K 36 It 38 K . 22 K 21 K 31

L 366 L- 393 L 333 L 386 L 344 .. 242 11.___ 240 .. 238 .. 249 .. 268

N....-__._._ 786 N______ 794 N____ 815 N 800 N 780

0.___.•.._ 685 0_______._ 770 0.._____ 791 0.____ 756 0 762

P---_._-- 241 P--_._- 272 P..._---- 317 P_---- 246 P.._- 260

Q. 40 Q 22 Q - 45 Q.--- 38 q 30

R 760 R.___•• 145 R.-___ 762 a, 736 R. 786

S _..._- 658 S__._.__ 588 S. 585 S_____ 628 S______. 604

T 936 T____ 879

T____ 894

T____ 958 T____. 928

U_ - 270 U_______ 233 U_______••_ 312 U______ 247 U____• 238 V.____ 163 V._,____ 173 V________•__•• 142 V____••___• 133 V___ 155

W____._. 166 W -- 163 W__•___•• 136 W_••••_____ 133 W___ 182

X--_.__ 43 x..____ 50 x.____.__..._ 44 X_._.__•__ 53 x.______ 41

y----- 191 y._------ 155 y--_._._.... 179 y._•••••_-----_. 213 y-------- 229

Z. 14 Z-______ 17 Z_.___._ 2 Z__._••• 11 Z________ 5

-- Total.__ 10,000 ._..._-.._--..__. 10,000 ----_.........----....--- 10,000 _.........._----- 10,000 -------- 10,000

148274-38-2
14 15

TABLE 3

(6) The frequencies of the letters of the alphabet are as follows:

~I

!!!

!!!!

lit

II!

I

I

ALPHABETICALLY ARRANGED

A______ 778 G__________ 174 L__________ 372 Q..--------- 8 V________• 112

B______ 141 H__________ 595 M._________ 288 R.._________ 651 W__________ 176

C______ 296 I_,________ 667 N__________ 686 S__________ 622 x._________ 27

D______ 402 J __________ 51 0_____ "____ 807 T__________ 855 y--------- 196

E______ 1 ,277 K__________ 74 P__________ 223 U__________ 308 Z__________ 17

F______ 197

ARRANGED ACCORDING TO FREQUENCY

E______ I ,277 R__________ 651 U__________ 308 y---------- 196 K._________ 74

T______ 855 S__________ 622 C__________ 296 W__________ 176 J __________ 51

0______ 807 H._________ 595 M__________ 288 G__________ 174 x._________ 27

A______ 778 D__________ 402 P__________ 223 B__________ 141 4 _________ 17

N______ 686 L__________ 372 F__________ 197 V__________ 112 Q..------_.- 8

I ______ 667

b. The data given in Fig. 3 and Table 3 represent the relative frequencies found in a large

volume of English telegraphic text of a governmental, administrative character. These frequencies will vary somewhat with the nature of the text analyzed. For example, if an equal

number of telegrams dealing solely with commercial transactions in the leather industry were

studied statistically, the frequencies would be slightly different because of the repeated occurrence

of words peculiar to that industry. Again, if an equal number of telegrams dealing solely with

military messages of a tactical character were studied statistically, the frequencies would differ

slightly from those found above for general governmental messages of an administrative character.

c. If ordinary English literary text (such as may be found in any book, newspaper, or printed

document) were analyzed, the frequencies of certain letters would be changed to an appreciable

degree. This is because in telegraphic text words which are not strictly essential for intelligibility

(such as the definite and indefinite articles, certain prepositions, conjunctions and pronouns) are

omitted. In addition, certain essential words, such as "stop", "period", "comma", and the like,

which are usually indicated in written or printed matter by symbols not easy to transmit telegraphically and which must, therefore, be spelled out in telegrams, occur very frequently. Furthermore, telegraphic text often employs longer and more uncommon words than does ordinary

newspaper or book text.

d. As a matter of fact, other tables compiled in the Office of the Chief Signal Officer gave

slightly different results, depending upon the source of the text. For example, three tables based

upon 75,000, 100,000, and 136,257 letters taken from various sources (telegrams, newspapers,

magazine articles, books of fiction) gave as the relative order of frequency for the first 10 letters

the following:

For 75,000 letters E T R N IO A S D L

For 100,000letters E T R I N°A S D L

For 136,257 letters E T RNA°I S L D

TABLE 4.-Frequency tablejor 10,000 letters oj literary English, as compiled by Bitt

Percent of

Frequency Percent of total in

total round

numbers

398 39.8 40

350 35.0 35

238 23.8 24

14 1.4 1

1,000 100.0 100

A__________ 74 G__________ 16 L__________ 36 Q..--------- 3 V__________ 15

B__________ 10 H__________ 34 M__________ 25 R.._________ 76 W__________ 16

C__________ 31 I __________ 74 N__________ 79 S__________ 61 X__________ 5

D__________ 42 J __________ 2 0__________ 75 T__________ 92 y---------- 19

E__________ 130 K__________ 3 P__________ 27 U__________ 26 Z__________ 1

F__________ 28

E__________ 130 I __________ 74 C__________ 31 Y__________ 19 X__________ 5

T__________ 92 S__________ 61 F___ ______ 28 G__________ 16 Q---------- 3 . N__________ 79 ~D---------- 42 P__________ 27 W__________ 16 K__________ 3

R__________ 76 L__________ 36 U__________ 26 V__________ 15 .J__________ 2

0__________ 75 H._________ 34 M__________ 25 •B__________ 10 Z__________ 1

A__________ 74 -"-

(7) The relative order of frequency of the letters is as follows:

TotaL . _

(8) The four vowels A, E, I,°(combined frequency 353) and the four consonants N, R, S, T

(combined frequency 308) form 661 out of every 1,000 letters of plain text; in other words, less

than ~, oj the alphabet is employed in writing %oj normal plain text.

(2) The relative positions in which the crests and troughs fall within the graph, that is, the

spatial relations of the crests and troughs, are rather definitely fixed and are determined by circumstances which have been explained in a preceding text." .

(3) The relative heights and depths of the crests and troughs within the graph, that is, the

linear extensions of the lines marking the respective frequencies, are also rather definitely fixed,

as would be found if an equal volume ofsimilar text were analyzed.

(4) The most prominent crests are marked by the vowels A,E, I, 0, and the consonants

N, R, S, T; the most prominent troughs are marked by the consonants J, K,Q, X, and Z.

(5) The important data are summarized in tabular form in Table 3.

6 Vowels: A E IOU Y _

20 Consonants:

5 High Frequency (D N R S T) . _

10 Medium Frequency (B C F G H L M P V W) _ 5 Low Frequency (J K Q X Z) _

3 Section VII, Elementary Military Cryptography.
260 telegrams referred to in paragraph 9 shows that the arithmetical average is 217 letters;

the statistical mean, or weighted average,' however, is 191 letters. These two results are,

however, close enough together to warrant the statement that the average length of telegrams

is approximately 200 letters. The frequencies given in Par. 9f have therefore been reduced to

a basis of 200 letters, and the following uniliteral frequency distribution may be taken as showing

the most typical distribution to be expected in 200 letters of telegraphic English text:

16

Hitt also compiled data for telegraphic text (but does not state what kind of messages) and

gives the following table:

TABLE 5.-Frequency table for 10,000 letters of telegraphic English, as compiled by Ritt

ALPHABETICALLY ARRANGED

A.__.._ 813 G...._._.__ 201 L_.__._..._ 392 Q.._._-_._- 38 V....._____ 136

B...___ 149 H.._.._. __. 386 M........__ 273 R______.___ 677 W.__ .______ 166

C___.__ 306 I ......._._ 711 N.......... 718 S....._.... 656 X__..____._ 51

D....._ 417 J._.c••__._ 42 0_.___.___. 844 T_.__._..__ 634 y_......._- 208

E______ 1 ,319 K..______._ 88 P._._____._ 243 U__..______ 321 Z__________ 6

F....._ 205

17

"'"''"'"''"'"''"'"''"'"''"'"''"'"''"'"''"'"''"'"''"'"''"'"''"'"'''""""''''''''''''''''''''''''''''''''''''''''''''''''''''1'1''''''

II-=cc

II!

I~i!

,jiiii

I ~II

I""

I

:::

:1m

ARRANGED ACCORDING TO FREQUENCY

E..____ 1 ,319 S__._....__ 656 U.._... ____ 321 F_._._.____ 205 K..________ 88

0._____ 844 T.__._.__._ 634 C______.___ 306 G._______._ 201 X._________ 51

A...... 813 D........._ 417 M......_... 273 W.......... 166 J ._____.... 42

N______ 718 L__________ 392 P_._____._. 243 B__._..____ 149 Q..._.. _--- 38

I._____ 711 H.... ____._ 386 y........_- 208 V..________ 136 Z.__.______ 6

R _____ 677

e. Frequency data applicable purely to English military text were compiled by Hitt,' from

a study of 10,000 letters taken from orders and reports. The frequencies found by him are given

in Tables 4 and 5.

11. Constancy of the standard or normal, uniliteral frequency distribution.-a. The

relative frequencies disclosed by the statistical study of large volumes of text may be considered

to be the standard or normal frequencies of the letters of written English. Counts made of

smaller volumes of text will tend to approximate these normal frequencies, and, within certain

limits," the smaller the volume, the lower will be the degree of approximation to the normal,

until, in the case of a very short message, the normal proportions may not obtain at all. It is

advisable that the student fix this fact firmly in mind, for the sooner he realizes the true nature

of any data relative to the frequency of occurrence of letters in text, the less often will his labors

toward the solution of specific ciphers be thwarted and retarded by too strict an adherence to

these generalized principles of frequency. He should constantly bear in mind that such data

are merely statistical generalizations, that they will be found to hold strictly true only in large

volumes of text, and that they may not even be approximated in short messages.

b. Nevertheless the normal frequency distribution or the "normal expectancy" for any

alphabetic language is, in the last analysis, the best guide to, and the usual basis for, the solution

of cryptograms of a certain type. It is useful, therefore, to reduce the normal, uniliteral

frequency distribution to a basis that more or less closely approximates the volume of text which

the cryptanalyst most often encounters in individual cryptograms. As regards length of messages, counting only the letters in the body, and excluding address and signature, a study of the

• Op. cit., pp. 6-7. 5 It is useless to go beyond a certain limit in establishing the normal-frequency distribution for a given

language. As a striking instance of this fact, witness the frequency study made by an indefatigable German,

Kaeding, who in 1898 made a count of the letters in about 11,000,000 words, totaling about 62,000,000 letters in

German text. When reduced to a percentage basis. and when the relative order of frequency was determined,

the results he obtained differed very little from the results obtained by Kasiski, a German cryptographer, from a

count of only 1,060 letters. See Kaeding, Haeufiqkeiisuioerterbuch, Steglitz, 1898; Kasiski, Die Geheimschriften

und die Dechiffrir-Kunst, Berlin, 1863.

FIGURS 4.

c. The student should take careful note of the appearance of the distribution 7 shown in

Fig. 4, for it will be of much assistance to him in the early stages of his study. The manner of

setting down the tallies should be followed by him in making his own distributions, indicating

every fifth occurrence of a letter by an oblique tally. This procedure almost automatically

shows the total number of occurrences for each letter, and yet does not destroy the graphical

appearance of the distribution, especially if care is taken to use approximately the same amount

of space for each set of five tallies. Cross-section paper is very useful for this purpose.

d. The word "uniliteral" in the designation "uniliteral frequency distribution" means

"single letter", and it is to be inferred that other types of frequency distributions may be encountered. For example, a distribution of pairs of letters, constituting a biliteral frequency distribution, is very often used in the study of certain cryptograms in which it is desired that pairs

made by combining successive letters be listed. A biliteral distribution of ABC D E F would

take these pairs: AB, BC, CD, DE, EF. The distribution could be made in the form of a large

square divided up into 676 cells. When distributions beyond biliteral are required (triliteral,

quadraliteral, etc.) they can only be made by listing them in some order, for example, alphabetically based on the 1st, 2d, 3d, ... letter.

S The arithmetical average Is obtained by adding each different length and dividing by the number of

different-length messages; the mean is obtained by multiplying each different length- by the number of messages

of that length, adding all products, and dividing by the total number of messages.

7 The use of the terms "distribution" and "frequency distribution", instead of "table" and "frequency

table", respectively, is considered advisable from the point of view of consistency with the usual statistical

nomenclature. When data are given in tabular form, with frequencies indicated by numbers, then they may

properly be said to be set out in the form of a table. When, however, the same data are distributed in a chart

which partakes of the nature of a graph, with the data indicated by horizontal or vertical linear extensions, or

by a curve connecting points corresponding to quantities, then it is more proper to call such a graphic representation of the data a distribution.
i6I

...

iiii

-=

""

;,~

I~i!! [I

Iii

IilI

II

'I:

II

1 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111IIIIIIIIIIIIIIII~"

I,

II"d

il

!Iil )

Ii

Ii

IitI

, 1

1111111I

19

b. In the preceding subparagraph the word "probably" was emphasized by italicizing it,

for there can be no certainty in every case of this determination. Usually these percentages in a transposition cipher are close to the normal percentages for plain text; usually, in a substitution cipher, they are far different from the normal percentages for plain text. But occasionally

a cipher message is encountered which is difficult to classify with

a reasonable degree of certainty

because the message is too short for the general principles of frequency to manifest themselves.

It is clear that if in actual messages there were no variation whatever from the normal vowel

and consonant percentages given in Table 3, the determination of the class to which It specific

cryptogram belongs would be an extremely simple matter. But unfortunately there is always

some variation or deviation from the normal. Intuition suggests that as messages decrease in

length there may be

a greater and greater departure from the normal proportions of vowels,

high, medium, and low-frequency consonants, until in very short messages the normal propertions may not hold at all. Similarly, as messages increase in length there may be a lesser and

lesser departure from the normal proportions, until in messages totalling

a thousand or more

letters there may be no difference at all between the actual and the theoretical proportions.

But intuition is not enough, for in dealing with specific messages of the length of those commonly

encountered in practical work the question sometimes arises as to exactly how much deviation

(from the normal proportions) may be allowed for in a cryptogram which shows

a considerable

amount of deviation from the normal and which might still belong to the transposition rather

than to the substitution class.

c. Statistical studies have been made on this matter and some graphs have been constructed

thereon. These are shown in Charts 1-4 in the form of simple curves, the use of which will now

be explained. Each chart contains two curves marking the lower and upper limits, respectively,

of the theoretical amount of deviation (from the normal percentages) of vowels or consonants

which may be allowable in

a cipher believed to belong to the transposition class.

d. In Chart 1, curve VI marks the lower limit of the theoretical amount of deviation from the

normal number of vowels to be expected in

a message of given length; curveV2 marks the upper

limit of the same thing. Thus, for example, in a message of 100 letters in plain English there

should be between 33 and 47 vowels (A

E IOU Y). Likewise, in Chart 2 curves HI andH

2

mark the lower and upper limits as regards the high-frequency consonants. Ina message of 100

letters there should be between 28 and 42 high-frequency consonants (0 N R 5 T). In Chart 3,

curves M

I and

M

2 mark the lower and upper limits as regards the medium-frequency consonants.

Ina message of 100 letters there should be between 17 and 31 medium-frequency consonants

(B C F GHLM P V W). Finally, in Chart 4, curvesL

I and

L

2 mark the lower and upper

limits as regards the low-frequency consonants. In

a message of 100 letters there should be

between 0 and 3 low-frequency consonants (J

KQ X Z). In using the charts, therefore, one

finds the point of intersection of the vertical coordinate corresponding to the length of the

message, with the horizontal coordinate corresponding to (1) the number of vowels, (2) the

number of high-frequency consonants, (3) the number of medium-frequency consonants, and

(4) the number of low-frequency consonants actually counted in the message. If all four points

of intersection fall within the area delimited by the respective curves, then the number of vowels,

high medium and low-frequency consonants corresponds with the number theoretically expected , , ..... in a normal plain-text message of the same length; since the message under investigation IS not

plain text, it follows that the cryptogram may certainly be classified asa transposition cipher.

On the other hand, if one or more of these points of intersection falls outside the area delimited

by the respective curves, it follows that the cryptogram is probably

a substitution cipher. The

distance that the point of intersection falls outside the area delimited by these curves is a more or

less rough measure of the improbability of the cryptogram's being transposition cipher.

SECTION IV

FUNDAMENTAL USES OF THE UNILITERAL FREQUENCY DISTRIBUTION

Paragraph

The four facts which can be determined froma study of the uniliteral frequency distribution fora eryptoDete=i;;~-t~-cl~-~-;'hi~h-~-~i~h;;-b~l~~~~~~~~~==~~~:::::::::::::::::::::::::::::::::::::::::::::::=~~:~~~~~~~~~~~~~~ ·~i Determining whether a substitution cipher is monoalphabetic or polyalphabetic________________________________ 14

Determining whether the cipher alphabet isa standard, ora mixed cipher alphabet______________________________ 15

Determining whether the standard cipher alphabet is direct or reversed______________________________________________ 16

12. The four facts which can be determined froma study of the unUiteral frequency distribution for a cryptogram. a. The following four facts (to be explained subsequently) can

usually be determined from an inspection of the uniliteral frequency distribution for a given

cipher message of average length, composed of letters:

(1) Whether the cipher belongs to the substitution or the transposition class;

(2) If to the former, whether it is monoalphsbetic or polyalphabetic in character;

(3) If monoalphabetic, whether the cipher alphabet is

a standard cipher alphabet ora mixed

cipher alphabet; ..

(4) If standard, whether it isa direct or reversed standard cipher alphabet.

b. For immediate purposes the first two of the foregoing determinations are quite important

and will be discussed in detail in the next two subparagraphs; the other two determinations will

be touched upon very briefly, leaving their detailed discussion for subsequent sections of the

text.

13. Determining the class to which

a cipher belongs.-a. The determination of the class

to whicha cipher belongs is usuallya relatively easy matter because of the fundamental difference

in the nature of transposition and of substitution as cryptographic processes. In

a transposition

cipher .the original letters of the plain text have merely been rearranged, without any change

whatsoever in their identities, that is, in the conventional values they have in the normal alphabet. Hence, the numbers of vowels (A, E, I, 0, U, Y), high-frequency consonants (0, N, R, 5, T),

medium-frequency consonants (B, C, F, G, H, L, M, P, V, W), and low-frequency consonants (J, K,

Q, X, Z) are exactly the same in the cryptogram as they are in the plain-text message. Therefore,

the percentages of vowels, high, medium, and low-frequency consonants are the same in the

transposed text as in the equivalent plain text. In

a substitution cipher, on the other hand, the

identities of the original letters of the plain text have been changed, that is, the conventional

values they have in the normal alphabet have been altered. Consequently, if

a count is made

of the various letters present in such

a cryptogram, it will be found that the number of vowels,

high, medium, and low-frequency consonants will usually be quite different in the cryptogram

from what they are in the original plain-text message. Therefore, the percentages of vowels,

high, medium, and low-frequency consonants are usually quite different in the substitution text

from what they are in the equivalent plain text. From these considerations it follows that if in

a specific cryptogram the percentages of vowels, high, medium, and low-frequency consonants

are approximately the same as would be expected in normal plain text, the cryptogram probably

belongs to the transposition class; if these percentages are quite different from those to be

expected in normal plain text the cryptogram probablybelongs to the substitution class.

(18)

--

Ii
20

e. Sometimes a cryptogram is encountered which is hard to classify with certainty even with

the foregoing aids, because it has been consciously prepared with a view to making the classification difficult. This can be done either by selecting peculiar words (as in "trick cryptograms")

or by employing a cipher alphabet in which letters of approximately similar normal frequeneie«

have been interchanged. For example, E may be replaced by 0, T by R, and so on, thus yielding

21

and Z; in the latter case, his eyes just as quickly note the presence of many low-frequency letters

and a corresponding absence of the usual high-frequency letters. '

g. Another rather quickly completed test, in the case of the simpler varieties of ciphers, is

to look for repetitions of groups ofletters. As will become apparent very soon, recurrences of

syllables, entire words and short phrases constitute a characteristic of all normal plain text.

Since a transposition cipher involves a change in the sequence of the letters composing a plain9

e

8 8

8

8

75

70

>;

:7

Z

I:> 8 6

6 .'!

IiiI ~6

S5

15 I 1>' is

'a 4 ! ! ~4 ,<l

.!!P

13 ,<l

'S

flo !3 1"1 3

a

"

" 2 13

2

IiiI

IS

2

-

I;

!I!

o 10 20 30 40 50 60 70 80 so I 0 I 0 I

Number of letters in message.

CUART No. I.-Curves marking the lower and upper limits ofthe theoretical amount of deviation from the normal number of vowels to beexpected

In messages of various lengths. (See Par. 1311.)

a cryptogram giving external indications of being a transposition cipher but which is really a

substitution cipher. If the cryptogram is not too short, a close study will usually disclose what

has been done, as well as the futility of so simple a subterfuge.

j. In the majority of cases, in practical work, the determination of the class to which a

cipher of average length belongs can be made from a mere inspection of the message, after the

cryptanalyst has acquired a familiarity with the normal appearance of transposition and of

substitution ciphers. In the former case, his eyes very speedily note many high-frequencyletters,

such as E, T, N, R, 0, and 5, with the absence of low-frequency letters, such as J, K, Q, X,

I I I

o 10 20 30 40 50 60 70 80 90 I

Number of letters in message.

CUART No. 2.-Curves marking the lower and upper limits of the theoretical amount of deviation from tilt normal number of h1gh-frequeney ClOIIlIO

nanta to beexpected in messages of various lengths. (Bee Par. 134'>

text meseage, such recurrences are broken up so that the cipher text no longer will show repetitions

of more or less lengthy sequences of letters. But if a cipher message does show many repetitions

and these are of several letters in length, say over four or five, the conclusion is at once warranted

that the c?pto~ram is most probably a substitution and not a transposition cipher. However,

for the beginner In cryptanalysis, it will be advisable to make the uniliteral frequency distribution,

and note the frequencies of the vowels, the high, medium, and low-frequency consonants. Then,

referring to Charts 1 to 4, he should carefully note whether or not the observed frequencies for

,.

.....

ii

iii

;~

==

ii
22

11111111111111111111111111111111111111111111111111111111111111111111111111111111111111I111111111111111111111111111111111111111111111111111111111111111111~"1111

,

,

I::

these categories of letters fall within the limits of the theoretical frequencies for a normal plaintext message of the same length, and be guided accordingly.

h. It is obvious that the foregoing rule applies only to ciphers composed wholly of letters.

If a message is composed entirely of figures, or of arbitrary signs and symbols, or of intermixtures

9

8

e :> 7

::;J

..::l 7

Cl 6 ro.

o

8

8 5

8'

'" 4

i

i

a 3

'l5

rl 3

.8

2

l2

r-l I

10 20 30 40 SO 60 70 80 90 100 110 120 130 140 ISO leo 110 180 190

Number of lett.ers In message.

CHART No. 3.-Curves marking the lower and upper limits of the theoretical amount of deviation from the normal number of medrum-trequencsconsonants to be expected In messages ofvarious lengths. (See Par. 13<1.)

of letters, figures and other symbols, it is immediately apparent that the cryptogramis a substitution cipher.

i. Finally, it should be mentioned that there are certain kinds of cryptograms whose class

cannot be determined by the method set forth in subparagraphs b, c, d above. These exceptions

will be discussed in a subsequent section of this text.'

14. Determining whether a substitution cipher is monoalphabetic or polyalphabetic.-a. It

will be remembered that a monoalphabetic substitution cipher is one in which a single cipher

alphabet is employed throughout the whole message, that is, a given plain-text letter is invariably

I Par. 47.

represented throughout the message by one and the same letter in the cipher text. On the other

hand, a polyalphabetic substitution cipher is one in which two or more cipher alphabets are

employed within the same message; that is, a given plain-text letter may be represented by two or

more different letters in the cipher text, according to some rule governing the selection of the

equivalent to be used in each case. From this it followsthat a single cipher letter may represent

two or more different plain-text letters.

b. It is easy to see why and how the appearance of the uniliteral frequency distribution for

a substitution cipher may be used to determine whether the cryptogram is monoalphabetic or

polyalphabetic in character. The normal distribution presents marked crests and troughs by

5 ,~

0-

0-

fil 3

f

'0

] 2

l

sr-l

o 10 20 30 40 50 60 70 60 90 100 110 120 I 0 140 ISO 160 I 0 180 200

Numher of letters in message.

CHART No. 4.-Curves marklng the lower and upper limits ofthe theoretlcsl amount of deviation from the normal number of low-frequency consonants to be expected In messagesofvarious lengths. (See Par.13d.)

virtue of two circumstances. First, the elementary sounds which the symbols represent are

used with greatly varying frequencies, it being one of the striking characteristics of every alphabetic language that its elementary sounds are used with greatly varying frequencies.! In' the

second place, except for orthographic aberrations peculiar to certain languages (conspicuously,

English and French), each such sound is represented by the same symbol. It follows, therefore,

that since in a monoalphabetic substitution cipher each different plain-text letter (=elementary

sound) is represented by one and only one cipher letter (=elementary symbol), the uniliteral

frequency distribution for such a cipher message must also exhibit the irregular crest and trough

appearance of the normal distribution, but with only this important modification-the ab"solute

2 The student who is interested in this phase of the subject may find the following reference of value: Zipf'

G. K., Selected Studie8 of the Principle of Relative Frequency in Language, Cambridge, Maes., 1932.

l
1111111 1111111 1111111 1111111 1111111 1111111 1111111 1111111 1111111 1111111 1111111 1111111 11I1I1I11I111I11I111I11I111I11I111I11I111I11I111I11I111I11I111I11I111~11I11II

i

II:;;

;'·1',',' ~~

'II

!I!

iii

o 30 40 0 60 7 o 0 10 I

2

25

2

22 -"-:-

21

2 .; I

III ."l

=co I

2l 17 III

'lS 1 III J

§ I III

= I

'tl I

I 12

II

1"1 1

7

bets is so large that ifuniliteral frequency distributions are made of the letters the distributions

are practically identical with those which are obtained by random selections of letters out of a hat.

g. In using this chart, one finds the point of intersection of the vertical coordinate corresponding to the length of the message, with the horizontal coordinate corresponding to the

observed number of blanks in the distribution for the message. If this point of intersection falls

closer to curve P than it does to curve R, the number of blanks in the message approximates or

corresponds more cl?sely to the number theoretically expected in a plain-text message than it

does to a ra~dom (CIpher-text) message of the same length; therefore, this is evidence that the

cryptogram IS monoalphabetic. Conversely, if this point of intersection falls closer to curve R

25

Number of letters In message.

CHART No. 5.-Curves showlng the average number of blanks theoreticallY e.s:pectedIn distributions for plain text (P) and for random text (R) for

messagesof VWOllS lengths. (Bee Par. 14/.)

than to curve P, the ~umber of blan~s in the message approximates or corresponds more closely

to the number theoretically expected in a random text than it does to a plain-text message of the

same length; therefore, this is evidence that the cryptogram is polyalphabetic.

h. Practical examples of the use of this chart will be given in some of the illustrative messages

to follow.

15. Determining whether the cipher alphabet is a standard, or a mixed cipher alphabet.-

a. As~uming that the uniliteral frequency distribution for a given cryptogram has been made, and

that It shows clearly that the cryptogram is a substitution cipher and is monoalphabetic in

character, a consideration of the nature of standard cipher alphabets 3 almost makes it obvious

how an inspection of the distribution will disclose whether the cipher alphabet involved is a

standard cipher alphabet or a mixed cipher alphabet. If the crests and troughs of the distribu-

• See Sec. VIII, Elementary Military Cryptography.

positiom oj the crests and trO'UgM 'IJJiJ1 not bethe same a8 in the normal. That is, the letters accompanying the crests and the troughs in the distribution for the cryptogram will be different from

those accompanying the crests and the troughs in the normal distribution. But the marked

irregularity of the distribution, the presence of accentuated crests and troughs, is in itself an

indication that each symbol or cipher letter always represents the same plain-text letter in that

cryptogram. Hence the general rule: A marked crest and trough appearance in the uniliteral

frequency di8tribution jora given cryptogram indicates that a single cipher alphabet is involved and

comtitutes one oj the tests jor a monoalphabetic substitution cipher.

c. On the other hand, suppose that in a cryptogram each cipher letter represents several

different plain-text letters. Some of them are of high frequency, others of low frequency. The

net result of such a situation, so far as the uniliteral frequency distribution for the cryptogram

is concerned, is to prevent the appearance of any marked crests and troughs and to tend to reduce

the elements of the distribution to a more or less common level. This imparts a "flattened

out" appearance to the distribution. For example, in a certain cryptogram of polyalphabetic

construction, K.=Ep, Gp, and Jp; R.=Ap, Dp, and Bp; X.=Op, Lp, and Fp. The frequencies of

K.,R., and X.willbe approximately equal because the summations of the frequencies of the several

plain-text letters each of these cipher letters represents at different times will be about equal.

If this same phenomenon were true of all the letters of the cryptogram, it is clear that the

frequencies of the 26 letters, when shown by means of the ordinary uniliteral frequency distribution, would show no striking differences and the distribution would have the flat appearance of

a typical polyalphabetic substitution cipher. Hence, the general rule: The absence oj marked

creBfs and trO'U{Jhs in theuniliteral jrequency di8tribution indicates that two or more cipher alphabets

are involDed. The jloJtened-out appearance oj the distribution constitutes one oj the tests jor a polyalphabetic substitution cipher.

d. The foregoing test based upon the appearance of the frequency distribution constitutes

only one of several means of determining whether a substitution cipher is monoalphabetic or

polyalphabetic in composition. It can be employed in cases yielding frequency distributions

from which definite conclusions can be drawn with more or less certainty by mere ocular examination. In those cases in which the frequency distributions contain insufficient data to permit

drawing definite conclusions by such examination, certain statistical tests can be applied. These

will be discussed in a subsequent text.

e. At this point, however, one additional test will be given because of its simplicity of application. It may be employed in testing messages up to 200 letters in length, it being assumed that

in messages of greater length ocular examination of the frequency distribution offers little or no

difficulty. This test concerns the number oj blanks in the frequency distribution, that is, the

number of letters of the alphabet which are entirely absent from the message. It has been

found from statistical studies that rather definite "laws" govern the theoretically expected number of blanks in normal plain-text messages and in frequency distributions for cryptograms of

different natures and of various sizes. The results of certain of these studies have been embodied

in Chart 5.

j. This chart contains two curves. The one labeled P applies to the average number of

blanks theoretically expected in frequency distributions based upon normal plain-text messages

of the indicated lengths. The other curve, labeled R, applies to the average number of blanks

theoretically expected in frequency distributions based upon perfectly random assortments of

letters; that is, assortments such as would be found by random selection of letters out of a hat

containing thousands of letters, all of the 26 letters of the alphabet being present in equal proportions, each letter being replaced after a record of its selection has been made. Such random

assortments correspond to polyalphabetic cipher messages in which the number of cipher alpha-
I

=I

-I

=:¥

-i

.]I

tion occupy positions which correspond to th~ relative posit~ons they occupy in ~h~ normal

frequency distribution, then the cipher alphabet IS

a standard CIpher alphabet. If this IS no~ the

case, then it is highly probable that the cryptogram has been prepared by the use of

a mixed

cipher alphabet.

. '1 bl

b.A mechanical test may be applied in dou?tful cas.es aris~g fro~ la~k of ~aten~l aV~1ae

for study. Just what this test involves, and an illustration of Its application will be given

m the

next section using specific examples.. 16. De;erming whether the standard cipher alphabet is direct or reversed.-Assu~g

that the frequency distribution for a given cryptogram shows cle~l~ thata standard CIpher

alphabet is involved, the determination as to whether the alphabet IS direct or reversed c~ a~so

be made by inspection, since the difference between the two is merelya ~atter of the d'/,~ect'Wn

in which the sequence of crests and troughs progresse~-t~ th? rig~t, asm normal reading or

writing, or the left. In

a direct cipher alphabet the.direction ill whic~ the. crests and tr~ughs

of the distribution should be read is the normal direction, from left to nght; illa reversed CIpher

alphabet this direction is reversed, from right to left.

SECTIONV

UNILITERAL SUBSTITUTION WITH STANDARD CIPHER ALPHABETS

Parllll'llph

Principles of solution by constructionand analyllis of the uniliteral frequenoy distribution______________________ 17

Theoretical example of solution, " •

" .-------------------- 18

Practical example of solution by the frequency method .----------_____________________ 19

Solution by completing the plain-component sequence .__________________ 20

Special remarks on the method of solution by completing the plain-component sequence____________________________ 21

Value of mechanical solution as

a short cut . .;• ..__ 22

17. Principles of solution by construction and analysis of the uniliteral frequency disttibution.-a. Standard cipher alphabets are of two sorts, direct and reversed. The analysis of

monoalphabetic cryptograms prepared by their use follows almost directly from

a consideration of

the nature of such alphabets. Since the cipher component of

a standard cipher alphabet consists

either of the normal sequence merely displaced 1, 2, 3, ... intervals from the normal point of

coincidence, or of the normal sequence proceeding in a reversed-normal direction, it is obvious

that the uniliteral frequency distribution for a cryptogram prepared by means of such a cipher

alphabet employed monoalphabetically will show crests and troughs whose relative positions

and frequencies will be exactly the same as in the uniliteral frequency distribution for the plain

text of that cryptogram. The only thing that has happened is that thewhole set of crests and

troughs of the distribution has been displaced to the right or left of the position it occupies in the

distribution for the plain text; or else the successive elements of the whole set progress in the

opposite direction. Hence, it followsthat the correct determination of the plain-text value of the

letter marking any crest or trough of the uniliteral frequency distribution will result at one

stroke in the correct determination of the plain-text values of all the remaining 25 letters respectively marking the other crests and troughs in that distribution. Thus, having determined the

value of a single element of the cipher component of the cipher alphabet, the values of all the

remaining letters of the cipher component are automatically solved at one stroke. In more

simple language, the correct determination of the value of a single letter of the cipher text

automatically gives the values of the other 25 letters of the cipher text. The problem thus

resolves itself intoa matter of selecting that point of attack which will most quickly or most

easily lead to the determination of the value of one cipher letter. The single word identification

will hereafter be used for the phrase "determination of the value of a cipher letter"; to identifya

cipher letter is to find its plain-text value.

b. It is obvious that the easiest point of attack is to assume that the letter marking the crest

of greatest frequency in the frequency distribution for the cryptogram representsEp

• Proceeding

from this initial point, the identifications of the remaining cipher letters marking the other crests

and troughs are tentatively made on the basis that the letters of the cipher component proceed

in accordance with the normal alphabetic sequence, either direct or reversed. If the actual

frequency of each letter marking

a crest or a trough approximates toa fairly close degree the

normal theoretical frequency of the assumed plain-text equivalent, then the initial identification

ec=E

p may be assumed to be correcfand therefore the derived identifications of the other cipher

letters may be assumed to be correct. If the original starting point for assignment of plain-text

values is not correct, or if the direction of "reading" the successive crests and troughs of the

(27)

--

i~

"~

g.

'Iii ,..

~i,.

!ill

i.

~;;

YI!

II.

11-

ii;;;

!!ii

il

iii

III

""

jii

III"II..

..

III

III

II
28

I IUIIII 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 IUIIII 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 IUIIII 1"1111 1"1111 1"1111

29

distribution is not correct, then the frequencies of the other 25 cipher letters will not correspond

to or even approximate the normal theoretical frequencies of their hypothetical plain-text equivalents on the basis of the initial identification. A new initial point, that is, a different cipher

equivalent must then be selected to represent Ep ; or else the direction of "reading" the crests and

troughs must be reversed. This procedure, that is, the attempt to make the actual frequency

relations exhibited by uniliteral frequency distribution for a given cryptogram conform to the

theoretical frequency relations of the normal frequency distribution in an effort to solve the

cryptogram, is referred to technically as "fitting the actual uniliteral frequency distribution for a

cryptogram to the thoretical uniliteral frequency distribution for normal plain text", or, more

briefly, as "fitting thejrequencydistrib1dionjor the cryptogram to the normaljrequencydistrib1ditm",

or, still more briefly, "fitting the distrib-ution to the normal." In statistical work the expression

commonly employed in connection with this process of fitting an actual distribution to a theoretical one is "testing the goodness of fit." The goodness of fit may be stated in various ways,

mathematical in character.

c. In fitting the actual distribution to the normal, it is necessary to regard the cipher component (that is, the letters A... Z marking the successive crests and troughs of the distribution)

as partaking of the nature of a wheel or sequence closing in upon itself, so that no matter with

what crest or trough one starts, the spatial and frequency relations of the crests and troughs are

constant. This manner of regarding the cipher component as being cyclic in nature is valid

because it is obvious thattherelative positionsandjrequemies oj thecrests and troughsojanyuniliteralfrequency distrib'ldion must remain the same regardle8s oj what letter is employed as the initial point

oj the distrib'ldion. Fig. 5 gives a clear picture of what is meant in this connection, as applied to

the normal frequency distribution.

- - ~~ ~~~ _~~ _~ ~~ ~~~ _~2

~~~~~~~~~ ~~~~~ ~~~~~~-~ ~~~~~~

ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEF

- ~~~ ~~

~~- ~~~ ~~ ~- ~~- ~~~~~~ ~-~~~~~~ ~~~~~ ~~~~~~~~~

FED C B A Z Y X W V U T S R Q P 0 N M L K J I H G ___ FED+---0-- C B A

FIGURE II.

d. In the third sentence of subparagraph b, the phrase "assumed to be correct" was advisedly employed in describing the results of the attempt to fit the distribution to the normal,

because the final test of the goodness of fit in this connection (that is, of the correctness of the

assignment of values to the crests and troughs of the distribution) is whether the consistent

substitution of the plain-text values of the cipher characters in the cryptogram will yield intelligible plain text. If this is not the case, then no matter how close the approximation between

actual and theoretical frequencies is, no matter how well the actual frequency distribution fits

the normal, the only possible inferences are that (1) either the closeness of the fit is a pure coincidence in this case, and that another equally good fit may be obtained from the same data, or

else (2) the cryptogram involves something more than simple monoalphabetic substitution by

means of a single standard cipher alphabet. For example, suppose a transposition has been

applied in addition to the substitution. Then, although an excellent correspondence between

the uniliteral frequency distribution and the normal frequency distribution has been obtained

the substitu~ion of the cipher letters by their assumed equivalents will still not yield plain text:

However, aside from such cases of double encipherment, instances in which the uniliteral frequency distribution may be easily fitted to the normal frequency distribution and in which at

th~ same t~me an ~ttempted ~imple substitution fails to yield intelligible text are rare. It may be

said that, m practical operations whenever the uniliteral frequency distribution can be made to

fit the normal frequency distribution, substitution of values will result in solution' and as a

corollary, whenever the uniliteral frequency distribution cannot be made to fit the normal

frequency distribution, the cryptogram does not represent a case of simple monoalphabetic

substitution by means of a standard alphabet. '

. 18. Theoretical example of solution.-a. The foregoing principles will become clearer by

notmg the cryptographing and solution of a theoretical example. The following message is to be

cryptographed.

HOSTILE FORCE.ESTlMATED AT ONE REGIMENT INFANTRY AND TWO PLATOONS CAVALRY

MOVING SOUTH ON QUINNIMONT PIKE STOP HEAD OF COLUMN NEARING ROAD JUNCTION SEVEN

THREE SEVEN COMMA EAST OF GREENACRE SCHOOL FIRED UPON BY OUR PATROLS STOP

HAVE DESTROYED BRIDGE OVER INDIAN CREEK.

. b.• First, s~lely for pu~oses of demonstrating certain principles, the uniliteral frequency distribution forthismessage IS presented in Figure 6.

FIGURE 6.

. c. Now let t~e f~regoing message be cryptographed monoalphabetically by the following

CIpher alphabet, Yielding the cryptogram and the frequency distribution shown below.

Plain ABC D E F G H I J K L M N 0 P Q R STU V W X Y Z

Cipher G H I J K L M N 0 P Q R STU V W X Y Z ABC D E F

Plain_______________HOSTI LEFOR CEEST IMATE DATON. EREGI MENTI NFANT RYAND

Cipher _____________NUYZO RKLUX IKKYZ OSGZK JGZUT KXKMO SKTZO TLGTZ XEGTJ

Plain_______________TWOPL ATOON SCAVA LRYMO VINGS OUTHO NQUIN NIMON TPIKE

Cipher ____________ZCUVR GZUUT YIGBG RXESU BOTMY UAZNU TWAOT TOSUT ZVOQK

Plain_______________STOPH EADOF COl.UM NNEAR INGRO ADJUN CTION SEVEN THREE

Cipher____________YZUVN KGJUL IURAS TTKGX OTMXU GJPAT IZOUT YKBKT ZNXKK

Plain ______________SEVEN COMMA EASTO FGREE NACRE SCHOO LFlRE DUPON BYOUR

Cipher____________YKBKT IUSSG KGYZU LMXKK TGIXK YlNUU RLOXK JAVUT HEUAX

Plain_______________PATRO LSSTO PHAVE DESTR OYEDB RIDGE OVERI NDIAN CREEK

Cipher _____________VGZXU RYYZU VNGBK JKYZX UEKJH XOJMK UBKXO TJOGT IXKKQ

148274-38-3
30 31

CRYPTOGRAM

NUYZO

S K T Z 0

RXESU

Y'ZUVN

I Z 0 U T

LMXKK

VGZXU

UBKXO

RKLUX

TLGTZ

BOT M Y

KG J U L

Y,K B K T

T G I X K

RYYZU

T JOG T

IKKYZ

X E G T J

UAZNU

I U R A S

ZNXKK

YIN U U

VNGBK

I X K K Q

o S G Z K

ZCUVR

TWA 0 T

TTKGX

YKBKT

R LOX K

JKYZX

JGZUT

GZUUT

T 0 S U T

OTMXU

IUS S G

J A V U T

UEKJH

KXKMO

Y I G B G

Z V 0 Q K

G J PAT

KGYZU

HEUAX

XOJMK

14. Troughs corresponding to B, C, D and F, G, Ff are seen at H, I, J and L, M, Nin Fig. '7. In

fact, the two distributions may be made to coincide exactly, by shifting the frequency distribution

for the cryptogram six intervals to the left with respcet to the distribution for the equivalent

plain-text message, as shown herewith.

iii,

IIII

IIII

u.,

A J C Z 0

I V B Z G

M U U Q B

V 0 Q VN

J C Z 0 F

I Z K P Q

M B B G A

E Q B P U

P B I U 0

Q T T M L

IBM Q 0

Z W I L N

J'IGtIU 9.

(2) From the presence of repetitions and sd many low-frequency letters such as B, Q, and

Z it is at once suspected that this is.a substitution cipher. But to illustrate the steps that must

be taken in difficult cases in order to be certain in this respect, a uniliteral frequency distribution

f. Let us suppose now that nothing is known about the cryptographing process, and that

only the cryptogram and its uniliteral frequency distribution is at hand. It is clear that simply

bearing in mind the spatial relations of the crests and troughs in a normal frequency distribution

would enable the cryptanalyst to fit the distribution to the normal in this case. He would

naturally first assume that Gc=Ap , from which it would follow that if a. direct standard alphabet

is involved, Hc=Bp , Io=Cp, and so on, yielding the following (tentative) deciphering alphabet:

Cipher ABC D E F G H I J K L M N 0 P Q R STU V W X Y Z

Plain U V WX Y Z ABC D E F, G H I J K L M N 0 P Q R S T

g. Now comes the final test: If these assumed values are substituted in the cipher text,

the plain text immediately appears. Thus:

NUYZO RKLUX IKKYZ OSGZK JGZUT

H 0 S TIL E FOR C E EST I MAT E D A TON eoo.

h, Itshould be clear, therefore, that the selection of Go to represent Ap in the cryptogro.phing

process has absolutely no effect upon the relative spatial and frequency relations of the crests

and troughs, of the frequency distribution for the cryptogram, If Qo had been selected to represent Ap , these relations would still remain the same, the whole series of crests and troughs being

merely displaced further to the right of the positions they occupy when Go=Ap •

19. Practical example of solution by the frequency method.-a. The case of directstandard

alphabet cipkers.-(1) The following cryptogram is to be solved by applying the foregoing

principles:

J'IGUU 7

FIGllBB 8.

e."If the two distributions are compared in detail the student will clearly ~derstand how

easy the solution of the cryptogram would be to one who kn~w not~~ abo~t how It w~ prepared.

For example, the frequency of the highest crest, rep~esentm~ Ep in FIg. 6 IS 28; at an interval of

four letters before Ep there is another crest representing Ap With frequency 16. Be.tween Aand E

there is a trough, representing the low-frequency letters B, C, D. On the other SIde of E, at an

interval of lour letters, comes another crest, representing I with frequency 14. Between E and I

there is another trough, representing the low-frequency letters F, G, H. Compare these crests

and troughs with their homologous crests and troughs in Fig. 7. In the latter, the letter

marks the highest crest in the distribution with a frequency of 28; four letters before K there IS

another crest, frequency 16, and four letters on the other side of Kthere is another crest, frequency

d Let the student now compare Figs. 6.and 7, which have been superimposed in Fig. 8

fer co~venieneeine::tamin.&tion. crests'and troughs are present in both distributions; moreover

their rela.tive positions and frequencies have not been changed in the~~htest particular", O~y the absolute position of the sequence as a whole has been displaced SIX intervals to the right in

Fig. 7, as compared with the absolute position of the sequence in Fig. 6. .

I

I

t
. 34 35

.""" '"'''' '"'''' '"'''' '"'''' '"'''' '"'''' '"'''' '"'''' '"'''' "'"'' "'"'' "'"'' '""""''''''''''''''''''''''''''''''''''''''''''''''''''''''1'''1''

I

I

~,

'One of the strips should bear the sequence repeated. This permits juxtaposing the two sequences at all 26

possible points of coincidence so &II tQ ~~v~ complete cipher alphabet showing at all times.

Plain_______________ ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ

Cipher ABCDEFGHIJKLMNOPQRSTUVWXYZ

The values given by this juxtaposition are substituted for the first 20 letters of the cryptogram

and the following results are obtained.

Cryptogram__________________ X K V K ROT B G JOT MIG B G R X E

1st Test-"Plain text" Y L W L S PUC H K PUN J H C H S Y F I

I

IE

This certainly is not intelligible text; obviously, the two components were not in the position

indicated in this first test. The cipher component is therefore slid one interval to the right

making Ac=Cp , and a second test is made. Thus , '

Plain_______________ ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ

Cipher_____________ ABCDEFGHIJKLMNOPQRSTUVWXYZ

Cryptogram__________________ X K V K ROT B G JOT MIG B G R X E .

2d Test-"Plain text" Z M X M T Q V D I L Q V 0 KID I T Z G

Neither does the second test result in disclosing any plain text. But, if the results of the two

tests are studied a phenomenon that at first seems quite puzzling comes to light. '. Thus, suppose

the results Of the two tests are superimposed in this fashion. . Cryptogram X K V K ROT B G JOT M ! G B,GR X E: ,

1st Test-"Plain text" Y L W L S PUC H K PUN J H C H S Y F

2nd Test-"Plain text" Z M X M T Q V D I L Q V 0 KID I T Z G

(5) Note what has happened. The net result of the two experiments Was merely to continue

the normal sequence begun by the cipher letters at the heads of the several colum'M. It is

obvious that ifthe normal sequence is completed in each column the re8'U1ts will be exactly the same

as though the whole set oj ~5 possible tests had actually been performed. Let the columns therefore

be completed, as shown in Fig. 11.

XKVKROTBGJOTMIGBGRXE

YLWLSPUCHKPUNJHCHSYF

Z M X M T Q V DI L Q V 0 KID I T Z G

ANYNURWEJMRWPLJEJUAH

BOZOVSXFKNSXQMKFKt~I

CPAPWTYGLOTYRNLGLWCJ

DQBQXUZHMPUZSOMHMXDK

ERCRYVAINQVATPNINYEL

FSDSZWBJ ORWBUQOJ OZFM

GTETAXCKPSXCVRPKPAGN

HUFUBYDLQTYDWSQLQBHO

IVGVCZEMRUZEXTRMRCIP

JWHWDAFNSVAFYUSNSDJQ

KXIXEBGOTWBGZVTOTEKR

LYJYFCHPUXCHAWUPUFLS

MZKZGDIQVYDIBXVQVGMT

NALAHEJRWZEJCYWRWHNU

OBMBIFKSXAFKDZXSXIOV

PCNCJGLTYBGLEAYTYJPW

QDODKHMUZCHMFBZUZKQX

*R E PEL I N V A DIN G C A V A L R Y

SFQFMJOWBEJOHDBWBMSZ

TGRGNKPXCFKPIECXCNTA

U H S H 0 L Q Y D G L Q J F D Y D 0 U B

VI TI PMRZEHMRKGEZEPV C

W J U J Q N S A F'I N S LH F A F Q W D

..

An examination of the successive horizontal lines of the diagram discloses OM and O1!ly one,line

of plain text, that marked by the asterisk and reading REP ELI N V A DIN G C A VA L R Y.

FIQUD 11.

C' A V'A L R Y

1GB G RX E

,I N V A DIN G

OTBGJOTM

CRY~TOGRAM

'PlaintexL.__., REP E L

Cryptogram____ X K V K R

X K V K RO T B G JOT'MIG B G,R XE

(3) The enciphering alphabet shown above represents a case wherein the sequence of letters

of both components of the cipher alphabet is the normal sequence, with the sequence formiug the

cipher component merely shifted six intervals in retard (or 20 intervals in advance) of the position it occupiesinthe normal alphabet. If, therefore, two strips of paper bearing the letters of

the normalsequence, equally spaced, are regarded as the two components of the cipher alphabet

and are juxtaposed at all of the 25 possiblepoints of coincidence, it is obvious that one of these

25 juxtapositions must'correspond to theaetual juxtaposition shown in the enciphering alphabet

directlyabove," It is equally obvious that if a record were kept of the results obtained by applying the values-given at each juxtaposition to the letters of the cryptogram, one of these results

would yield the plain text of the cryptogram.

(4) Let the work be systematized and the results set down in an orderly manner for examination. It is obviously unnecessary to juxtapose the two components so that Ac=Ap , for on

the assumption of a direct standard alphabet, juxtaposing two direct normal components at

their normal point of coincidence merely yields plain text. The next possible juxtaposition,

therefore, is Ac=Bp • Let the juxtaposition of the two sliding stripstherefore be Ac=Bp, as shown

here:

he will note that the relative positions and extensions of the crests and troughs are identical;

they merely progress in opposite directions.

20. Solution by completing the plain-oomponent sequenoe.--a. The case oj dired, 8'landard

alphabet ciphers.-(l) The foregoing method of analysis, involving as it does the construction of

a uniliteral frequency distribution, was termed a solution by the jrequencymethod because it involves the construction of a frequency distribution and its study. There is, however, another

method which is much more rapid, almost, wholly mechanical, and which, moreover, does not

necessitate the construction or study of any frequency distribution whatever. An understanding of the method follows from a consideration of the method of encipherment of a message

by the use of a single, direct standard cipher alphabet.

(2) Note the following encipherment:

Message REPEL INVADING CAVALRY

ENCIPHERING ALPHABET

Pla.uL___________ ABC D E F G H I J K L M N 0 P Q R STU V W X Y Z

Cipher G H I J K L M N 0 P Q R STU V W X Y Z ABC D E F

ENCIPHERMENT

.i

i

"" r
86 37

(4) This does not yield.intelligible text, and therefore the reversed component is slid one

space forward and a second test is made. Thus:

Plain_______________ ABCOEFGHIJKLMNOPQRSTUVWXYZABCOEFGHIJKLMNOPQRSTUVWXYZ

CipheL___________ 2YXWVUTSRQPONMLKJIHGFEDCBA

(6) Since each: column in Fig. 11 is nothing but a normal sequence, it is obvious that instead

of laboriously writing down these columns of letters every time a cryptogram is to be examined,

it would be more convenient to prepare a set of strips eaeh bearing the normal sequence doubled

(to permit complete coincidence for an entire alphabet at any setting), and have them available

for examining any future cryptograms. In using such a set of sliding strips in order to solve a

cryptogramprepared by means of a single direct standard cipher alphabet, or to make a test to

determine whether a cryptogram has been so prepared, it is only necessary to "set up" the letters

of the cryptogram on the strips, that is, align them in a single row across the strips (by sliding

the individual strips up or down). The successive horizontal lines, calledgemratrices (singular,

generatrix), are then examined in a search for intelligible text. If the cryptogram really belongs

to this simple type of cipher, one of the generatrices will exhibit intelligible text all the way

across'; this text will practically invariably be the plain text of the message. T~ method of

analysis maybe termed a 8olution by completing the plain-componem sequence. Sometimes it is

referred to as "running down" the sequence. The principle upon which the method is based

constit~",,one of, the eryptanalyst'l! most valuable tools." , '

,b./f~ C4!!~(Tj,rever,8ed8ta1ulardaJ.ph~ets.-,-(l) The method described under subpar. a may

be;~i>P~Jin,sUgh~lym()~t¥1 fo~inthe.~aseof a cryptogrem.enciphered by a single

reversed standard alphabet. The basic principles are identical in the, two ,cases.

(2) To show ite;isn.~arY;toexperiIQ.~n~with two sliding eomponents as before, except

that in case one of:;t~ <'OmPl)~entsm,U$tbe-a~eversed normalsequence, the other, a direct

normal sequence. ,. ,', , ' , ,.', \

(3) Let the two components be juxtaposedA toA, asshown below" and then let the resultant

values be substituted f~rthe lett8rs,ofthe cryptogram. Thus: , . .. .,,;, • \; :.. \- _ .' I, I, t

CRYPTOGRAM

P C R C V YT,-'L: G, 0 y, T A E G /L G VP I

Plain "ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ

Cipher______________ ZYXWVUTSRQPONMLKJIHGFEDCBA .

Cryptogram • " ,P CR,CV Y T L GO,:Y ,T ,A E G L G V P I

1st Test-"Plain text" ,L', Y J Y F C, H P U X C H'A W U P U F L S

Cryptogram ~--- P C R C V .y T L G 0

2d Test-"Plain text" MZ K Z G 0 I Q V Y o I B X V

L G V P I

Q V GMT

.(6) It is seen that the lettel'lofthe "'plaintext" given by the second trial are merely the

~ntinuantsof the normal sequences initiated by the letters of the "plain text" given by the first

trial. If these sequences are "run down"-that is, completed within the columns-the results

must obviously be the same as though successive tests exactly similar to the first two were

applied to the cryptogram, using one reversed normal and one direct normal component. If the

oryptogram.has really ~een prepared by means of a single reversed standard alphabet, one of

the generatrices of the diagram that results from completing the sequences must yield intelligible

text.

(7) Let the diagram be made, or better yet, if,the student has alrea'dy at hand the set of

sJidin8:strips.referred to in th~ footnote page 36, let him "setup" the letters given by the

first trial., Fig. 12 shows 'the diagram and mdicates the plain-text generatrix.

PC R C V Y T L G,O Y T A E G L G V P I

L Y J Y F C H P U X C HAW U P U F L S

M Z K Z G 0 I Q V Y D I B XV Q V GMT

N A L A H E J R W Z E J C Y W,R WH N U

OBMBIFKSXAFKOZXSXIOV

P CN C J G L T Y B G LEA Y T Y J P W QOODKHMUZCHMF~ZUZKQX

*R E PEL I N V A 0 I N G C A V A L R Y

S ,F Q F M J 0 W B EJ 0 H 0 BW B M S Z

TG RG N K P XC F K PIE C X C-N T .A

U H S H 0 L Q Y 0 G L Q J FO Y 0 O.U B

VITIPMRZEHMRKGEZEPVC

W J U J Q N S A FIN S L H FA FQ W0

X K V K ROT B G JOT M IG B G RXE

YLWLSPUCHKPUNJHCHSYF

ZMXMTQVOILQVOKIOITZG

ABYNURWEJMRWPLJEJUAH

B 0 Z 0 V S X F K N S X QM K F K V B I

CPAPWTYGLOTYRNLGLWCJ

OQBQXUZHMPUZSOMHMXDK

ERCRYVAINQVATPNINYEL

FSOSZWBJORWBUQOJOZFM

GTE T A X C K P S X C V R P K P A ,G N

HUFUBYOLQTYOWSQLQBHO

IVGVCZEMRUZEXTRMRCIP

JWHWOAFNSVAFYUSNSDJQ

K X I X E B GOT W B GZ V TOT E K R

!/

i

.1

1

(5) Neither does the second test yield intelligible text. But let the results of the two tests

be superimposed. Thus:

I It is recommended that the student prepare a set of 25 strips !4 by*by 15 inches, made of well-seasoned

wood, and glue alphabet stripll to the wood. The alphabet on each strip should be a double or repeated alphabet

With all letters equally spaced.

Cryptogram__________________ P C R C V

1st Test-"Plain text" L Y J Y F

2d Test-"Plain text" M Z K Z G

Y:r'LGO

C H P U X

D I Q V Y

Y T A E G

C HAW U

o I B X V

L G V P I

P U F L S

Q V GMT

FIOURJ: 12.

. (8) The only differ~nce in procedure between this case and the preceding one (where the

CIpher alphabet was a. direct standard alphabet) is that the letters of the cipher text are first

"deciphered" by means of any reversed standard alphabet and then the columns are "run down",

according to the normal ABC • • • Z sequence. For reasons which will become apparent very

soon, the :first step in this method is technically termed converting the cipher letters into their

plain-componem equivalents; the second step is the same as before, viz, completing the plain-componentsequence.

i

II

'1=

Ii

i;

II~

11=

"

I., :,=

!;

'=

I!

ijl!

[I
6 There is but one other pOllSibility, already referred to under Par. l7d, which involves the case where transposition and monoalphabetlo substitution processes have been applied in successive steps. This is unusual

however, and will be discussed in its proper place. ' Ii

"""'"''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''"''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''1''

1

I

1

I

39

mind he will have no difficulty whatsoever in realizing when the principle is applicable, what a

powerful cryptanalytic tool it can be, and what results he may expect from its application in

specific instances.

d. In the two foregoing examples of the application of the principle, the plain component

was a normal sequence but it should be clear to the student, if he has grasped what has been said

in the preceding subparagraph, that this component may be a mixed sequence which, if known

(that is, if the sequence of letters comprising the sequence is known to the cryptanalyst), can be

handled just as readily as can a plain component thatis a normal sequence.

. e. It i~ e~tirelyimmaterial at what points the plain and the ciph~r components are juxtaposed

ill the preliminary step of converting the cipher letters into their plain-component equivalents.

For example, in the case of the reversed alphabet cipher solved in Par. 20b, the two components

were arbitrarily juxtaposed to give the value A=A, but they might have been juxtaposed at any

of the other 25 possible points of coincidence without in any way affecting the final result, viz, the

production of one plain-text generatrix in the completion diagram.

22. Value of mechanical solution as a short cut.--a. It is obvious that the very first step

the student should take in his attempts to solve an unknown cryptogram that is obviously a

substitution cipher is to try the mechanical method of solution by completing the plain-component

sequence, using the normal alphabet, first direct, then reversed. This takes only a very few

minutes and is conclusive in itsresults. Itsaves the labor and trouble of constructing a frequency

distribution in case the cipher is of this simple type. Later on it will be seen how certain variations of this simple type may also be solved by the application of this method. Thus, a very

easy short cut to solution is afforded, which even the experienced cryptanalyst never overlooks

in his first attack on an unknown cipher.

b. It is important now to note that if neither of the twoforegoing attempts is 8UCcessjul in

bringing plain text to light ftnd the cryptogram is quite obviously monoalphabetic in character, tM

cryptanalyst is warranted in assuming that the cryptogram involves a mixed Cipher alphabet.a The

steps to be taken in attacking a cipher of the latter type will be discussed in the next section.

38

21. Specialremarbon the method of solution by completing the plain-oomponentsequenoe.-

a. The terms employed to designate the steps in the solution set forth in Par. 20b, viz, "converting the cipher letters into their plain-eomponent equivalents" and "completing the plaincomponent sequence", accurately describe the process. Their meaning will become more clear

as the student progresses with the work. It may be said that whenever the plain component of

a cipher alphabet is a known sequence, no matter how it is composed, the difficulty and time

required tosoIve any cryptogram involving the use of that plain component is practically out

in half. In some cases this knowledge facilitates, and in other cases is the only thing that makes

possible the solution of a very short cryptogram that might othe7"lUi8e defy solution. Later on an

example will be given to illustrate what is meant in this regard.

b. The student should take note, however, of two qualifying expressions that were employed

in a preceding paragraph to describe the results of the application of the method. It was stated

that "one of the generatrices will exhibit intelligible text alltheway across; this text will practicaUy

invariably be the plain text." 'Will there ever be a case in which more than one generatrix will

yield intelligible text throughout its extent? That obviously depends almost entirely on the

number of letters that are aligned to ft)rm a generatrix, If a generatrix contains but a very few

letters, only five, for e.xOiliple, it may happen as a result of pure ohanee that there will be two or

more generatrices shoWing wh9JtIDight"bel'mtelligibletext." Note'inFig, 11, for example, that

there are several cases:m;wmch a.letter and 4-letter English 'Nords (ANY, VAIN, GOT, TIP, etc.)

appear on generatricesthQt ttre'not correCt, these words b~ing formed by pure chance. But there

is not a single case, int~ diagram, ofa.5-letier orlonger won! appearing fortuitously, because

obviously the longer the word 'the smaller the plOoobility of·its ,appearance purely by chance;

and the probability that two ~neratricesof'15'letters eaehwill both yield intelligible text along

their entire length is exceedingly remote,so remote, in fact, that inpractical cryptography such

a case may be considerednonexistent.! . .

c. The student should ob!el"'Ve·that in reality there is no differenee whatsoever in principle

between the two methodspresented in subpars. a and bof'Par. 20. In the former the preliminary

step of converting the cipher letters mto their plain-component equivalents is apparently not

present but in reality it is there. The reason for its apparent absence is that in that case the

plain component of the cipher al~abet is identical in all respects with the cipher component, so

that the cipher letters require no conversion, or, rather, they are identical with the equivalents

that would result if they were converted on thebasie Ac=Ap. In fact, if the solution process had

been arbitrarily initiated by converting the cipher letters into their plain-component equivalents

at the setting Ac=Op, for example, and the cipher component slid one interval to the right thereafter, the results of the first and second tests of Par. 20a would be as follows:

Cryptogram . . X K V K ROT B G'JOT MIG B G R X E

1st Test-"Plain text" L Y J Y F C H P U X C HAW U P U F L S

2nd Test-"Plain text"__. . M Z K Z G D I Q V Y D I B X V Q V GMT

Thus, the foregoing diagram duplicates in every particular the diagram resulting from the first

two tests under Par. 20b: a first line of cipher letters, a second line of letters derived from them

but showing externally no relationship with the first line, and a third line derived immediately

from the second line by continuing the direct normal sequence. This pointis brought to attention

only for the purpose of showing that a single, broad principle is the basis of the general method of

solution by completing the plain-component sequence, and once the student has this firmly in

4 A person with patience and an inclination toward the curiosities of the science might construct a text of IIi

Or more letters which would yield two "intelligible" texts on the plain-component completion diagram.

I

I

II
SECTION VI

UNILITEBAL SUBSTITUTION WITH MIXED CIPHER ALPHABETS

Paraeraph

Basic reason for the low degree of cryptographic security afforded by monoalphabetic cryptograms involving standard cipher alphabets .... -.-- 23

Preliminary steps in the analysis of a monoalphabetie, mixed-alphabet cryptogram_________________________________ 24

Further data concerning normal plain text • ----------------------------- 26

Preparation of the work sheet.. •__._._•••__• • • • ._••_. • • ••_._.__ 26

TrUiteral-frequency c;listributions__•• • ._. -__•__•• - 27

Classifying the cipher letters into vowels and consonants ---------------------- 28

Further analysis of the letters representing vowels and consonants . ---------- 29

Substituting deduced values in the cryptogram.__._._._. • •• • -_____________________________ 30

Completing the solution • • ._._. • • ------------- 31

Ge.ueral remarks on the foregoing solutioD._••• • • .---- ••• •••• 32

Tb.e "p.11>bable-word" method; its value .and applicability ------------ 33

Solution of additional cryptograms produced by the same cipher component .____ 34

23. Ba:siCJ:l:lIWIOJa. fol.' the 10. degree ofcryptographio security a1forded by IIlonoalphabetic

c;r1Pt~P'aJJUJ invo1rinc Bta.ndard cipheralphabets.-The student has seen fthat the solution. of

monoalphabetic crypto~ams involving standard cipher alphabets is a very easy matter. Two

methods of analysis were described, one involving the conszruction of a frequency distribution,

the other not requiring this kind of tabulation, being. almost mechanical in nature and eorrespondingly rapid. In the first of these two methodsit was necessary to make a correct assumption

/l.S to the. value of but one of the 26 lette:fSofthe ciph~r alphabet and the valuesof the remaining

25 letters at once become known; in the second method it was not necessary to assume a value

for even a single cipher letter. The student should understand what constitutes the basis of this

situation, viz, the fact that the two components of the cipher alphabet are composed of known

sequences. What if one or both of these components are, for the cryptanalyst, 'Unknown sequences?

In other words, what difficulties will confront the cryptanalyst. if the cipher component of the

cipher alphabet is a mixed sequence? Will such an alphabet be solvable as a whole at one stroke,

or will it be necessary to solve its values individually? Since the determination of the value of

one cipher letter in this case gives no direct clues to the value of any other letter, it would seem

that the solution of such a cipher should involve considerably more analysis and experiment than

has the solution of either of the two types of ciphers so far examined occasioned. A typical

example will be studied.

24. Preliminary steps in the analysis of a monoalphabetic, mixed alphabet cryptogram.-

a. Note the following cryptogram:

SFDZF IOGHL PZFGZ DYSPF HBZDS GvHTF UPLVD FGYVJ VFVHT GADZZ AITYD

ZYFZJ ZTGPT VTZBD VFHTZ DFXSB GIDZY VTXOI YVTEF VMGZZ THLLV XZDFM

.HTZAI TYDZY BDVFH TZDFK ZDZZJ SXISG ZYGAV FSLGZ DTffilT CDZRS VTYZD

OZFFH TZAIT YDZYG AVDGZ ZTKHI TYZYS DZGHU ZFZTG UPGDI XWGHX ASR~

DFUID EGHTV EAGXX

b. A casual inspection of the text discloses the presence of several long repetitions as well as

of many letters of normally low frequency, such as F, G, V, X,and Z; on the other hand, letters of

(40)

41

normally high frequency, such as the ·vowels, and the consonants Nand R, are relatively scarce.

The cryptogram is obviously a substitution cipher and the usual mechanical tests for determining

whether it is possibly of the monoalphabetic, standard-alphabet type are applied. The results

being negative, a uniliteral frequency distribution is immediately constructed and is as shown

in Figure 13.

~~

~~~ ~~

s , ~~~~ ~~.~ :::~~

~~-~::::~~~~:::~~~ ~~ ~~~~~-~~~ ABC D E F G H I J K L MN 0 P Q R S T U·V WX Y Z

8 • 1 23 3 19 19 15 10 3 2 5 2 0 3 II 0 2 10 22 5 18 1 8 1. 35

FIGun 18

c. The fact that the frequency distribution shows very marked crests and troughs means

that the cryptogram is undoubtedly monoalphabetic: the fact that it has already been tested

(by the method of completing the plain-component sequence) and found not to be of the monoalphabetic, standard-alphabet type, indicates with a high degree of probability that it involves

a mixed cipher alphabet. A few moments might be devoted to making a careful inspection of the

distribution to insure that it cannot be made to fit the normal; the object of this would be to

rule out the possibility that the text resulting from substitution by a standard cipher alphabet

h~d not subsequently been transposed. But this inspection in this case is hardly necessary, in

View of the presence of long repetitions in the message.! (See Par. 13g.)

d. One might, of course, attempt to solve the cryptogram by applying the simple principles

of frequency. One might, in other words, assume that Zc (the letter of greatest frequency)

represents E", De (the letter of next greatest frequency) represents Tp, and so on. If the message

were long enough this simple procedure might more or less quickly give the solution. But the

message is relatively short and many difficulties would be encountered. Much time and effort

would be expended unnecessarily, because it is hardly to be expected that in a message of only

235 letters the relative order of frequency of the various cipher letters should exactly coincide

with, or even closely approximate the relative order of frequency of letters of normal plain text

found in a count of 50,000 letters. It is to be emphasized thatthe beginner must repress the naiural

tendency to place too much confidence in the generalized principles ojjrequencyand to rely too much.

upon them. It is far better to bring into effective use certain other data concerning normal

plain text which thus far have not been brought to notice.

25. Further data concerning normal plain text.-a. Just as the individual letters constituting

a large volume of plain text have more or less characteristic or fixed frequencies, so it is found

that digraphs and trigraphs have characteristic frequencies, when a large volume of text is

studied statistically. In Appendix I, Table 6, are shown the relative frequencies of all digraphs

appearing in the 260 telegrams referred to in Paragraph ge. It willbe noted that 428 of the 676

possible pairs of letters occur in these telegrams, but whereas many of them occur but once or

twice, there are a few which occur hundreds of times.

b. In Appendix 1 willalso be found several other kinds of tables and lists which will be useful

to the student in his work, such as the relative order of frequency of the ·50 digraphs of greatest

I This possible step is mentioned here for the purpose of making it clear that the plain-component sequence

oompletion method cannot solve a case in which transposition has followed or preceded monoalphabetic substitution with standard alphabets. Cases of this kind will be discussed in a later text. It is sufficient. to indicate

at this point that the frequency distribution for such a combined substitution-transposition cipher would present

the characteristics of a standard alphabet cipher-and yet the method of completing the plain-component

sequence would fail to bring out any plain text.

I 1"11111"11111"11111"11111"11111"11111"11111"11111"1111IUIIII 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"11111"11111"11111"11111"1111
I

.'I

=f

-'I

4:2

frequency, the relative order of frequency of doubled letters, doubled vowels, doubled consonants,

and so on. It is suggested. that the student refer to this appendix now, to gain an idea of the

data available for his future reference. Just how these data may be employed will become apparent very shortly.

26. Preparation of the work sheet.-a. The details to be considered in this paragraph may

at first appear to be superfluous but long experience has proved that systematization of the

work, and preparation of the data in the most utilizable, condensed form is most advisable, even

if this seems to take considerable time. In the first place if it merely serves to avoid interruptions and irritations occasioned by failure to have the data in an instantly available form, it

will pay by saving mental wear and tear. In the second place, especially in the case of complicated cryptograms, painstaking care in these details, while it may not always bring about

success, is often the factor that is of greatest assistance in ultimate solution. The detailed

preparation of the data may be irksome to the student, and he may be tempted to avoid as much

of it as possible, but, unfortunately, in the early stages of solving a cryptogram he does not know

(nor, for that matter, does the expert always know) just which data are essential and which

may be neglected. Even though not all of the data may turn out to have been necessary, as a

general rule, time is saved in the end if all the usual data are prepared as a regular preliminary

to the solution of most cryptograms, '

b. First, the cryptogram is recopied in the form of a work sheet. This sheet should be of a

good quality of paper so as to withstand considerable erasure. If the cryptogram is to be

copied by hand, cross-section paper of, ~-inch squares "is ,extremely useful. The writing should

be in ink, and plain, carefully made roman capital letters should be used in all cases. If the

cryptogram is to be copied on a typewriter, the ribbon employed should be impregnated with an

ink that will not smear or smudge under the hand. . .

c. The arrangement of the characters of the cryptogram on the work sheet isa matter of

considerable importance. If the cryptogram as first obtained is in groups of regular length

(usually five characters to a group) and if the uniliteral frequency distribution shows the cryptogram to be monoalphabetic, the characters should be copied without regard to this grouping.

It is advisable to allow two spaces between letters, and to write a constant number of letters

per line, approximately 25. At least two spaces, preferably three spaces, should be left between

horizontal lines. Care should be taken to avoid crowding the letters in any case, for this is

not only confusing to the eye but also mentally irritating when later it is found that not enough

space has been left for making various sorts of marks or indications. If the cryptogram is originally in what appears to be word lengths (and this is the case, as a rule, only with the cryptograms

of amateurs), naturally it should be copied on the work sheet in the original groupings. If

further study of a cryptogram shows that some special grouping is required, it is often best to

recopy it on a fresh work sheet rather than to attempt to indicate the new grouping on the old

work sheet.

d. In order to be able to locate or refer to specific letters or groups of letters with speed,

certainty, and without possibility of confusion, it is advisable to use coordinates applied to the

lines and columns of the text as it appears on the work sheet. To minimize possibility of confusion, itis best to apply letters to the horizontal lines of the text, numbers to the vertical columns.

In referring to a letter the horizontal line in which the letteris located is usually given first. Thus,

referring to the work sheet shown below, coordinates A17 designate the letter Y, the 17th letter

in the first line. The letter I is usually omitted from the series of line indicators so as to avoid

confusion with the figure 1. If lines are limited to 25 letters each, then each set of 100 letters of

the text is automatically blocked off by remembering that 4 lines constitute 100 letters.

e. Above each character of the cipher text may be some indication of the frequency of that

character in the whole cryptogram. This indication may be the actual number of times the

•

character occurs, or, if colored pencils are used, the cipher letters may be divided up into three

categories or groupe-high frequency, medium frequency, and low frequency. It is perhaps

simpler, if clerical help is available, to indicate the actual frequencies. This saves constant

reference to the frequency tables, which interrupts the train of thought, and saves considerable

time in the end.

f· After the speci81frequency distribution, explained in Par. 27 below, has been constructed,

repetitions of digraphs and trigraphs should be underscored. In so doing, the student should be

particularly watchful of trigraphic repetitions which can be further extended into tetragraphs

and polygraphs of greater length. Repetitions of more than ten characters should be set off by

heavy vertical lines, as they indicate repeated phrases and are of considerable assistance in

solution. If a repetitionoontinues from one line to the next, put an arrow at the end of the

underscore to signal this fact. Reversible digraphs should also be indicated by an underscore

with an arrow pointing in both directions. Anything which strikes the eye as being peculiar,

unusual, or significant as regards the distribution or recurrence of the characters should be

noted. All these marks should, if convenient, be made with ink so as not to cause smudging.

The work sheet will now appear as shown herewith (not all the repetitions are underscored):

1 2 a 4 II 8 7 8 9 10 11 12 13 14 III 18 17 18 19 20 21 22 23 24 211

ro W 23 U W ro 3 W U II II U W W U 23 U ro II W U 4 U 23 ro

A S F 0 Z FlO G HLP Z F G Z 0 Y S P F H B ·Z 0 S

...-.-... - W M U 22 W II II II M 23 W W U M 3 M W U U 22 W 8 23 U U

B GVHTFUPLVDFGYVJVFVHTGADZZ

8 ro 22 U 23 U U W U a U 22 W • 22 M 22 M 4 23 M W U 22 M

C A IT Y 0 Z Y F Z J Z T G P T VT Z B 0 V F H T Z.

...-.-...

23 W 8 ro 4 W ro 23 U U U 22 8 3 ro U M 22 3 W U 2 W M U

D DFXSBGIDZYVTXOIYVTEFVMGZZ

+---

22 U I I M 8 U W 2 U 22 M 8 W22 U M U 4 U W U

E T H L L V X Z 0 F MH T Z A I T Y 0 Z Y B 0 V F H - .

22 U 23 W 2 U 23 U U 3 W 8 W W W M U W 8 U W W • W U

F ~T K Z 0 Z Z J S X I S G Z Y G A V F S L G Z

23 22 U U 22 1 M 2 W M 22 U M 23 3 M W W U 22 M 8 W 22

GOT H H TeO Z R S V T Y ZOO Z F F H T Z A I T.

U 23 U U W 8 U W M M 22 2 U W 22 U M U ro 23 M W U II

H ~Y 0 Z Y G A V 0 G Z Z T K H I T Y Z Y S 0 Z G H U

U W M 22 W I II W W 8 1 W U 8 8 W 2 II M W • W 23

J ZFZTGUPGDIXWGHXASRUZDFUID

3 W U 22 U 3 8 W 8 8

K EGHTVEAGXX

27. Triliteral.fr\quency distributions.-a. In what has gone before, a type of frequency

distribution known as a uniliteral frequency distribution was used. This, of course, shows only

the number of times each individual letter occurs. In order to apply the normal digraphio and

,i

~IIIII I I IUIIII 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 IUIIII 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 IUIIII 1"1111 1"1111 1"1111 I"
• 44

trigraphie frequency data (given in Appendix 1) to the solution of a cryptogram of the type now

being studied, it is obvious that the data with respect to digraphs and trigraphs occurring in the

cryptogram should be compiled and should be compared with the data for normal plain text. In

order to accomplish this in suitable manner, it is advisable to constructa slightly more complicated form of distribution termed a triliteralfrequency di8trilrution. 2

b. Givena cryptogram of 50 or more letters and the task of determining what trigraphs are

present in the cryptogram, there are three ways in which the data may be arranged or assembled.

One may require that the data show (1) each letter with its two succeeding letters; (2) each letter

with its two preceding letters; (3) each letter with one preceding letter and one succeeding letter.

c.A distribution of the first of the three foregoing types may be designated asa "triliteral

frequency distribution showing two suffixes"; the second type may be designated as

a "tri.

literal frequency distribution showing two prefixes"; the third type may be designated as a "triliteral frequency distribution showing one prefix and one suffix." Quadriliteral and

pentaliteral frequency distributions may occasionally be found useful.

d. Which of these three arrangements is to be employed at a specific time depends largely

upon what the data. are intended to show. For present purposes, in connection with the solution

of a monoalphebetie.substitution cipher employing

a mixed alphabet, possibly. the third arrangement, that showiIig one prefix and one suffix, is most satisfactory.

e. It is convenient to use~'7ineh eross~etion paper for the construction ofa triliteral frequency distribution in the form of:a di&tribution showing crests and troughs, such as that in

Figure 14. In,that figure the prefix to each letter to be recorded is inserted in the left half of the

cell directly above the cipher letter beiDg recorded; the suffix to each letter is inserted in the right

half of the cell directly above the letter b~g recorded; and in each case the prefix and the

suffix to the letter being recorded oooupythe same cell, the prefix,being directly to the left of the

suffix. The number in parentheses gives the total frequency for each letter. • Heretofore such a distribution has been termed a "trigraphic frequency table." It Is thought that the word

"triliteral" is more sUitable, to correspond with the designation "unlliteral" in the case of the distribution of the

single letters. Atrigraphic distribution ofA B·C DE P' would consider only the trigraphs ABC and D E P',

whereasa triliteral distribution would consider the groups ABC, BCD, C D E, and D E P'. (See also Par. lId.)

The use of the word "distribution" to replace the word "table" has already been explained. •

45

§ts8 ~,~ ~,f:; t; fi3 i:ia i:i fa §,t N.~

~r:H:3~~~~~i=f~~i3e;~ ~g

~~:2~tri~~~ ~g

Cl Er:8

I ~~Fii~f:;~:jf~:~~f:;~~~~96 >~

i IC"lCQ H~p..~p.. j ~I~CQ rz. Cl rz. ::>€

of:;I

e i:: E-t>tE-< N O N ~Cl~~~N~OXN~N~~~~N>Cl~~rz. E-t8 t H&:E-<::C NHNH::C>::CO::CH::C > >P-.NH::C::C g Hrz.

&:~~ ~o>...:lCl~~8P-.rr ril~ ...::j <~~rz.H'J

~~ tr:8

G'l 0Z a~

....

E-4

.... CQCQCQCQ

E-4 ClE-<...:lfz.N Q..€ ~6~~ ::>Cl::>fIJ...:l 1"'1

1"'1 &:i::~~ i NHO

O>lH 08

JO:t

!

0 ~~~~CQ Z€

1"'1 ~~~tL~ :!!

...:I

j:Q &:~ :&61 NE-lE-lOH

-e O::CHN<

E-4

!=l

g tog: ,",,8

1"'1

G'l Z iS~ ~6 1"'1

!=l ~~~~~ z tL~tL~t-!J ~~~ ..,8 00 »NNN § M!a ~.~ !;i ~. § H~

lQlQ~~~

l=l. E-l~::>Ht&:&:~!;...:lE-tE-t~~...:l e ~~:l::l:~ ClClCl~ E-lrz.> Cl :c~ .. . E-<E-<I%.ClH

I:l ~ffii~~~~~~~~~~~~~~~5 ~~

Cl)Cl)OOCOlQlQ ::>NXrz.fIJ~~~>>l~N~8~::CClHOlao! t-!J~~~tLt-!J ONI%.N>O o~o P-.NNfIJ o ::CNOCl <Clrz.

>QE-t r:rJ€

~g~~ lra~

ClfIJ>H>HHO

~~ClNClNNCl <€

148274-38--4

.111 m

iIi

!I!
'""1"""1"""1"""1""'111'"'111'"'111'"'111'"'111'"'111'"'111'"'1111",111,",111,",111,",111,",111,",111'"'111'"'111'"'111'"'111'"111

Consonants

De' r, Fo' Go, Yo

46

J. The trilitetal frequency distribution is now to be examined with a view to ascertaining

what digraphs and trigraphs occur two or more times in the cryptogram. Consider the pair

of columns containing the prefixes and suffixes to De in the distribution, as shown in Fig. 14.

This pair of columns shows that the following digraphs appear in the cryptogram:

Digraphs baaed on prepea (arranged Digraphs baaed on sujJi:&ea (arranged

aa one reads up the column) as one reads up the column)

rn,W,w,m,ID,ro,oo, m,M,OO,~,m,m,oo,

W. ID, ZD, ro, BD, ZD, ZD, DF, DZ, DF. DZ, DV, DF. DZ.

ZD. CD, ZD. ro. VD, SD, GD, DT, DZ. DO. DZ, DG, DZ, DI.

ZD. ID DF, DE

The nature of the triliteral frequency distribution is such that in finding what digraphs are

present in the cryptogram it is immaterial whether the prefixes or the suffixes to the cipher

letters are studied, so long ae oneis consistent in the study. For example, in the foregoing list of

digraphs based on the prefixes to De, the digraphs rn, ZD, ZD, m, eto., are found; if now, the

student willrefer to the suffixes of Fe' Ze, Ve, etc., he willfind the very same digraphs indicated.

This being the case, the question may be raised as to what value there is in listing both the'

pre~ and the suffixes to the cipher letters. The answer is that by so doing the trigraphs are

indicated at the same time. For example, in the case of De, the following trigraphs are indicated:

FDZ. ZDY. ZDS, VDF, ADZ, YDZ, BDV, ZDF, IDZ. ZDF. YDZ. BDV, ZDF.

~.~.~,~.~,~,~,~,~.~.

:·i, The repealed digraphs and trigraphs can now be found quite readily. Thus, in the case

of De',examining the list of digraphs based on suffixes, the following r~petitions are noted:

DZ appears 9 times

DF appears 5 times

DV appears 2 times

Examining the trigraphs with De as central letter, the following repetitions are noted:

ZDF appears 4 times

roz appears 3 times

BDV appears 2 times

h. It is unnecessary, of course, to go through the detailed procedure set forth in the preceding subparagraphs in order to find all the repeated digraphs and trigraphs. The repeated

trigraphs with De as central letter can be found merely from an inspection of the prefixes and

suffixes opposite Do in the distribution. It is necessary only to find those cases in which two or

more prefixes are identical at the same time that the suffixes are identical. For example, the

distribution shows at once that in four cases the prefix to Do is Ze at the same time that the

suffix to this letter is Fe- Hence, the trigraph ZDFappears four times; The repeated trigraphs

may all be found in this manner.

i. The most frequently repeated digraphs and trigraphs are then assembled in what is

termed a condensed table ofrepetitions, so as to bring this information prominently before the eye.

As a rule, digraphs which occur less than four or five times, and trigraphs which occur less than

three or four times may be omitted from the condensed table as being relatively of no importance

in the study of repetitions. In the condensed table the frequencies of the individual letters

forming the most important digraphs, trigraphs, etc., should be indicated.

28. Classifying the cipher letters into vowels and consonants.-a. Before proceeding to a

detailed analysis of the repeated digraphs and trigraphs, a ver.y importantstep can be taken which

will be of assistance not only in the analysis of the repetitions but also in the final solution of

the cryptogram. This step concerns the classification of the high-frequency letters into two

47

groups-e-vowels and consonants. For if the cryptanalyst can quickly ascertain the equivalents

of the four vowels, A, E, I, and 0, and of only the four consonants, N, R, S, and T, he will then

have the values of approximately two-thirds of all the cipher letters that occur in the cryptogram;

the values of the remaining letters can almost be filled in automatically.

b. The basis for theclassification will be found to rest upon a comparatively simple phenomenon: the associational or combinatory behavior of vowels is, in general, quite different

from that of consonants. If an examination be made of Table 7-B in Appendix 1, showing the

relative order of frequency of the 18 digraphs composing 25 percent of English telegraphic text,

it will be seen that the letter E enters into the composition of 9 of the 18 digraphs; that is, in

exactly half of all the cases the letter E is one of the two letters forming the digraph. The

digraphs containing E are as follows:

ED EN ER ES

NE RE SE TE VE

The remaining nine digraphs are as follows:

AN NO OR ST

IN NT TH

ON TO

c. None of the 18 digraphs is a combination of vowels. Note now that of the 9 combinations

with E, 7 are with the consonants N,R,S, and T, one is with D, one is with V, and none is with any

vowel. In other words, Ep combines most readily with consonants but not with other vowels, or

even with itself. Using the terms often employed in the chemical analogy, E shows a great

"a.ffinity" for the consonants N, R,S, T, but not for the vowels. Therefore, if the letters of highest

frequency occurring in a given cryptogram are listed, together with the number of times eachof

them combines with the cipher equivalent of Ep, those which show considerable combining power

or affinity for the cipher equivalent of Epmay be assumed to be the cipher equivalents of N, R, S,

Tp ; those which do not show any affinity for the cipher equivalent of Ep may be assumed to be the

cipher equivalents of A, I, 0, Up. Applying these principles to the problem in hand, and examining the triliteral frequency distribution, it is quite certain that Ze=Ep, not only because Zeis the

letter of highest frequency, but also because it combines with several other high-frequency letters,

such as Do, Fe' Go, etc. The nine letters of next highest frequency are: .

W W M U U ro ro

D T F G V H Y S I

Let the combinations these letters form with Zo be indicated in the followingmanner:

Number of times z, occurs as prefix, =

Cipher Letter D(23) T(22) F(19) G(19) V(16) H(15) Y(14) S(IO) I(10)

Number of times Ze occurs as suffix, "'"

::::

d. Consider De. It occurs 23 times in the message and 18 of those times it is combined with

Ze, 9 times in the form ZeDe (..:...E8p ) , and 9 times in the form DeZo (=8Ep). It is clear that De

must be a consonant. In the same way, consider Te, which shows 9 combinations with Zo, 4 in the

form ZoTe (=E8p ) and 5 in the form TeZe (=8Ep). The letter Teappears to represent a consonant,

as do also the letters Fe' Ge, and Yeo On the other hand, consider V~, occurring in all 16 times but

never in combination with Ze;it appears to represent a vowel, as do also the letters Ho'Se, and Ie.

So far, then, the followingclassification would seem logical:

VowelB

Ze(=Ep), s; He' So, r,
48

29. l'urther analysis of, the letters representing v&wels and consonant8.~. Op is usually

the vowel of second highest frequency. Is it possible to determine which of the letters V,H, 5, I o

is the cipher equivalent of Op?' Let reference be made again to Table 6 in Appen<fu: I, where it

is seen that the 10 most frequently occurring diphthongs a.re: .

Diphthong ._IO OU EA EI AI IE AU' EO AY UE

Frequency .41 37 35 27 17 13 13 12 12 11

IfV,H,5, Ie are really the cipher equivalents of A,I, 0, Up (not respectively), perhaps it is possible

to determine which is which by examining the combinatiomtkey make a1M'fl,{/ themsel1J68 and 'lUith.

Ze (=Ep). ' Let the combinations of V, H, S, I, and Z that occur in the message be listed. There

are only the following:

ZZo---4

VH-:2

HH-1

HI-l

5V-1

I5-1

ZZo is of course EEp. Note the doublet HHo; if H, is a vowel, then the chances are excellent that

Ho=Opbecause the doublets M p, IIp,UUp, are practically non-existent, whereas the double vowel

combination OOp is of next highest frequency to the double vowel combination EEp. If Ho=Op,

then Vomust be I p because the digraph VHooccurring two times in the message could hardly be

AOp, orUOp, Whe",8S the diphthong lOp is the one of high frequency in English. So far then, the

tentative (because so far unverified) results of the analysis are as follows:

Zo=Ep Ho=Op Vo=Ip

This leaves only two lettel1l, I o and 50 (already ~lassified as voweIa) to be separated into Ap aod

Up. Note the digraphs:

Hl o= 08p

5Vo=8Ip

150= 88,

CDEFGHIJKLMNOPQRSTUVWXYZ

Z V TH DGFI

F G

If the second alternative is selected, then

HIo=OAp

5Vo=Ulp

ISo=AUp

30. Substituting deduced values in the cryptogram.-a. Thus far the analysis has been

almost purely hypothetical, for as yet not a single one of the values deduced from the foregoing

analysis has been tried out in the cryptogram. It is high time that this be done, because the

final test of the validity of the hypotheses, assumptions, and identifications made in any cryptographic study is, after all, only this: do these hypotheses, assumptious, and identifications

ultimately yield verifiable, intelligible plain-text when consistently applied to the cipher text?

b. At the present stage in the process, since there are at hand the assumed values of but 9

out of the 25 letters that appear, it is obvious that a continuous "reading" of the 'cryptogram

can certainly not be expected from a mere insertion of the values of the 9 letters. However the

substitution of these values should do two things. First, it should immediately disclose the

fragments, outlines, or "skeletons" of "good" words in the text; and second, it should disclose

no places in the text where "impossible" sequences of letters are established. . By the first is

meant that the partially deciphered text should show the outlines or skeletons of words such

as may be expected to be found in the communication; this will become quite clear in the next

subparagraph. By the second is meant that sequences, such as "AOOEN" or "TNRSENO" or the

like, obviously not possible or extremely unusual in normal English text, must not result from

the substitution of the tentative identifications resulting from the analysis. The appearance

of several such extremely unusual or impossible sequences at once signifies that one or more of

the assumed values is incorrect.

Total_____________ 59

Hlo=OUp,frequency value=37

SVo=Alp , frequency value=17

I50=UAp, frequency value= 5

Total ._____ 25

Only two alternatives are open:

(1) Either Io=Ap and 50=Up ,

(2) Or Io=Up and 50=Ap •

If the first alternative is selected, then

HIo=OUp

5Vo=AIp

ISo=UAp

The eye finds it difficult to choose between these alternatives; butsuppose the frequency values of

the plain-text diphthongs as given in Table 6 of Appendix 1 are added for each of these alternatives,

giving the following:

Hlo=OAp , frequency value= 7

5Vo=Ulp , frequency value= 5

ISc=AUp, frequency value= 13
51

J

F

B

A 5 FD ZF I 0 G HLP Z F G Z D Y S P F H B Z D 5

A5RESULTOFYESTERDAY50PERA

G V H T F U P L V D F G Y V J V F V H T GAD ZZ

T ION S B Y FIR 5 T D I V I 5 ION T H R E E

AITYDZYFZJZTGPTVTZBDVFHTZ

C HUNDRED5EVENTYNINEPRI50NE

D DFX5BGIDZYVTXOIYVTEFVMGZZ

R seA P T U RED INC L U DIN G S I X TEE

E THLLVXZDFMHTZAITYDZYBDVFH

N 0 F F ICE R S X 0 N E HUN D RED P R I 5 0

TZDFKZDZZJ5XISGZYGAVFSLGZ

NERSWEREEVACUATEDTHISAFTE

G DTHHTCDZRSVTYZDOZFFHTZAIT

R N 0 0 N Q REM A I N 0 E R LE S SON E HUN

H YDZYGAVDGZZTKHITYZYSDZGHU

DREDTHIRTEENWOUNDEDARETOB

ZFZTGUPGDIXWGHXA5RUZDFUID

ESE N T B Y T R U C K T 0 C HAM S E R S BUR

K EGHTVEAGXX

GTONIGHTXX

016

TVTZBDVFHTZDF

(2) N I N E ? R ITO N E R T

S 5

d. No impossible sequences are brought to light, and, moreover, several long words, nearly

complete, stand out in the text. Note the following portions:

A21

H B Z D 5 G V H TrF

(1) O? ERA S ION T

T S

F~

SLGZDTHHT

(3) A? 5 ERN 0 0 N

T

The words are obviously OPERATIONS, NINE PRISONERS, and AFTERNOON. The value G. si

clearly Tp; that of F. is Sp; and the following additional values are certain:

Bo=Pp Lo=Fp

31. Completing the solution.-a. Each time an additional value is obtained, substitution

is at once made throughout the cryptogram. Thisleads to the determination of further values,

in an ever-widening circle, until all the identifications are firmly and finally established, and the

message is completely solved. In this case the decipherment is as follows:

123 • 687 8 9 ro II a n u u u u u m

• u u 1 M 2 ro U U M • 3 W U 8 ro

G DTHHTCDZRSVTYZDOZFFHTZAIT

RNOON RE AIN ER ETTONE N

5 5

• W 2 3 ro 8 ro ro u W 8 U ro 6 W

F TZDFKZDZZJSXISGZYGAVF5LGZ

NERT EREE A A5E 5 ITA SE

S T T S T

u a 6 U 8 • 2 U M 8 ro u _ U 4 U wu

E THLLVXZDFMHTZAITYDZYBDVFH

NO I ERT ONE N RE RITO

5 S

u u a 6 6 U u u a u u u 8

B GVHTFUPLVDFGYVJVFVHTGADZZ

S ION T I R T 5 I I T ION S R E E

T S 5T S T

8 ro u u a 6 U • u u

C AITYDZYFZJZTGPTVTZBDVFHTZ

N RE TE EN5 NINE RITONE

5 T 5

M W W 6 6 ro 8 1 U 8 8 ro 2 6 W 6 ro

J ZFZTGUPGDIXWGHXASRUZDFUID

ETENS 5R SO A ERT R

S T T T 5

u _ U W 8 U 2 U ro U U ro W U 6

H YDZYGAVDGZZTKHITYZYSDZGHU

RE S IR5EEN 0 N E ARE50

T T T

a W U U a 8 W 8 8

K EGHTVEAGXX

SON I 5

T T

8 W • ro _ u u u 8 a ro u u a u 2

D DFX5BGIDZYVTXOIYVTEFVMGZZ

R T A 5 REI N I N TIS E E

5 T S T

c. Here are the results of substituting the nine values which have been deduced by the

reasoning based on a classification of the high-frequency letters into vowels and consonants

and the study of the members of the two groups:

1 2 3 • 6 8 7 8 9 ro II a u u re u m

ro ro 3 U 6 6 u ro 6 U • ro

A 5FDZFIOGHLPZFGZDY5PFHBZD5

ATRET so ETSER A TO ERA

5 S T ST 5

I
J

52

, Message: AS RESULT OF YESTERDAYS OPERA'J,'IONS BY FIRST DIVISION THREE

HUNDRED SEVENTY NINE PRISONERS CAPTURED INCLUDING SIXTEEN OFFICERS ONE

HUNDRED PRISONERS WERE EVACUATED THIS AFTERNOON REMAINDER LESS ONE HUNDRED

THIRTEEN WOUNDED ARE TO BE SENT BY TRUCK TO CHAMBERSBURG TONIGHT

b. The solution should, as a rule, not be considered complete until an attempt has been

made to discover all the elements underlying the general system and the specific key to a message.

In this case there is no need to delve further into the general system, for it is merely one of

monoalphabetic substitution with a mixed cipher alphabet. It is necessary or advisable, however, to reconstruct the cipher alphabet because this may give clues that later may become

valuable.

c. Cipher alphabets should, as a rule, be reconstructed by the cryptanalyst in the form of

enciphering alphabets because they will then usually be in.the form in which the encipherer

used them. This is important for two reasons. First, if the sequence in the cipher component

gives evidence of system in its construction or if it yields clues pointing toward its derivation

from a" keyword or a key-phrase, this may often corroborate the identifications already made

and may lead directly to additional identifications. A word or two of explanation is advisable

here. For example, refer to the skeletonized enciphering alphabet given at the end of par. 29b:

Plain_____________ A" BCD E F G H I J K L M N 0 P Q R STU V W X Y Z

. 'Cipher -'_-'____ S Z V T H D G F I

F G

Suppose the cryptanalyst, looking at the sequence DGFI or DFGI in the cipher component, suspects the presence of a keyword-mixed alphabet. Then DFGI is certainly a more plausible

sequence than DGFI. Again, noting the sequence S • • • Z • . . V • • • • TH ".' D, he might

have an idea that the keyword begins after the Z and that the TH is followed by AB or BC. This

would mean that "either P, Qp=A, Boor B, Co' Assuming that P, Qp=A, B., he refers to the frequency distribution and finds that the assumptions Pp=Aoand Qp=Boare not good; on the other

hand, assuming that P, Qp=B, Co, the frequency distribution gives excellent corroboration.

A trial of these values would materially hasten solution because it is often the case in cryptanalysis that if the value of a very low-frequency letter can be surely established it will yield

clues to other values very quickly. Thus, if Qp is definitely identified it almost invariably will

identify Up, and will give clues to the letter following the Up, since it must be a vowel. In the

case under discussion the identification PQp=BCowould have turned out to be correct. For the

foregoing reason an attempt should always be made in the early stages of the analysis to determine, if possible, the basis of construction or derivation of the cipher alphabet; as a rule this

can be done only by means of the enciphering alphabet, and not the deciphering alphabet. For

example, the skeletonized deciphering alphabet corresponding to the enciphering alphabet

directly above is as follows:

Cipher ABC D E F G H I J K L M N 0 P Q R STU V WX y Z

Plain______________ R T SOU A N I E

S T

Here no evidences of a keyword-mixed alphabet are seen at all. However, if the enciphering

alphabet has been examined and shows no evidences of systematic construction, the deciphering

alphabet should then be examined with this in view, because occasionally it is the deciphering

alphabet which shows the presence of a key or keying element, or which has been systematically

derived from a word or phrase. The second reason why it is important to try to discover the basis

,I

I

63

of construction or derivation of the cipher alphabet is that it affords clues to the general type of

keywords or keying elements employed by the enemy. This is a psychological factor, of course,

and may be of assistance in subsequent studies of his traffic. It merely gives a clue to the general

type of thinking indulged in. by certain of his cryptographers.

d. In the case of the foregoing solution, the complete enciphering alphabet is found to be as

follows:

Plain______________ ABC D E F G H I J K L M N 0 P Q R STU V WX y Z

Cipher___________ S U X Y Z LEA V N W OR T H BCD F G I J K M P

Obviously, the letter Q, which is the only letter not appearing in the cryptogram, Should follow

P in the cipher component. Note now that the latter is based upon the keyword LEAVENWORTH,

and that this particular cipher alphabet has been composed by shifting the mixed sequence based

upon this keyword five intervals to the right so that the key for the message is Ap=So' Note

also that the deciphering alphabet fails to give any evidence of keyword construction based upon

the word LEAVENWORTH.

Cipher___________ ABC D E F G H I J K L M N 0 P Q R STU V W X Y Z

Plain______________ H P Q R G S T 0 U V W F X J L Y Z MAN B I K C 0 E

e. H neither the enciphering or the deciphering alphabet exhibits characteristics which

give indication of derivation from a keyword by some form of mixing or disarrangement, the

latter is nevertheless not finally excluded as a possibility. The student is referred to Section IX

Of Elementary Military Cryptography, wherein will be found methods for deriving mixed alphabets

by transposition methods applied to keyword-mixed alphabets. For the reconstruction of such

mixed alphabets 'the cryptanalyst must use ingenuity and a knowledge of the more common

methods of suppressing the appearance of keywords in the mixed alphabets.

32. General notes on the foregoing solution.-a. The example solved above is admittedly

a more or less artificial illustration of the steps in analysis, made so in order to demonstrate

general principles. It was easy to solve because the frequencies of the various cipher letters corresponded quite well with the normal or expected frequencies. However, all cryptograms of

the same monoalphabetical nature can be solved along the same general lines, after more or less

experimentation, depending upon the length of the cryptogram, the skill, and the experience of

the cryptanalyst.

b. Itis no cause for discouragement if the student's initial attempts to solve a cryptogram of

this type require much more time and effort than were apparently required in solving the foregoing purely illustrative example. It is indeed rarely the case that every assumption made by the

cryptanalyst proves in the end to have been correct; more often is it the case that a good many

of his initial assumptions are incorrect, and that he loses much time in casting out the erroneous

ones. The speed and facility with which this elimination process is conducted is in many cases

all that distinguishes the expert from the novice.

c. Nor will the student always find that the initial classification into vowels and consonants

can be accomplished as easily and quickly as was apparently the case in the illustrative example.

The principles indicated are very general in their nature and applicability, and there are, in

addition, some other principles that may be brought to bear in case of difficulty. Of these, perhaps the most useful are the following:

(1) In normal English it is unusual.to find two or three consonants in succession, each of high

frequency. If in a cryptogram a succession of three or four letters of high-frequency appear in

succession, it is practically certain that at least one of these represents a vowel,"

3 Sequences of seven consonants are not impossible, however, &sin STRENGTH THROUGH.
54

(2) Successions of three vowels are rather unusual in English.' Practically the only time

this happens is when a word ends in two vowels and the next word begins with a vowel,"

(3) When two letters already classified as vowel-equivalents are separated by II. sequence of

six or more letters, it is either the case that one of the supposed vowel-equivalents is incorrect,

or else that one or more of the intermediate letters is a vowel-equivalent.·

(4) Reference to Table 7-B of Appendix 1 discloses the following:

Diatn"bution 01firs' 18 digrapheJorming S5 perCMlt 01EngZilh'ezt

Number of consonant-consonant digrapha.. • •__._. • • ~. ._.______________ 4:

Number of consonant-vowel digraphs ._._. • .: ._•••• 6

Number of vowel-consonant digrapha... • • • • ._•••~___________ 8

Number of vowel-vowel digraphs •__• ._. • • • ._________ 0

DiI'n"bution 01firtlt 58 digraphllorming 60 percent oJ EngZilh t«I:t

Number of consonant-consonant digraphs.. • .__ 8

Number of consonant-vowel digraphs ••• • •• • .____ 23

Mumber of vowel-consonant digraphs_. •__•••.__._. •• • • • • • .•_ 18

Number of vowel-vowel digraphs ._. •__•__•__••_•• •• ••_:__._. .: • • •__• 4:

The latter tabulation shows that of the first 53 digraphs which form 50 percent of English text,

41 of them, that is, over 75 percent, are combinations of a vowel with a consonant. In short,

in normal English the vowels and the high..frequency consonants are in the long run distributed fairly evenly and regularly throughout the text. ,

(5) As a rule, repetitions of trigraphs in the cipher text are composed of high-frequency

letters forming high-frequency combinations. The latter practically always contain at least one

vowel; in fact, if reference is made to Table 1o-A of Appendix 1, it will De noted that 36 of the 56

trigraphs having a frequency of 100 or more contain one vowel, 17 of them contam two vowels,

and only three of them contain no vowel. In the case of tetrsgraph repetitions, Table, ll-A of

Appendix 1 shows that no tetragraph listed therein fails to contain at least one vowel; ~8 of them

contain one vowel, 25 contain two vowels, and 2 contain three vowels.

(6) Quite frequently when two known vowel-equivalents are separated by six or more letters

none of which seems to be of sufficiently high frequency to represent one of the vowels A E I 01

the chances are good that the cipher-equivalent of the vowel U or Yis present.

(7) The letter Q is invariably followed by U; the letters J and Vare invariably followed by a

vowel.

d. In the foregoing example'the amount of experimentation or "cutting and fitting" was

practically nil. (This is not true of real cases as a rule.) Where such experimentation is neces4 Note that the word RADIOED, past tense of the verb RADIO, is coming into usage.

6 A sequence of seven vowels is not Impossible, however, as in THE WAY YOU EARN.

• Some cryptanalysts place a good deal of emphasis upon this principle as a method of locating the remaining

vowels after the first two or three have been located. They recommend that the latter be underlined throughout

the text and then all sequences of five or more letters showing no underlines be studied attentively. Certain

letters which occur in several such sequences are sure to be vowels. An arithmetical aid in the study is as follows:

Take a letter thought to be a good possibility as the cipher equivalent of a vowel (hereafter termed a po3ribZe

lJowel-equivalent) and find the length of each interval from the possible vowel-equivalent to the next known (fairly

8urely determined) vowel-equivalent. Multiply the interval by the number of times this interval is found. Add

the products and divide by the total number of intervals considered. This will give the mean interval for that

possible vowel-equivalent. Do the same for all the other posslble vowel-equivalents. The one for which the

mean is the greatest is most probably a vowel-equivalent. Underline this letter throughout the text and repeat

the process for locating additional vowel-equivaients, if any remain to be located.

.1

j

1\

Ii

I

II

I

!I

I

I

55

sary, the underscoring of all repetitions of several letters is very essential, as it calls attention to

peculiarities of structure that often yield clues.

e. After a few basic assumptions of values have been made, if short words or skeletons of

words do not become manifest, it is necessary to make further assumptionsfor unidentified letters.

Thisis accomplished most often by assuming a word.' Now there are two places in every message

which lend themselves more readily to successful attack by the assumption of words than do

any. other places-the very beginning .and the very end of the message. The reason is quite

obVIOUS, fo~ although words may begin or end with almost any letter of the alphabet, they

usually begm and end with but a few very common digraphs and trigraphs. Very often the

association of letters in peculiar combinations will enable the student to note where one word

ends and the next begins. For example suppose, E, N, S, and T have been definitely identified,

and a sequence like the following is found in a cryptogram:

••• ENTSNE •••

Obviously the break between two words should fall either after the S of E N T S or after the T

of E N T, so that two possibilities are offered: ... EN T S / N E •••, or ... E NT / S N E

. ... Since in English there are very few words with the initial trigraph S N E, it is most '

likely that the proper division is ... E NT S / N E . ... Obviously, when several word

divisions have been found, the solution is more readily achieved because of the greater ease with

which assumptions of additional new values may be made.

.88. T~e "probable word" method; its value and applicabUity.-a. In practically allcryptanalytio studieevshort-cuts can often be made by assuming the presence of certain words in the

message under study. Some writers attach so much value to this kind of an "attack from the

rear" that they practically elevate it to the position of a method and call it the "intuitive method"

or the "probable-word method." It is, of course, merely a refinement of what in every-day

language is called "assuming" or "guessing" a word in the message. The value of making a

"good guess" can hardly be overestimated, and the cryptanalyst should never feel that he is

accomplishing a solution by an illegitimate subterfuge when he has made a fortunate guess

leading to solution. A correct assumption as to plain text will often save hours or days of labor,

and sometimes there is no alternative but to try to "guess a word", for occasionally a system is

encountered the solution of which is absolutely dependent upon this artifice.

b. The expression "good guess" is used advisedly. For it is "good" in two respects. First,

the cryptanalyst must use care in making his assumptions as to plain-text words. In this he

must be guided by extraneous circumstances leading to the assumption of probable words-not

just any words that come to his mind. Therefore he must use his imagination but he must

nevertheless carefully control it by the exercise of good judgment. Second, only if the "guess"

is correct and leads to solution, or at least puts him on the road to solution, is it a good guess.

But, while realizing the usefulness and the time and labor-saving features of a solution by assuming a probable word, the cryptanalyst should exercise discretion in regard to how long he may

continue in his efforts with this method. Sometimes he may actually waste time by adhering

to the method too long, if straightforward, methodical analysis will yield results more quickly.

c. Obviously, the "probable-word" method has much more applicability when working

upon material the general nature of which is known, than when working upon more or less

isolated communications exchanged between correspondents concerning whom or whose activities

7 This prOCeBB does not involve anything more mysterious than ordinary, logical reasoning: there is nothing

of the subnormal or supernormal about it. If cryptanalytic success seems to require processes akin to those of

medieval magic, if "hocus-pocus" is much to the fore, the student should begin to look for items that the claimant

of such success has carefully hidden from view, for the mystification of the uninitiated. (See Par. 33 in this

eonneetlon.)
11,

1"11111"11111"11111"11111"11111"11111"11111"11111"1111IUIIII 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 IUIIII 1"1111 1"1111 1"1111 1"11 1

57

8 General Givierge in his Cours de CrY'Ptographie (p. 121) says: "However, expert cryptanalysts often

employ such details as are cited above [in connection with Assuming the presence of 'probable words'], and the

experience of the years 1914 to 1918, to cite only those, prove that in practice one often has at his disposal elements of this nature, permitting assumptions much more audacious than those which served for the analysis

of the last example. The reader would therefore be wrong in imagining that such fortuitous elements are

encountered only in cryptographic works where the author deciphers a document that he himself enciphered.

Cryptographic correspondence, if it is extensive, and if sufficiently numerous working data are at hand, often

furnishes elements so complete that· an author would not dare use all of them in solving a problem for fear of

being accused of obvious exaggeration."

nothing is known. For in the latter case there is little or nothing that the imagination can seize

upon as a background or basis for the aesumptions."

d. Very frequently, the choice of probable words is aided or limited by the number and

positions of repeated letters. These repetitions may be patent-that is, externally visible in

the cryptographic text as it originally stands-or they may be latent-that is, externally invisible

but susceptible of being made patent as a result of the analysis. For example, in a monoalphabetic substitution cipher, such as that discussed in the preceding paragraph, the repeated letters

are directly exhibited in the cryptogramj later the student will encounter many cases in which

the repetitions are latent, but are made patent by the analytical process. When the repetitions

are patent, then the pattern or jormula to which the repeated letters conform is of direct use

in assuming plain-text words; and when the text is in word-lengths, the pattern is obviously of

even greater assistance. Suppose the cryptanalyst is dealing with military text, in which case

he may expect such words a~ Dl;VI~ION, BATTALION, etc., to .be present in the text. The

positions of the repeated letter I in DIVISION, of the reversible digraph AT, TA in BATTALION,

and 80 on, constitute for the experienced cryptanalyst tell-tale indications of the presence of

these words, even when the text is not divided up into its original word lengths.

6. The important aid that a study of word patterns can afford in cryptanalysis warrants the

use of d,efiniw terminology and the establishment of certain data having a bearing thereon. The

phenomenon herein under discussion, namely, that many words are of such construction as

regaI:~ tQ,6 l\vmber and positions of repeated letters as to make them readily identifiable, will be

term¢ idiomorphiam (froJ:ll the Greek "idios" =one's own,individual.peculiar-l- "morphe"=form).

Words which show this phenomenon will be termed idiomorphie. It will be useful to deal with

the idioIllQrphisms symbolically. andsystematically as. described below.

j. When dealing with cryptograms in which the word lengths are determined or specifically

shown, it is convenient to indicate their lengths and their repeated letters in some easily recognized manner or by formulas. This is exemplified, in the case of the word DIVISION, by the

formula ABCBDBEFj in the case of the word BATTALION, by the formula ABCCBDEFG. If the

oryptanalyst, during the course of his studies, makes note of striking formulas he has encountered, with the words which fit them, after some time he will have assembled a quite valuable

body of data. And, after more or less complete lists of such formulas have been established in

some systematic arrangement, a rapid comparison of the idiomorphs in a specific cryptogram

with those in his lists will be feasible and will often lead to the assumption of the correct word.

Such lists can be arranged according to word length, as shown herewith:

The normal sequence initiated by each of these conversion equivalents is now completed, with

the results shown in Fig. 15. Note the plain-text generatrix, CLOSEYOURS, which manifests

itself without further analysis. The rest of the message may be read either by continuing the

LFOOH EAZXX

C ERN W

L B H E F

C ERN W o F 0 S E

Cryptogram.i., lYE W K

Equivalents.r., P Y B F R

lYE WK

1 Interval 2 Intervals 3 Intervals Repeated digraphs -DiD- AbbAcy AbeyAnce COCOa

-EvE- ArAbiA hAbitAble dERER

-EyE- AbiAtive lAborAtory ICICle

dIvIsion AboArd AbreAst ININg revIsIon -AciA- AbroAd bAGgAGe

etc. etc. etc. etc.

g. When dealing with cryptographic text in which the lengths of the words are not indicated

or otherwise determinable, lists of the foregoing nature are not so useful as lists in which the

words (or parts of words) are arranged according to the intervals between identical letters in the

following manner: '

34. Solution of additional cryptograms produced by the same cipher component.-a. To

return, after a ra~her long digression, to the cryptogram solved in pars. 28-31, once the cipher

component of a CIpher alphabet has been reconstructed, subsequent messages which have been

enciphered by means of the same cipher component may be solved very readily, and without

recourse to the principles of frequency, or application of the probable-word method. It has been

seen that the illustrative cryptogram treated in paragraphs 24-31 was enciphered by juxtaposing

the cipher component against the normal sequence so that Ap=Sc' It is obvious that the cipher

component may be set against the plain component at anyone of 26 different points of coincidence, each yielding a different cipher alphabet. After a cipher component has been reconstructed,

however, it becomes a known sequence, and the method of converting the cipher letters into their

plain-component equivalents and then completing the plain-component sequence begun by

each equivalent can be applied to solve any cryptogram which has been enciphered by that

cipher component.

b. An example will serve to make the process clear. Suppose the following message, passing

between the same two stations as before, was intercepted shortly after the first message had

been solved:

It ia assumed that the same cipher component was used, but with a different key letter. First

the initial two groups are converted into their plain-component equivalents by setting the

cipher component against the normal sequence at any arbitrary point of coincidence. The

initial letter of the former may as well be set against A of the latter, with the following result:

Plain__ ABC D E F G H I J K L M N 0 P Q R STU V W X Y Z

Cipher___________ LEA V N W 0 R T H BCD F G I J K M P Q S U X Y Z

II

t

;I

DID, EVE, EYE.

ADD, ALL, ILL, OFF, etc.

ARAB, AWAY, etc.

AREA, BOMB, DEAD, etc.

etc.

3/aba

abb

4/abac

abca

abbc

abcb

etc.

I

I

;

I

I

-Ii

!!,'.
FIOUB. 14.

I

I

I

'I

I

1

i

A B C D E

F G H I-J K

L M N 0 P

1-

Q R S T U

V W X Y Z

W

H

(1) I

T

E

SECTION VII

MULTILITERAL SUBSTITUTION WITH SINGLE-EQUIVALENT CIPHER ALPHABETS

(59)

~~~=y~~~~i=~~~~~~~-~~-~i~~~~:~-~~~~=::::=:::::::::::::::::::::::::::::::::::::::=::::=~~E . 36. Analysis of multiliteral, monoalphabetic substitution systems.-a. Substitution methods

in general may be classifiedinto uniliteral and multiliteral systems.' In the former there is a

s~rict Uone-to-on?" correspondence between the length of the units of the plain and those of the

CIpher text;th~t 18, each letter of the plain text is replaced by a single character in the cipher text.

In t~e latter this correspondence is no longer Ip:l o but may be Ip:2 0 , where each letter of the plain

text I~ re~lac~d by a ~ombination of two characters in the cipher text: or Ip:3., where a 3-character

co~bmatlOnm the CIphertext represents a single letter of the plain text, and so on. A cipher in

which the correspondence of the Ip:l. type is termed uniliteral in character; one in which it is of

the Ip:2 0 type, biliteral; Ip:3 o, triliteral, and so on. Those beyond the Ip:lo type are classed together as multuiteral.

. b', When a multiliteral system employs biliteral equivalents, the cipher alphabet is said to be

bipartite, Such alphabets are composed of a set of 25 or 26 combinations of a limited number of

characters taken in pairs. An example of such an alphabet is the following.

Plain .---.------ ABC D E F G H I J K L M

Cipher WW WH WI WT WE HW HH HI HT HT HE IW IH

Plain N 0 P Q R STU V W X Y Z

Cipher II IT IE TW TH TI TT TE EW EH EI ET EE

This alphabet is derived from the square shown in Fig. 15.

(2)

W HIT E

. c. If a messag~ is.enciphered by means of the fo~eg~ing.bipartite alphabet the cryptogram is

still monoalphabetic in character. A frequency distnbution based upon pairs of letters will

I See Sec. VII, Advanced Military Cryptography.

I

,

I

same process, or, what is even more simple, the key letter of the message may now be determined

quite readily and the message deciphered by its means.

IYEWKCERNW

PYBFRLBHEF

Q Z C G S MC I F G

RADHTNDJGH

S B E I U 0 E K H I

T C F J V P F L I J

UDGKWQGMJK

VEHLXRHNKL

WFIMYSIOLM

XGJNZTJPMN

YHKOAUKQNO

ZILPBVLROP

AJMQCWMSPQ

BKNRDXNTQR

*C LOS E YOU R S

DMPTFZPVST

ENQUGAQWTU

FORVHBRXUV

GP S WI C S Y V W

HQTXJDTZWX

IRUYKEUAXY

JSVZLFVBYZ

KTWAMGWCZA

LUXBNHXDAB

M V Y COl Y E B C

NWZDPJZFCD

OXAEQKAGDE

c. In order that the student may understand without question just wha.t is involved in the

latter step, that is, discovering the key letter after the first two or three groups have been deciphered by the conversion-completion process, the foregoing example will be used. It was noted

that the first cipher group was finally deciphered as follows:

Cipher I YEW K

Plain_____________ C LOS E

Now set the cipher component against the normal sequence so that Cp=10 , Thus:

Plain_____________ ABC D E F G H I J K L M N 0 P Q R STU V W X Y Z

Cipher F. G.I J K M P Q S U X Y Z LEA V N W 0 R T H BCD

It is seen here that when Cp=Io then Ap=F.. This is the key for the entire message. The

decipherment may be completed by direct reference to the foregoing cipher alphabet. Thus:

Cipher I YEW K C ERN W 0 F 0 S ELF 0 0 H E A ZX X

Plain C LOS E YOU R S TAT ION A T TWO P M X X

Message: CLOSE YOUR STATION AT TWO PM

d. The student should make sure that he understands the fundamental principles involved in

this quick solution, for they are among the most important principlesin cryptanalytics. How useful they are will become clear as he progresses into more and more complex cryptanalytic studies.

!

1.,.
DANIEL.

______________________1

j

I

I

I

I

I

1

61

• New York Tribune. Extra No. 44,The Cipher Dispatche8, New York, 1879.

148274-38---ri

of the cryptographic text are hidden in some manner or other has, however, no effect upon the

strict monoalphabeticity of the scheme. .

86. Historically interesting examples.-a. Two examples of historical interest will be cited

in this connection as illustrations. During the campaign for the presidential election of 1876

many cipher messages were exchanged between the Tilden managers and their agents Inseversl

states where the voting was hotly contested. Two years later the New York Tribune 4 exposed

many irregularities in the campaign by publishing the decipherments of many of these messages.

These decipherments were achieved by two investigators employed by the Tribune, and the

plain text of the messages seems to show ihat illegalattempts and measures to carry the election

for Tilden were made by his managers. Here is one of the messages:

JACKSONVILLE, Nov. 16 (1876).

GEO. F. RANEY, Tallahassee.

Ppyyemnsnyyypimashnsyyssitepaaenshns

pensshnsmmpiyysnppyea.apielssyeshainsssp

eeiyyshnynsssyepiaanyitnsehyyspyypinsyy

ssitemeipimmeisseiyyeissiteiepyypeeiaass

imaayespnsyyianssseissmmppnspinssnpinsim

imyyitemyysspeyymmnsyyssitspyypeepppma

a a y y p i i t

L'Eng1e goes up tomorrow.

GEO. F. RANEY, Tallahassee:

Have Marble and Coyle telegraph for influential men from Delaware and Virginia. Indications of weakening here. Press advantage and watch Board. L'Engle goes up tomorrow.

DANIEL.

Examination of the message discloses that only ten different letters are used. Itis probable,

therefore, that what one has here is a cipher which employs a bipartite alphabet and in which

combinations of two letters represent single letters of the plain text. The message is therefore

rewritten in pairs and substitution of arbitrary letters for the pairs is made, as seen below:

PP YY EM NS NY YY PI MA SH NS YY SS etc.

ABC DEB F G H D B I etc.

A triliteral frequency distribution is then made and analysis of the message along the lines

illustrated in the preceding section of this text yields solution, as follows:

JACKSONVILLE, Nov. 16.

T 0 daY

a b b b a

p

R=baaaa

S=baaab

T=ba.aba

u...:V=baabb

.W::;babaa

X=babab

Y=babba

Z=babbb

60

I-J=abaaa

K=-a.ba,ab

L=ab~ba

M=ababb

tl=abbaa

O=abbab

P=abbba

Q=abbbb

WEI L

a a b a

E

A=aaaaa

B=;:aaaab

C=aaaba

D=aaabb

E=aabaa

F=aabab

G=aabba

H=aabbb

I

I ~~~~ 1__

ALl i s

a a b b b

H

obviously have all the characteristics of a simple, uniliteral distribution for a monoalphabetic

substitution cipher.

d. Ciphers of this type, as well as of those of the multiliteral (triliteral, quadraliteral, ...)

type are readily detected externally by virtue of the fact that the cryptographic text is composed

of but a very limited number of different characters. They are handled in exactly the same manner as are uniliteral, monoalphabetic substitution ciphers. So long as the same character, or

combination of characters, is always used to represent the same plain-text letter, and so long as a

given letter of the plain text is always represented by the same character or combination of

characters, the substitution is strictly monoalphabetic and can be handled in the simple manner

described under Par. 31 of this text.

6. An interesting example in which the cipher equivalents are quinqueliteral groups and yet

the resulting cipher is strictly monoalphabetic in character is found in the cipher system invented

by Sir Francis Bacon over 300 years ago. Despite its antiquity the system possesses certain

f-eatures of merit which are well worth noting. BaconI proposed the following cipher alphabet,

composed of permutations of two elements taken five at a time: a

\

Instead of employing such an obvious device as capital and small letters, suppose that an "a"

element be indicated by a very slight shading, or a very slightly heavier stroke. Then a secret

message might easily be thus enfolded within an external message of exactly opposite meaning.

The number of possible variations of this basic scheme is very high. The fact that the characters

2 For a true picture of this cipher, the explanation of which is often distorted beyond recognition even by cryptographers, see Bacon's own description of it as contained in his De AUf/mentis Scientiarum (The Advancement 01

Learning), as translated by any first-class editor, such as Gilbert Watts (1640) or Ellis, Spedding, and Heath

(1857, 1870). The student is cautioned, however, not to accept as true any alleged "decipherments" obtained

by the application of Bacon's cipher to literary works of the 16th century; These readings are purely subjective.

• In the 16th Century, the letters:t andJ were used interchangeably, as were also Uand V. Bacon's alphabet

was called by him a "biliteral alphabet" because it employs permutations of two letters. But from the cryptanalytic standpoint the significant point is that each plain-text letter is represented by a 5-character equivalent.

Hence, present terminology requires that this alphabet be referred to as a quinqueliteral alphabet.

If this were all there were to Bacon's invention it would be hardly worth bringing to attention.

But what he pointed out, with great clarity and simple examples, was how such an alphabet

might be used to convey a secret message by enfolding it in an innocent, external message which

might easily evade the strictest kind of censorship. As a very crude example, suppose 'that a

message is written in capital and lower ease letters, any capital letter stAmding fol' 8.n"aJJ element

of the cipher alphabet, and any small letter, for a "bJJ element. Then the external sentence

"All is well with me today" can be made to contain the secret message "Help." Thus:

i

I;

.

!,

iii

,

I

•

__ i

I

I
62

There were, of course, several messages of like nature, and examination disclosed that

only 26 different numbers in all were used. Solution of these ciphers followed very easily, the

decipherment of the one given above being as follows:

JACKSONVILLE, Nov. 17.

(63)

SECTION VIII

MULTILITERAL SUBSTITUTION WITH MULTIPLE-EQUIVALENT CIPHER

ALPHABETS

Parqraph Purpose of providing multiple-equivalent cipher alphabetB •__• .____________ 37

Solution of a simple example ••_. .:.. .__________ 38

Solution of more complicated example;•••• •__• •• • .__________________________________ 39

A subterfuge to prevent decomposition of eipher text into component unit8.__••• ._ 40

37. Purpose of providing multiple-equivalent cipher alphabets.-a. It has been seen that

the characteristic frequencies ofletters composing normal plain text, the associations they form

in combining to form words, and the peculiarities certain of them manifest in such text all afford

direct clues by means of which ordinary monoalphabetic substitution encipherments of such

plain text may be more or less speedily solved. This has led to the introduction of simple

methods for disguising or suppressing the manifestations of monoalphabeticity, so far as possible.

Basically these methods are multiliteral and they will now be presented.

b. Multiliteral substitution may be of two types: (1) That wherein each letter of the plain

text is represented by one and only one multiliteral equivalent. For example, in the Francis

Bacon cipher described in Par. 35e, the letter Kp is invariably represented by the permutation

abaab. For thisreason this type of system may be more completely described as monoalphobetic, multiliteral 8'Ubstitution with single-equivalent cipher alphabets.

(2) That wherein, because of the large number of equivalents made available by the combinations and permutations of a limited number of elements, each letter of the plain text may be

represented by several multiliteral equivalents which may be selected at random. For example,

if 3-letter combinations are employed there are available 263 or 17,576 equivalents for the 26

letters of the plain text; they may be assigned in equal numbers of different equivalents for the

26 letters, in which case each letter would be representable by 676 different 3-letter equivalents'

or they may be assigned on some other basis, for example, proportionately to the relative

frequencies of plain-text letters. For this reason this type of system may be more completely

described as monoalphabetic, multiliteral substitution with multiple-equivalem cipher alphabets.

Some authors term such a system "simple substitution with multiple equivalents"; others term

it monoalphabetic substitution with variants. For the sake of brevity, the latter designation will

be employed in this text.

c. The primary object of monoalphabetic substitution with variants is, as has been mentioned above, to provide several values which may be employed atrandom in a simple substitution

of cipher equivalents for the plain-text letters. In this connection, reference is made to Section

X of Elementary Military Oryptography, wherein several of the most common methods for

producing and using variants are set forth.

d. A word or two concerning the underlying theory from the cryptanalytic point of view of

monoalphabetic substitution with variants, may not be amiss. Whereas in simple or singleequivalent, monoalphabetic substitution it is seen that-

(1) The same letter of the plain text is invariably represented by but one and always the

same character of the cryptogram, and

t

If

o

N

9

FIGURJ: 16.

SPA Y M E

:5 4 5 6 7 8

'H I

1 2

- - - - - - - - - - K S D - - - - - - - - - 1-

L N W P

- - - - - - 1-

R H T

I--- - - - - - - - 1-

U 0

I--- 1-- - - - - - IX A F

I-- - - - - - - - 1-

B G

I-- 1-- - II C V Y

I-- - - - - - - - IE M J

I-- - - - - - - - 1-

H 1

I 2

S :5 Q)

'S P 4

::l

Z A 5

0

Y 6 .....

.....

Q) M7 .....

III

I""l E 8

N 9

T 0

S. PASCO and E. M. L'ENGLE:

Cocke will be ignored, Eagan called in. Authority reliable.

DANIEL.

c. The Tribune experts gave the following alphabets as the result of their decipherments:

AA=O EN=Y IT=D NS=E PP=H SS=N

A1=U EP=C MA=B NY=M SH=L YE=F

E1=1 IA=K MM--G PE=T SN=P Y1=X

EM=V IM=S NN::;J PI=R SP=W YY=A

20=D 33=N 44=H 62=X 77=G 89=Y

25=K 34=W 48=T 66=A 82=1 93=E

27=5 39=P 52=U 68=F 84=C 96=M

31=L 42=R 55=0 75=B 87=V 99=J

They did not attempt to correlate these alphabets, or at least they say nothing about a possible

relationship. The present author has, however, reconstructed the rectangle upon which these

alphabets are based, and it is given below (fig. 16).

2d Letter or Number

It is amusing to note that the conspirators selected as their key a phrase quite in keeping with

their attempted illegalities-HIS PAYMENT-for bribery seems to have played a considerable

part in that campaign. The blank squares in the diagram probably contained proper names,

numbers, etc.

,I

"i

i

-r

I

•
:i

-<

•

i

64

(2) The same character of the cryptogram invariably represents one and always the same

letter of the plain text;

In multiliteral substitution with multiple equivalents (monoalphabetic substitution with

variants) it is seen that-

(1) The same letter of the plain text may be represented by one or more different characters

of the cryptogram, but

(2) The same oharacter of the cryptogram nevertheless invariably represents one and always

the same letter of the plain text. .

38. Solution of a simple example.-a. The following cryptogram has been enciphered by a

set of four alphabets similar to the following:

ABC D E F G H I-J K L M N 0 p Q R STU V W X Y Z

08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 01 02 03 04 05 06 07

353637383940 41 4243 44 4546474849 50 26 27 28 29 30 31 323334

68 69 70 71 72 73 74 75 51 52 53 54 55 56 57 58 59 60 61 S2 63 64 65 66 67

S7 88 89 90 91 92 93 94 95 96 97 98 99 00 76 77 78 79 80 81 82 83 84 85 86

Tb.ekeyword here is TRIpI. In enciphering a message the equivalents are to be selected at

random from among the four variants for each letter. The steps in solving a message produced

by such a scheme will now be scrutinized.

CRYPTooiuM

68321 09022 48057 65111 88648 42036 45235 09144 05764 22684

00225 57003 gr357 14074 8252440768 51058 93074 92188 47264

09328 04255 06186 79882 85144 45886 32574 55136 56019 45722

76844 68350 45219 71649 90528 65106 11886 44044 89~69 70553.

18491 06985 48579 33684 50957 70612 09795 29148 56109 08546

62062 65509 32800 32568 97216 44282 34031 84989 68564 53789

1Z530 77401 68494 3854411368 87616 56905 20710 58864 67472

22490 09136 62851 24551 35180 14230 50886 44084 06231 12S76

05579 58980 29503 99713 32720 36433 82689 04516 52263 21175

06445 72255 68951 86957 76095 67215 53049 08567 gr30

b. Assuming that the foregoing remarks had not been made and that the cryptogram has

just been submitted for solution with no information concerning it, the first step is to make a

preliminary study to determine whether the cryptogram involves cipher or code. The cryptogram appears in 5-figure groups, which may indicate either cipher or code. A few remarks will

be made at this point with reference to the method of determining whether a cryptogram composed of figure groups is in code or cipher, using the foregoing example.

c. In the first place, if the cryptogram contains an even number of digits, as for example

-4:94 in the foregoing message, this leaves open the possibility that it may be cipher, composed of

247 pairs of digits; were the number of digits an exact oddmultiple of five, such as 125,135, etc.,

the possibility that the cryptogram is in code of the 5-figuregroup type must be considered, Next,

a preliminary study is made to see if there are many repetitions, and what their characteristics

I The letter corresponding to the lowest number in each line of the diagram showing the cipher alphabets

is a key letter. Thus, in the lstJine Ol=Tj in the 2d line 26=Rj etc.

"I;

I

II

!

I IUIIII 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 IUIIII 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"11111"11111"11111"11111"

65

are. If the cryptogram is code of the 5-figure group type, then such repetitions as appear should

generally be in whole groups offive digits, and they should be visible in the text just as the message stands, unless the code message has undergone encipherment also. If the cryptogram is in

cipher, then the repetitions should extend beyond the 5-digit groupings; if they conform to any

definite groupings at all they should for the most part contain even numbers of digits since each'

letter is probably represented by apair of digits. If no Clues of the foregoing nature are present,

doubts will be dissolved by making a detailed study of frequencies.

d. A simple 4-part frequency distribution is therefore decided upon. Shall the alphabet be

assumed to be a 25- or a 26-character one? If the former, then the 2-digit pairs from 01 to 00

fall into exactly four groups each corresponding to an alphabet. Since this is the most common

scheme of drawing up such alphabets, let it be assumed to be true of the present case. The

following distributions result from the breaking up of the text into 2-digit pairs.

01-//1 26-//1 51-iHI. 76-iHI. I

02- 27- 52-iHI. 77-1

03-1111 28-/ 53-III 78-

04-1 29-1 54- 79-1

05-iHI. 30-11/ 55-1111 80-111

06-iHI. I 31- 56-iHI. 81-

07-111 32-4HJ I 57-iHI.I 82-11I1.

08- 33-1 58-II 83-1

09-1111 34-1 59- 84-iHI. I

10-11I1 35-11 60- 85-iHI. I

ll-iHI. 36-!HJ 61- 86-//1

12-11I 37-1 62-11 87-

13-1 38- 63- 88-1//1

14-1 39-1 64-iHI. I 89-iHI.

15-1 40-11/ 65- 90---iHI. I

16-11I 41- 66-1 91-1/1

17- 42-111I 67-11 92-1

18-iHI.I 43-1 68-iHI. /I 93-1

19- 44-iHI. I 69-11 94-1

20-1 45-iHI. I 70---1 95-111

21-1/ 46-111 71-1 96-

22-iHI. 47- 72-1111 97-iHI. I

23-11 48-111 73- 98-1

24- 49-iHI. 74-1111 99-

25-1 50-iHI. 75-1 00-11

e. If the student will bring to bear upon this problem the principles he learned in Section V

of this text, he will soon realize that what he now has before him are four, simple, monoalphabetic frequency distributions similar to those involved in a. monoalphabetic substitution cipher

using standard cipher alphabets. The realization of this fact immediately provides the clue to

the next step: "fitting each of the distributions to the normal." (See Par. 17b). This can be
II

66 67

03,23,78

35, and 77

SETB

71-12-02-51-23-05-77

11-82-51-02-03-05-35

11-91-02-02-23-37-35

97-12-51-03-78-69-77

01, 16, 79

13,42,68

In the solution of cases of this kind, repetitions would play their usual role, with the modifications

noted below in Par. 39. Once an entering wedge has been forced, through the identification

of one or more repeated words such as BATTALION, DIVISION, etc., the entire enciphering

rectangle would soon be reconstructed. It may be added that the frequency distribution for

the text of a single long message or several short ones enciphered by such a system would show

characteristic phenomena, the most important of which are, first, that the distribution for a

rectangle such as shown in Fig. 17 would practically follow the normal and, second, that the

distribution for the 2d digit of pairs would show more marked crests and troughs than the

distribution for the 1st digit. For example, the initial digits 1,4, and 7 (for the numbers 10--19,

40--49, and 70--79, inclusive) would apply to the distribution for the letters A to J, inclusive; the

initial digits 2, 5, and 8 would apply to the distribution for the letters K to T, inclusive. The

total weighted frequency values for these two groups of letters are about equal. Therefore,

the frequencies of the initial digits 1, 2, 4, 5, 7, and 8 would be approximately equal. But

consider the final digit 5 in the numbers 15, 45, 75, 25, 55, and 85; its total frequency is composed of the frequency of Ep plus the frequency of Op; whereas in the case of the final digit 6,

its total frequency is composed of the frequency ofFp plus the frequency of Qp. The two cases

would show a marked difference in frequency. Of course, the letters may be inserted within

the enciphering rectangle in a keyword-mixed or even in a random order; the numbers may be

applied to the rectangle in a random order. But these variations, while increasing the difficulty

in solution, by no means make the latter as great as may be thought by the novice.

39. Solution of a more complicated example.-a. As soon as a beginner in cryptography

realizes the consequences of the fact that letters are used with greatly varying frequencies

in normal plain text, a brilliant idea very speedily comes to him. Why not disguise "the

natural frequencies of letters by a system of substitution using many equivalents, and let

the numbers of equivalents assigned to the various letters be more or less in direct proportion

to the normal frequencies of the letters? Let E, for example, have 13or more equivalents; T, 10;

N, 9; etc., and thus (he thinks) the enemy cryptanalyst can have nothing in the way of tell-tale

or characteristic frequencies to use as an entering wedge.

b. If the text available for study is small in amount and if the variant values are wholly

independent of one another, the problem can become exceedingly difficult. But in practical

military communicationssuch methods are rarely encountered, became the volume oj textis mooJly

great enough to permit oj the establishment of equivalent values. To illustrate what is meant,

suppose a set of cryptograms produced by the monoalphabetic-variant method described above

shows the following two sets of groupings in the text:

SETA

12-37-02-79-68-13-03-37-77

82-69-03-79-13-68-23-37-35

82-69-51-16-13-13-78-0~35

91-05-02-01-68-42-78-37-77

An examination of these groupings would lead to the following tentative conclusions with regard

to probable equivalents:

12, 82, 91

05,37, 69

02, and 51

The establishment of these equivalencies would sooner or later lead to the finding of additional

sets of equal values. The completeness with which this can be accomplished will determine

it

\

I

1

i

1 2 3 4 5 6 7 8 9 0

- - - - - - - - 1=

1, 4, 7 A B C 0 E F G H I J

- - - - - - - - - 2, 5, 8 K L M N 0 P Q R S T

- - - - - - - - -

3, 6. 9 U V W X Y Z - • : ;

:FIGtlllJ: 17

done without difficulty in this case (remembering that a 25-1etter alphabet is involved and

assuming that I and J are the same letter) and the following alphabets result:

01-I~ 26-U 51-N 76-E

02-K 27-V 52-0 77-F

03-L 28-W 53-P 78-G

04--M 29--X 54-Q 79-H

05-N 30-Y 55-R 80-I-J

06-0 31-Z 56-5 81-K

07-P 32-A 57-T 82-L

08-Q 33-B 58-U 83-M

09--R 34-C 59-V 84-N

10-S 35-0 60-W 85-0

11-T 36-E 61-X "86-P

12-U 37-F 62-Y 87-Q

13-V 38--G 63-Z 88-R

14-W 39-H 64-A 89-5

15-X 40-I-J 65-B 90-T

16--Y 41--K 66-C 91-U

17-Z 42-L 67-0 92-V

18-A 43-14 68-E 93-W

19-B 44-N 69--F 94-X

20-C 45-0 7o---G 95-Y

21-0 46-P 7l-.....H 96-Z

22-E 47-Q 72-I-J 97-A

23-F 48-R 73-K 98-B

24-G 49--5 74-L 99-C

25-H 50-T 75-M 00-0

j. The keyword is seen to be JUNE and the first few groups of the cryptogram decipher as

follows:

68 32 10 90 22 48 05 76 51 11 88 64 84 20 36 45 23

E A 5 T ERN E N T RAN CEO F

g. From the detailed procedure given above, the student should be able to draw his own

conclusions as to the procedure to be followed in solving cryptograms produced by methods

which are more or less simple variations of that just discussed. In this connection he is referred

to Section X of Elementary Ml1itary Cryptography, wherein a few of these variations are mentioned.

h. Possibly the most important of the variations is that in which a rectangle such as that

shown in Fig. 17 is employed.

-!

~ ~.

i

-,

-.

i

!

i
68

the ease or difficulty of solution. Of course, if many equivalencies can be established the

problem can then be reduced practically to monoalphabetic terms and a speedy solution can

be attained. .

c. Theoretically, the determination of equivalencies may seem to be quite an easy matter,

but practically it may be very difficult, because the cryptanalyst can never be certain that a

combination showing what may appear to be a variant value is really such, and is not a different

word. For example, take the groups17-82-31-82-14-63, and

27-8~o-82-14-63

Here one might suspect that 17 and 27 represent the same letter, 31 and 40 another letter. But

it happens that one group represents the word MANAGE, the other DAMAGE.

d. When reversible combinations are used as variants, the problem is perhaps a bit more

simple. For example, using the accompanying Fig. 18 for encipherment, two messages with

the same initial words, REFERENCE YOUR, may be enciphered as follows:

K,Z Q,V B.H M.R D,L

D

M

N

C

I -W

P S

E B

R L

:&'JG11U 11.

V G

A H

T 0

F U

A B C D E

I---- - - IF G H I~ K

f--- - f--

L M N 0 P

- Q R S T U

f--- - - - D,M,N,C V W X Y Z

V,A,T,F

W,S,B,L

I,P,E,R

G,H,O,U

·············································r

69

Thepbrase COMMANDER OF SPECIAL TROOPS might be enciphered thus:

COM MAN D E R 0 F

n m m " m W N

These would normally then be arranged in 5-letter groups, thus:

VIEBP HIUFT IEABT MWOPW GT •••

. b. Itwill be noted, however, that only 20 of the 26 letters of the alphabet have been employed

as row and column indicators, leavingJ, K, Q,X, Y, and Z unused. Now, suppose these five letters

are used as nulls, not inpairs, butas individual lettersinserted at random just before the real text is

arranged in 5-letter groups. Occasionally, a pair of nulls is inserted. Thus, for example:

VIEXB PHKIU FJXTI EAJBT MWOQP WGKTY

The cryptanalyst, after some study, suspecting a biliteral cipher, proceeds to break up the text

into pairs:

VI EX BP HK IU FJ XT IE AJ BT MW OQ PW GK TY

Compare this set of 2-letter combinations with the correct set. Only 4 of the 15 pairs are "proper"

units. It is easy to see that without a knowledge of the existence of the nulls, and even with a

knowledge, if he does not know which letters are nulls, the cryptanalyst would be confronted with

a problem for the solution of which a fairly large amount of text might be necessary. The

careful employment of the variants also very materially adds to the security of the method because repetitions can be rather effectively suppressed.

c. From the cryptographic standpoint, the fact that in this system the cryptographic text

is more than twice.as long as the plain text constitutes a serious disadvantage. From the

cryptanalytic standpoint, the masking of the cipher units constitutes the most important source

of strength of the system; this, coupled with the use of variants, makes it a bit more difficult

system to solve, despite its monoalphabeticity.

note of the last phrase; the mere insertion of symbols having the same characteristics as the

symbols of the cryptographic text, except that they have no meaning, is not what is meant.

This class of nulls rarely achieves the purpose for which they are intended. What is really meant

can best be explained in connection with an example. Suppose that a 5 x 5 checkerboard design

with the row and column indicators shown in Fig. 19 is adopted for encipherment. Normally,

the cipher units would consist of 2-letter combinations of the indicators, invariably giving the

row indicator first (by agreement).

j

1

!

OUR

SRBJC H

RWJBN H

E Y

R S L H P

RLSHP

E N C

:&'JGURE 18.

D W W Z N

D W Z W N

N H A 0 E

- - D T M F P

-- Q B U I V

- - G X R C S

- - Z L Y W K

E R

XL S H C

XSLHN

REF

NHWDR

C H D WR

(1)

(2)

W,S

F,X

The experienced cryptanalyst, noting the appearance of the very first few groups, assumes that

he is here confronted with a case involving biliteral reversible equivalents, with variants.

e. The probable-word method of solution may be used, but with a slight variation introduced by virtue of the fact that, regardless of the system, letters oj low jrequency in plain tezt

remain infrequent. Hence, suppose a word containing low-frequency letters, but in itself a

rather common word strikingly idiomorphic in character is sought as a "probable word"; for

example, words such as QAYALRX, ATTAC~, and ,ERE,EARE. Writing such a word on a slip of

paper, it is slid one interval at a time under the text, which has been marked so that the high

and low-frequency characters are indicated. Each coincidence of a low-frequency letter of the

text with a low-frequency letter of the assumed word is examined carefully to see whether the

adjacent text letters correspond in frequency with the other letters of the assumed word; or, if

the latter presents repetitions, whether there are correspondences between repetitions in the

text and those in the word. Many trials are necessary but this method will produce results

when the difficulties are otherwise too much for the cryptanalyst to overcome.

40. A subterfuge to prevent decomposition of cipher text into component units.-a. A few

words should be added with regard to certain subterfuges which are sometimes encountered in

monoalphabeticsubstitution with variants, and which, if not recognized in time, cause considerable delays. These have to deal with the insertion of nulls so as to prevent the cryptanalyst

from breaking up the text into its real cryptographic units. The student should take careful

G,J

C,N

P,T

, li < j .'( I

_____________________________________..-_l: _
SECTION IX

POLYGRAPHIC SUBSTITUTION SYSTEMS

Paragraph

Monographic and polygraphic substitution systems__________________________________________________________________________ 41

Tests for identifying digraphio substitution_____________________________________________________________________________________ 42

General procedure in the analysis of digraphle substitution ciphers_____________________________________________________ 43

Analysis of digraphlo substitution ciphers based upon 4-square checkerboard designs______________________________ 44

Analysis of ciphers based upon other types of checkerboard designs a 45

Analysis of the Playfair cipher system___________________________________________________________________________________________ 46

41. Monographic and polygraphic substitution systems.-a. The student is now referred

to Sections VII and VIII of Advanced Military Oryptography, wherein polygraphic systems of

substitution are discussed from the cryptographic point of view. These will now be discussed

from the cryptanalytic point of view.

b. Although the essential differences between polyliteral and polygraphic substitution are

treated with some detail in Section VII of Advanced Military Oryptography, a few additional

words on the subject may not be .smies at this point.

c. The two primary divisions of substitution systems into (1) uniliteral and multiliteral

methods and into (2) monographic and polygraphic methods are both based upon considerations

as to the number of eume'1JJ8 cons~tuting,theplain-text and the equivalent cipher-text units, In

uniliteral as well as in monographic substitution, each plain-text unit consists of.a single element

and each' cipher-text unit consists of a single element. The two terms uniliteral and monographic are therefore identical in significance, as defined cryptographically. It is when the

terms multiliteral and polygraphic are examined that an essential difference is seen. In multiliteral substitution the plain-text unit always consists of a single element (one letter) and the

cipher-text unit consists of a group of two or more elements; when biliteral, it is a pair of elements,

when trilitersl, it is a set of three elements, and so on. Iii what win herein be designated as

true or complete polygraphic substitution the plain-text unit consists of two or more elements

forming an indivisible compoundj the cipher-text unit usually consists of a corresponding number

of elements.' When the number of elements comprising the plain-text unrts is fixed and always

two, ~he system is digraphic,' when it is three, the system is trigraphicj when it is four, tetragraphtcj and so on.' It is important to note that in true or complete polygraphic substitution

the elements combine to form indivisible compounds having properties different from those of

either of the constituent letters. For example, in uniliteral substitution ABp may yield XYo and

ACp may yield XZe ; but in true digraphic substitution ABp may yield XYe and ACp may yield QNe•

A difference in identify of one letter affects the whole result," An analogy is found in chemistry,

when two elements combine to form a molecule, the latter usually having properties quite

different from those of either of the constituent elements. For example: sodium, a metal, and

1 The qualifying adverb "usually" is employed because this correspondence is not essential. For example,

if one should draw up a set of 676 arbitrary single signs, it would be possible to represent the 2-letter pairs from

AA to ZZ by single symbols. This would still be a dlgraphic system.

, In this sense a code system is merely a polygraphic substitution system in which the number of elements

constituting the plain-ten units is variable.

a For this reason thetwo letters are marked by a ligature, that is, by a bar acrO/38 their tops.

(70)

71

chlorine, a gas, combine to form sodium chloride, common table salt. Furthermore, sodium nd -

fluorine, also a gas similar in many respects to chlorine, combine to form sodium fluoride, which

is much different from table salt. Partial and pseudo-polygraphic substitution will be treated

under subparagraphs d and e below.

d. Another way of looking at polygraphic substitution is to regard the elements comprising

the plain-text units as being enciphered individually and polyalphabetically by a fairly large

number of separate alphabets. For example, in a digraphic system in which 676 pairs of plaintext letters are representable by 676 cipher-text pairs assigned at random, this is equivalent to

having a set of 26 different alphabets for enciphering one member of the pairs, and another set

of 26 different alphabets for enciphering the other member of the pairs. According to this

viewpoint the different alphabets are brought into play by the particular combination olletters

forming each plain-text pair. This is, of course, quite different from systems wherein the various

alphabets are brought into play by more definite rules; it is perhaps this very absence of definite

rules guiding the selection of alphabets which constitutes the cryptographic strength of this type

of polygraphic system.

e. When regarded in the light of the preceding remarks, certain systems which at first glance

seem to be polygraphic, in that groupings of plain-text letters are treated as units, on closer

inspection are seen to be only partially polygraphic, or pseudo-polygraphic in character. For

example, in a system in which encipherment is by pairs and yet one of the letters in each pair is

enciphered monoalphabetically, the other letter, polyalphebetically, the method is only p8'UBdopolygraphic. Cases of this type are shown in Section VII of AdvancM, Military Qryptogrq,phy.

Again, in a system in which encipherment is by pairs and the encipherments of the left-hand

and right-hand members of the pairs show group relationships, this is not pseudo-polygraphic

but only partially polygraphic. Cases of this type are also shown in the text referred to above.

f. The fundamental purpose of polygraphic substitution is again the suppression of the

frequency characteristics of plain text, just as is the case in monoalphabetic substitution with

variants; but here this is accomplished by a different method, the latter arising from a somewhat

different approach to the problem involved in producing cryptographic security. When the substitution involves replacement of singleletters in a monoalphabetie system, the cryptogram can

be solved rather readily. Basically the reason for this is that the principles of frequency and the

laws of probability, applied to individual units of the text (single letters), have avery good

opportunity to manifest themselves. A given volume of text ofsay n plain-text letters, enciphered

purely monoalphabetically, affords n cipher characters, and the same number of cipher units.

The same volume of text, enciphered digraphically, still affords n cipher characters but only

cipher units. Statistically speaking, the sample within which the laws of probability now apply

has been cut in half. Furthermore, from the point of view of frequency, the very noticeable

diversity in the frequencies of individual letters, leading to the marked crests and troughs of

the uniliteral frequency distribution, is no longer so strikingly in evidence in the frequencies of

digraphs. Therefore, although true digraphic encipherment, for example, cuts the cryptographic

textual units in half, the difficulty of solution is not doubled, but, if a matter of judgment arising

from practical experience can be expressed or approximated mathematically, squared or cubed.

g. Sections VII and VIII of Advanced Military Oryptography show various methods for the

derivation of polygraphic equivalents and for handling these equivalents in cryptographing and

decryptographing messages. The most practicable of those methods are digraphic in character

and for this reason their solution will be treated in a somewhat more detailed manner than will

trigraphic methods. The latter can be passed over with the simple statement that their analysis

requires much text to permit of solution by the frequency method, and hard labor. Fortunately,

they are infrequently encountered because they are difficult to manipulate without extensive

I

_______________Il
72 73

table of 676 cells containing digraphs showing reciprocal equivalence between plain and ciphertext digraphs. Suppose the message begins as follows (in which the assumed values have been

inserted):

XQ VO ZI LK AP OL ZX PV QN IK OL UK AL HN LK VL

FO TH IN NT RE NT NO IN

BN OZ KU DY EL LE YW

SI ON TO

The words FOURTH INFANTRY REGIMENT are readily reoognized. The reciprocal pairs ELo

and LEo suggest ATTACK. The beginning of the message is now completely disclosed: FOUR~

INFANTRY REGIMENT NOT YET IN POSITIONTO ATTACK. The values more or less automatically determined are VOo=URp, ALo=TYp, HNc=ETp, VLo=POp, OZo=Tlp, YWo=CKp.

c. Once a good start has been made and a few words have been solved, subsequent work

is quite simple and straightforward. A knowledge of enemy correspondence, including data

regarding its most common words and phrases, is of great assistance in breaking down new

digraphic tables of the same nature but with different equivalents.

d. The foregoing remarks also apply to the details of solution in cases of partially

digraphic substitution. .

44. Analysis of digraphio substitution oiphers based upon 4-square oheokerboard desIgns.-

a. In Section VIII of Advanced Military Oryptography there are shown various examples of digraphic substitution based upon the use of checkerboard designs. These may be consider~d

cases of partially digraphic substitution, in that in the checkerboard system there are certain

relationships between plain-text digraphs having common elements and their correspon~g

cipher-text digraphs, which will also have common elements. For example, take the following

4-square checkerboard design:

tables" If the latter are required they must be compiled in the form of a book or pamphlet. If

one is willingto go that far, one might as well include in such document more or less extensive lists

of words and phrases, in which case the system falls under the category of code and not cipher.

42. Tests for identifying digraphic substitution.-a. The tests which are applied to determine whether a given cryptogram is digraphic in character are usually rather simple. If there

are many repetitions in the cryptogram and yet the uniliteral-frequenoy distribution gives no

clear-cut indications of monoalphabeticity; if most of the repetitions contain an even number

of letters; and if the cryptogram contains an even number of letters, it may be assumed to be

digraphic in nature.

b. The studentshould first try to determine whether the substitution is completely digraphic,

or only partially digraphic, or pseudo-digraphic in character. As mentioned above, there are

cases in which, although the substitution is effected by taking pairs of letters, one of the members

of the pairs is enciphered monoalphabetically, the other member, polyalphabetically, A distribution based upon the letters in the odd positions and one based upon those in the even

positions should be made. If one of these is clearly monoalphabetic, then this is evidence that the

message represents a case of pseudo-digraphism of the type here described. By attacking the

monoalphabetio portion of the messages, solution can soon be reached by slight variation of the

usual method, the polyalphabetic portion being solved by the aid of the context and considerations. based· upon the probable nature of the substitution chart. (See Tables 2, 3, and 4 of

Admneetl Military Oryptography.) It will be noted that the charts referred to show definite

symmetry in their construction.

c. On the other hand, if the foregoing steps prove fruitless, it ma.y be assumed that the

cryptogram is completely digraphio in character.

d. Just as certain statistical tests may be applied to a cryptogram to establish its monoalphabeticity, 80 also maya statistical test be applied to a cryptogram for the purpose of establishing its digraphicity. The nature of this test and its method of application will be discussed

ina subsequent text.

43. General prooedure in the analysis of digraphio substitution oiphers.-a. The analysis of

cryptograms which have been produced by digraphio substitution is accomplished largely by

the application of the simple principles of frequency of digraphs, with the additional aid ofsuch

special circumstances as may be known to or suspected by the cryptanalyst. The latter refer

to peculiarities which may be the result of the particular method employed in obtaining the

equivalents of the plain-text digraphs in the cryptographing process. In general, however;

only if there is sufficient text to disclose the normal phenomena of repetition will solution be

feasible or possible.

b. However, when a digraphie system is employed in regular service, there is little doubt

but that traffic will rapidly accumulate to an amount more than sufficient to permit of solution

by simple principles of frequency. Sometimes only two or three long messages, or a half dozen

of average length are sufficient. For with the identification of only a few cipher digraphs,

larger portions of messages may be read because the skeletons of words formed from the few

high-frequency digraphs very definitely limit the values that can be inserted for the intervening

unidentified digraphs. For example, suppose that the plain-text digraphs TH, ER, IN, IS, OF,

NT,and TO have been identified by frequency considerations, corroborated by a tentatively

identified long repetition; and suppose also that the enemy is known to be using a quadricular

1

2

B W G R M 0 P A U L

I-- - - - I-- - - IN Y V X E H Z Q D F

I-- - - IS I C T K K I T S C

I-- - - I-- U P L A 0 M W R B G

I-- -

D Z F Q .H E Y X N V

- - - - - 1-

W A L E S C X K P B '--- - - - IF H U I T 0 M Y D V

f---- - - - 1-

P X B K C S A E W L

f---- - - - IN Z R Q G G Z Q N R

f---- - - - - D M V Y 0 T H I F U

3

4

• A patent has been granted upon a rather ingenious machine for automatically accomplishing true polygraphic substitution, but it has not been placed upon the market. See U. S. Patent No. 1845947 issued in 1932

to Weisner and Hill. In U. S. Patent No. 1515680 issued to Henkels in 1924, there is described a mechanism

which also produces polygraphic substitution.

Here BCp=OWc, BOp=OFo, BSp=OPo, BGp=ONo and BTp=ODo' In each cas~ when Bp.is the initial

letter of the plain-text pair, the initial letter of the cipher-text equiva}ent 18 00 , This,?f course,

is the direct result of the method; it means that the encipherment 18 monoalphabetic for the
74 75

(3) At first glance this may appear to the untrained eye to be a monoalphabetic frequency

distribution but upon closer inspection it is noted that aside from the frequencies of four or five

:::: -- ~:::::~

-~:::::~~ ::::_~

-~~ ~~~~~ ~-~~~~ -- :::::

~~~::::~~~~~ ::::~~~~~~~-~~ ~:::::

~~~~~~~~~ ~~~~~~~~~~~ -~~::::

ABCDEFGHIJKLMNOPQRSTUVWXYZ

II w 8 WOO" 0 8 U n w W 9 8 II II 0 1 U 7 3

FIGURE 21.

letters the frequencies for the remaining letters are not very dissimilar. There are, in reaIity, no

very marked crests and troughs, certainly not as many as would be expected in a monoalphabetic

substitution cipher of equal length.

(4) The message having been carefully examined for repetitions of 4 or more letters, all of

them are listed:

Frequency Located in lines

TFHHAYZLQCIAAIQUCHTP (20 letters)______________________________________ 2 H and K. QMLFEQQIGOI (11 letters)______________________________________________________ 2

°and F. XIFBEX (6 letters)________________________________________________________________ 2 o and D. FEQQ___________________________________________________________________________________ 3 O,D,F. QMLF___________________________________________________________________________________ 3 O,F,J. BFHM__________________________________________________________________________________ 2 Band G. BSPK__________________________________________________________________________________ 2 A andE. GOIH__________________________________________________________________________________ 2 D andJ.

Since there are quite a few repetitions, two of considerable length, since all but one of them

contain an even number of letters, and since the message also contains an even number of letters,

344, digraphic substitution is suspected. The cryptogram is transcribed in 2-letter. groups, for

greater convenience in study. It is as follows:

Message transcribed in pairs

2 3 • II 8 7 8 9 10 II U 13 14 111

A. HF CA PG OQ IL BS PK MN DU KE OH QN FB OR UN

B. QC LC HQ BQ BF HM AF XS 10 KO QY FN SX MC GY

0. XI FB EX AF DX LP MX HH RG KG QK QM LF EQ QI

D. GO IH MU EO RD CL TU FE QQ CG QN HF XI FB EX

E. FL BU QF CH QO QM AF TX SY CB EP FN BS PK NU

F. QI TX EU QM LF EQ QI GO IE UE HP IA NY TF LB

G. FE EP ID HP CG NQ IH BF HM HF XC KU PD GQ PN

H. CB CQ LQ PN FN PN IT OR TE NC CB CN TF HH AY

J. ZL QC IA AI QU CH TP CB IF GW KF CQ SL QM CB

K. OY CR QQ DP RX FN QM LF ID GC CG 10 GO IH HF

L. IR CG GG NO LN OZ TF GE ER RP IF HO TF HH AY .

M. ZL QC IA AI QU CH TP

It is noted that all the repetitions listed above break up properly into digraphs except in

one case, viz, FEQQ in lines 0, D, and F. This seems rather strange, and at first thought one

might suppose that a letter was dropped out or was added in the vicinity of the FEQQ in line D.

But it is immediately seen that the FE QQ in line D has no relation at all to the .F EQ Q. in

lines

°and F, and that the F EQ Q in line D is merely an accidental repetition.

FHHAY.

L Q MC B

o I H H F

F H HAY...

XCKUP DGQPN

o B C N T

K F C Q S

C G lOG

I F HOT

F H M H F

R TEN C

B I F G W

F I DG C

E ERR P

first half of each of thesefive plain-text pairs, polyalphabetic for the second half. This relationship holds true for four other groups of pairs beginning with Bp • In other words, there are five

alphabets employed, not 25. Thus, this case differs from the case discussed under Par. 42b

only in that the monoalphabeticity is not complete for one-half of all the pairs, but only among

the members of certain groups of pairs. In a completely digraphic system using a 676-cell

randomized square, such relationships are entirely absent and for this reason the system is

cryptographically more secure than the checkerboard system.

b. From the foregoing, it is clear that when solution has progressed sufficiently to disclose

a few values, the insertion of letters within the cells of the checkerboard design to give the plaintext and cipher relationships indicated by the solved values immediately leads to the disclosure

of additional values. Thus, the solution of only a few values soons leads to the breakdown of

the entire checkerboard 'design.

c. (1) The following example will serve to illustrate the procedure. Let the message be as

follows:

1 2 3 • 41 8 7 8 9 W II ~,~ U W W" n • 00

A. H F CAP G 0 Q I L B S P K M N D U K E 0 H Q N F B 0 RUN

B. Q C L C H Q B Q B F H MA F X S 10K 0 Q Y F N S X MCG Y

Q. X I F B E X A F D X L P MX H H R G K G Q K Q ML F E QQI.

D.'.G O'IH M U E 0 R D C L T U F E Q Q C G Q N H F X ! F B E X

E. F L B U Q F C H Q 0 Q M'AF T X S Y C B E P F NB S P K N U

F. Q I T X E U Q ML F E Q Q I G 0 lEU E H P I ANY T F L B

G. FEE P I D H P C G N Q I H B

H. C B C Q L Q P N F N P NIT 0

1. ..Z L Q C I A A I Q U C H T P C

J. 0 Y C R Q Q D P R X F N Q M L

K. I R C G G G N D L N 0 Z T F G

L.•Z L Q C I A A I Q U C HT P

(2) The cipher having been tested for standard alphabets (by the method of completing

the normal components) and found to give negative results, a uniliteral-frequency distribution

is made. It is as follows:

i
76 17

2

3

2

3

FIOURII 236.

FIOUllB 2311.

A B C D E

------ ',I -,...-

F G H I-J K

---- --...,.-.-

L M N 0 P

---- -- -

Q R S T U

------ -- - V W X Y Z

- - - - - --iA B C D E

- - - ----- F G H 1-J K

- - -- -----

L M N 0 P

- ---- -...---- Q R S T U

- - --- - f-- - --- - V W X Y Z

A B C D E

- - ------;--

F G H 1-J K

- -- --- - L M N 0 P L

-- ----IQ R S T U Q

------ ----I--

V W X Y Z

----- - A B C D E

- ---- ----iF G H 1-J K

- ---- ----iF L M N 0 P

- ---- -.----IM Q R S T U

- ---- ----IV W X Y Z

4

4

1

1

148274-38--6

(8) The recurrence of the group QMLF, three times, and at intervals suggesting thatit might

be a sentence separator, leads to the assumption that it is the word STOP. The.letters Q, M,

and F are therefore inserted in the appropriate cells in Sections 3 and 4 of the diagram. Th,ua

(Fig. 23b):

(7) In another common type of checkerboard system known as the Playfair cipher, described

in Par. 46, one of the telltale indications besides the absence of the letter J is the absence of double

letters, that is, two successive identical letters. The occurrence of the double letters"GG, HH,

and QQ in the message under investigation eliminates the possibility of its being a Playfair

cipher. The simplest thing to assume is that a 4-square checkerboard is involved. Onewith

normal alphabets in Sections 1 and 2 is therefore set down (Fig. 23a).

I

8 2 2

- - - - - - - - - - - - - - - - - - - - - - - - - 2 1 2 1

- - - - - - - - - - - - - - - 1 5 4 3 1 1 2 1

- - - - - - - - - - - - - - - - - - - - - - - - - 1 1 1

- - - - - - - - - - - - - - - - - - - - - - - - - 1 2 2 1 1 2

- - - - - - - - - - - - - - - - - - - - - - - - -----,

3 2 1 4

- - - - - - - - - - - - - - - - - -"- - - - 1 1 1 3 1 1 1

- - - - - - - - - - - - - - - - - - - - - - - - - 4 3 2 1 2 1

- - - - - - - - - - - - - - - - - - - - - - - - - 3 2 1 2 3 1 2 1 1

f-- - - - - - - - - - - - - - - - - - - - - - - - - 1 1 1 1 1 f-- - - - - - - - - - - - - - - - - - - - - - - - - 1 1 3 1 1 1

- - - - - - - - - - - - - - - - - - - - - - - - - 1 1 1 1

f-- - - - - - - - - - - - - - - - - - - - - - - - - 1 1 1 1 1

- r-- I- - - - - - - - - 1 1 2 1 1

--.:- - - - - - - - - - - - - - I-- - - - - - - - - - 1 I 2 .3

- - - - - - - - - - - - - - - - - - -r- - - - 1-

3 I 3 I 5 2 1 2 2" 1

I--- - - - - - - - - - - - - - - - - - - - - - - II 1 1 1 f-- - - - - - - - - - - - - - - - - - - - - - - - - 1 1 1

- - - - - - - - - - - --'-- 1 4 2 1 2

I--- - - - - - - - - - - - - - - - - - - - - - - - - 1 1

f--- - - - - - I-- - i-- - - - - - - - - - - - - -

- - - - - - - - - - - - - - - - - - - - - -

---J- - - .....;.- - - - - 1 2 1

- - - - - - - - -

- - - - - - - - - - - - - - - - - - - - - - - - - 2

I The distinction between "digraphic" and "biliteral" is based upon the following consideration. In a

biliteral (or diliteral) distribution every two successive letters of the text would be grouped together to form flo

pair. For example, a biliteral distribution of ABCDEF would tabulate thepairaAB, BC, CD, DE, and EF. In flo

digraphio distribution only suocessive pairs of the text are tabulated. For example, ABCDEF would yield only

AB, CD, and EF.

(5) A digraphic frequency distribution I is made and is shown in Fig. 22.

ABC D E F G H I K L M N 0 P Q R STU V W X y Z

(6) The appearance of the foregoing distribution for this message is quite characteristic of

that for a digraphic substitution cipher. There are many blank cells; although there are many

cases in which a digraph appears only once, there are quite a few in which a digraph appears

two or three times, four cases in which a digraph appears four times, and two cases in which a

digraph appears five times. The absence of the letter J is also noted; this is often the case in a

digraphic system based upon a checkerboard design.

--

;j

A

B

C

D

E

F

G

H

I

K

L

M

N

0

P

Q

R

S

T

U

V

W

X

Y

Z

-I

I

!

-J

--"~I

----"
78 79

(9) Now, if the placement of P in Section 3 is correct, the cipher equivalent of THp will be

peal and there should he a group of adequate frequency to correspond. Noting that PNa occurs

three times, it is assumed to beTHp and the letter N is inserted in the appropriate cellin Section 4.

Thus (Fig. 23d):

These placements seem logical. Moreover, in Section 3 the number of cells between L and

Qis just one less than enough to contain all the letters Mto P, inclusive, and suggests that either

N or 0 is in the keyword portion of the sequence, that is, near the top of Section 3. Without

making a commitment in the matter, suppose both N and 0, for the present, be inserted in the

cell between M and P. Thus (Fig. 23c):

M. ,ZL QC IA AI QU CH TP

NQ IH BF HM HF XC KU PO GQ PN

TH

PN IT OR TE NC CB CN TF HH AY.

TH

CR

E. FL BU QF CH QO QM AF TX SY OB EP FN BS PK NU

ST

LF EQ QI GO IE UE HP IA NY TF LB

OP

CG

F. QI TX EU QM

ST

G. FE EP 10 HP

H. CB CQ LQ PN FN

TH

J. ,ZL QC IA AI QU TP CB IF GW KF CQ SL QM CB

ST

K. OY CR QQ DP RX FN 31QM=-...::: L::.. F 10 GC CG 10 GO IH HF

ST OP

h m 00 00 IT HH n ,

(10) ltis about time to try out these assumed values in the message. The proper insertions

are made, with the following results:

2 • C Ii 0 7 8 II 10 11 12 13 1C 13

A. HF CA PG OQ IL BS PK MN" DU KE OH QN FB O~ UN

B. QC LC HQ BQ BF HM AF XS 10 KO QY FN SX MC GY

c. XI FB EX AF DX LP MX HH RG KG QK QM &F EQ QI

ST 'OP

D. ,GO IH MU EO RD CL TtJ FE" QQ CG QN HF XI FB EX

3

2

A B C D E

I-- - - IF G H 1-.1 K

I-- - - 1-

L M N 0 P L - - - --- - 1-

Q R S T U M H P Q

- - - - I--- - - IV W X Y Z r--- - - - - - 1-

A B C D E - - - IF G H 1-.1 K - - --- - - IF L M N 0 P

- - - - - 1-

M Q R S T U

- - -, - - :-

V W X Y Z

1

4

I

I

-I

i

1

'I

1

4

A B C D E - - - - F G H I-J K - - - - - - - - - -

L M N 0 P L - - Q R S T U M M P Q

I--- - - 1-- - - - IV W X Y Z

- - - 1-

A B C D E

I--- - - - I-- - - IN F G H I-J K

I-- - - - - - - - IF L M N 0 P - 1-

M Q R S T U

I--- - - - 1-- - - IV W X Y Z

:3

2

(11) So far no impossible combinations are in evidence. Beginning with group H4 in the

message is seen the following sequence:

PNFNPN

TH •• TH

Assume it to be THAT THE. Then ATp=FNe, and the letter Nis to be inserted in row 4 column 1.

But this is inconsistent with previous assumptions, since N in Section 4 has already been tentatively placed in row 2 column 4 of Section 4. Other assumptions for FNa are made: that it is,

ISp (THIS TH ...)i that it is ENp (THEN TH .••); but the same inconsistency is apparent. In fact

the student will see that FNa must represent a digraph ending in F, G,H, I-,.J, or K, since N, is

tentatively located on the same line as these letters in Section 2. Now FNa occurs 4 times in

the message. The digraph it represents must be one of the following:

DF. 00. OH. DI. OJ. OK

IF. IG. IH. II. IJ,. IK

JF. JG. JH. JI. JJ. JK

OF. OG. OH. 01. OJ. OK

TK.

YF. YG. YH. YI. YJ. YK

--~
81

::1

Of these the only one likely to be repeated 4 times is OF, yielding THO F '1' H which may be

PNFNPN

a part of

4, assume Gand Hdirectly follow it, and that Bcomes before it. How much before? Suppose a

trial be made. Thus (Fig. 23j):

I

J

,I

~I

.~-------------------~------------jl---------------------------

(12) Going back to the assumption that T H. • T H

PNFNPN

3

3

2

2

FlOUllll: 23f.

FlOUllll: zaf.

A B C D E C

I--- - - 1-- - I--- IF G H I~ K

- - - 1-- - - - 1-

L M N 0 P F G H K L

I--- .. - 1-- - - IQ R S T U M N

0 P Q

r--- - - 1-- - - - IV W. X Y Z

- - - '-- - - - 1-

A B C 0 E -..,.- - - - - - - - IN F G H I-J K

,--- - - ,-- B F G L M N 0 P

I-- - - - 1-

H M Q Q R S T U

- - - - !-

- - - - r--

V W X Y Z

A B C 0 E C

I-- - - - - - - - - F G H I-J K C

I-- - - - - - - - L M N 0 F' F G H K L

I-- -- Q R S T U M 8 P Q

I--- - - - I---- - - IV W X Y Z .....-- - - - I-- - - 1-

A B C D E

I---- - - - I-- - - IN F G H I-J K

I-- - - - - - - 1-

B B B F G L M N 0 ?

I-- - - - I--- - - 1-

H M Q Q R S T U

- - - - - I- - IV W X Y Z

1

1

4

4

By re(erring now to the frequency distribution, Fig. 22, after a very few minutes of experimentation it becomes apparent that thefoUowing is correct: 2

3

.• SOUTHOFTHE .,'

C Q L Q P N F NP NIT

• SOU THO F T H"E •

or C Q L Q P N F N P NIT

A B C 0 E

I--- f-- - - -

F G H I~ K

I--- I-- 1-

L M N 0 P F G H K L.

I--- - - Q R S T U M N

0 P Q

I--

V W X Y Z

- - - 1-

A B C D E

r---- - - I--

N F G H I~ K

I--- - IF L M N 0 P

I--- - - --'f--- - - I--

M Q Q R S T U

----- - - - - - - - -

V W X Y Z

4

1

• NORTHOFTHE.

CQLQPNFNPNIT

• NOR TH 0 F THE •

C Q L Q P N F N P NIT or

In either case, the position of the F in Section 3 is excellent: F • • • L in row 3. There are 3

cells intervening between F and L, into which G, H,I-J, and Kmay be inserted. It is not nearly

so likely that G, H, and K are in the keyword as that I should be in it. Let it be assumed that

this is the case, and let the letters be placed in the appropriate cells in Section 3. Thus (Fig. 23e):

it is seen at once from Fig. 23e that the latter is apparently correct and not the former, because

LQo equals OUp and not ORp. If 6Sp=CQo, this means that the letter Cof the digraph CQo must be

placed in row 1 column 3 or row 2 column 3 of Section 3. Now the digraph CBo occurs 5 times,

CGo, 4 times, CHo, 3 times, CQo, 2 times. Let an attempt be made to deduce the exact position of

C in Section 3 and the positions of B, G, and Hin Section 4. Since F is already placed in Section

Let the resultant derived values be checked against the frequency distribution. Ifthe position of

H in Section 3 is correct, then the digraph ONp , normally of high frequency should be represented

several times by HFo• Reference to Fig. 22 shows a frequency of 4 times.' And fIMc, with 2 occurrences, represents NSp • There is no need to go through all the possible corroborations.

is part of the expression
82

.: (13) The ideJitificatioD&giveJi by these placements Me inserted in the ten, and solution

is very rapidly completed. The final checkerboard and deciphered text are given below.

A. H F CAP G O'Q I L B S P Kif ND UK E 0 H Q N F B 0 RUN

ONE HUN D RED FIR S TF I E L DAR TIL L E R Y F , .

B. QC tCH· QB Q B F H'M AF X S {OK(jQ'~F N'S "X MC·'(ty

ROM P 0 SIT ION st. V ~C f N I 'T tOFB ARLO W

C. X I F B E X A F D X '. L P M X,R H. ,R G K G Q K Q M L F 'E Q Q I

W ILL B E1 N G ENE R A L SUP P 0 R T S TOP D URI

D. G 0 I H M UE 0 R D C L T U F E Q Q C G Q N H F X I F B E X

N GAT T AC K S P E C I A L A T TEN T ION W ILL B E

E. F L B U Q FC H Q 0 Q M AFT, XS Y CB EP F NBS P K N U

P A I D T O~. S SIS TIN GA D V A N C E OFF IRS T B

F. Q I T X E U Q M L F E Q Q I G 0 I E U E H P I ANY T F L B

RIG A D ES TOP D U R·I N GAD V A N C E I T W ILL P

G. FEE P I D H P C G N Q I H B F H M H F X C K U P D G Q P N

LACEC ONCEN TRATI ONSON WOODS NORTH

H. C B C Q L QPN F N . P N I'T OR'T E N C C B C N T F H HAY

ANDSO UTHOF THAYE RFARM ANDHI LLSIX

J. Z L Q C I A A I QU C H T PCB I F G W K F C Q S L Q M C B

Z E ROE I G H T D A S HA AND 0 N WOO D SEA S TAN

K.OYCRQ QDPRX FNQML'FIDGC CGIOG OIHHF

DWEST THERE OFSTO PCOMM ENC1N GATON

L. I R C G G G N D L N 0 Z T F GEE R R P I F HOT F H HAY

ETENP MSMOK EW1LL BEUSE DONH1 LLS1X

M. Z L Q C I A A I Q U C H T P

ZEROE 1GHTD ASHA

M A N U F 0 S Q L P - - - - - - C T R I G W ,Z Y V X - - - - - - B D E H K D k H B E - - - - - 1-

L 0 P Q S A F U M N - - - 1-- - V W X Y Z T G I C R

d. (1) It is interesting to note how much simpler the matter becomes when the positions

of the plain-text and cipher-text sections are reversed, or, what amounts to the same thing,

when in encipherment the plain-text pairs are sought in the sections containing the mixed a.1pbAbets, and their cipher equivalents are taken from the sections containing the normal alphabets.

For example, referring to Fig. 23h, suppose that sections 3-4 be used as the source of the plain.-

text pairs, and sections 1-2 as the source of the cipher-text pairs. Then ONp=DG., EHp=AU~lJ etc.

(2) To solve a message enciphered in that manner, it is necessary merely to make a square

in which all foursections are normal alphabets, and then perform two steps. First, the cipher text

pairs are converted into their normal alphabet equivalents merely by "deciphering'" the message

with that square; the result of this operation yields two monoalphabets, one composed:of the odd

letters,the other of the even letters. The second step is to solve these two monO'-alphabeta.

(3) Where the same mixed alphabet is inserted in sections 3 and4,the problem is still

easier, since the letters resulting from the conversion into normal-alphabet equiv&.lentsallbe10ng

to the same, single-mixed alphabet.

46. Analysis of ciphers based upon other types of oheokerboarddeaignl.-The solution

of cryptograms enciphered by other types of checkerboard designs is accomplished along lines

very similar to those set forth in the foregoing example of the solution of a message prepared by

means of a 4-square checkerboard design. There are, unfortunately,no means or tests whichcah

be applied to determine in the early stages of the analysis exactly what type of design is involved

in thefirsl case under study. The author freely admits that the solution outlined in subparagraph

e is quite artificial in that nothing is demonstrated in step (7) that obviously leads to or warrants

the assumption that a 4-square checkerboard is involved. This pOint wu passed over with the

quite bald statement that this was "the simplest thing to assume"-and then the solution

proceeds exactly as though this mere hypothuiB has been definitely established. ' F()r~e_mple, the

very first results obtained were based upon assuming that a certain +letter repetition represented

the word STOP and immediatelyinserting certain letters in approprWle cells in a 4-"'q1U1.re. checkerboard. Several more assumptions were built on top of that and very rapid strides were made.

What if it had not been a 4-square checkerboard at all? What if it had been a 2-square checkerboard of the type shown in Fig. 24?

The only defense that can be made of what may seem to the student to be purely arbitrary

procedure based upon the author's advance information or knowledge is the following: In the

first place, in order to avoid making the explanation a too-long-drawn-out affair, it is necessary

(and pedagogical experience warrants) that certain alternative hypotheses be passed over in

silence. In the second place, it may now be added, afterthe principles and procedure have been

elucidated (which at this stage is the primary object of this text) that if good results do not follow

from a first hypothesis, the only thing the cryptanalyst can do is to reject that hypothesis, and

formulate a second hypothesis. In actual practice he may have to reject a second, third, fourth,

. . . nth hypothesis. In the end he may strike the right one-or he may not. There is no

guaranty of success in the matter. In the third place, one of the objects of this text is to show

how certain systems, if employed for military purposes, can readily be broken down. Assuming

3

A B C D E S 0 C I E - -- - - - F G H 1-J K T Y A B D - - - - - - L M N 0 P F G H K L - - - - I~ - - - - 1- Q R S. T U M N P Q R - - -.-.- - - I~ V W X Y Z U V W X Z

(---po

E -X -

P -

U L A -

B -

C -

D 17 - --- - - - - S I 0 N A F G H 1-J K - - - --- - - - - - B C D F G L M N 0 P - - - - - - 'H K M Q R Q R S T U - - - - - ··T V W y "Z· V ·W X Y Z

; ,

1

, 4

1"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"11111"1111 IUIIII 1"1111 1"1111 1"1111
85

CASE 1. Letters at opposite corners of a rectangle. The following illustrative relationships

are found:

Reciprocity is complete.

CASE 2. Two letters in the same line or column. The following illustrative relationships

are found:

THp=YFe

HTp=FYo

YFp=THe

FYp=HTe

"From this it is seen that of the 24 equations that can be formed when each letter of the

square is employed either as the initial or final letter of the group, five willindicate a repetition of

a corresponding letter of plain text.

"Hence, RULE II. Afterithas beendetermined,in the equation 1.2=3.4, that,say,ENp=FAo1

there is a probability of one in five that any other group beginning with Fe indicates Eap , and that

any group ending in Aeindicates aNp •

ENrFA.

EMrFLo

ETrFPo

EWrFVo

EFrFGo

also

ANp==NK.

GNrFK.

ONrMK.

CNp=TK.

XNrWK.

ANp==NKo

NAp==KNe

But NKp does not= ANe, nor does KNp=NA•.

Reciprocity is only partial.

(3) The foregoing gives rise to the following:

RULEI. (a) Regardless of the position of the letters in the square, if

1.2=3.4, then

2.1=4.3

(6) If 1 and 2 form opposite corners of a rectangle, the following equations obtain:

1.2=3.4

2.1=4.3

3.4=1.2

4.3=2.1

(4) A letter considered as occupying a position in a row can be combined with but four other

letters in the same row; the same letter considered as occupying a position in a column can be

combined with but four otherletters in the same column. Thus, thisletter can be combined with

only 8 other letters all told, under Case 2, above. But the same letter considered as occupying

a corner of a rectangle can be combined with 16 other letters, under Case 1, above. Commander

Smith derives from these facts the conclusion that "it would appear that Case 1 is twice as probable as Case 2." He continues thus (notation my own):

"Now in the square, note that:

B A N K R

I---- --- - - 0 E F G H

I---- - - I-J L M 0 Q r--- - -- U P T C Y - - - --IS V W X Z

FIOl1U 2Ila.

• This elpher was really invented by Sir Charles Wheatstone but receives its name from Lord Playfair,

who apparently was its sponsor before the British Foreign Office. See Wemyss Reid, Memoir80f Lyon Playjair,

London. 1899. A detailed description of this cipher will be found in Sec. VIII, Advanced Military Cryptography.

7 Mauborgne, Lieut. J. 0., U. S. A. An advanced problem in cryptography and its 80lution, Leavenworth, 1914.

Bitt, Captain Parker, U. S. A. Manual for the 80lution of military cipher8, Leavenworth, 1918.

Smith, Lieut. Commander W. W., U. S. N. In Cryptography by Andre Lsngie, translated by J. C. B.

Macbeth, New York, 1922.

8 The Playfair square accompanying Commander Smith's solution is based upon the keyword BANKRUPTCY.

"to be distributed between the first and fourth lines of the square." This is a simple departure from the original

Playfair scheme in which the letters of tbll keyword are written from left to right and in consecutive lines from

the top downward.

that a checkerboard system is in UBe, and that daily changes in keywords are made, it is possible

that the traffic of the first day might give considerable difficulty in solution, if the type of

checkerboard were not known to the cryptanalyst. But the second or third day's traffic would

be easy to solve, because by that time the cryptanalytic personnel would have analyzed the

system and thus learned what type of checkerboard the enemy is using.

46. Analysis of the Playfair cipher system.-a. An excellent example of a practical, partially

digraphie system is the Playfair cipher," It was used for a number of years as a field cipher by

the British .Army, before and during the World War, and for a short time, also during that

war, by certain units of the American Expeditionary Forces.

b. Published solutions 7 for this cipher are quite similar basically and vary only in minor

details. The earliest, that by Lieut. Mauborgne, used straightforward principles of frequency to

establish the values of three or four of the most frequent digraphs. Then, on the assumption

that in most cases in which a keyword appears on the first and second rows the last five letters

of the normal alphabet, VWXYZ, will rarely be disturbed in sequence and will occupy the last row

oithe square, he "juggles" the letters given by the values tentatively established from frequency

considerations, placing them in various positionsin the square, together with VWXYZ, to correspond

to the plain-text cipher relationships tentatively esiablished. A later solution by Lieut. Frank

Moorman, as described in Hitt's Manual, assumes that in a Playfair cipher prepared by means

of a square in which the keyword occupies the first and second rows, if a digraphic frequency

distribution is made, it will be found that the letters having the greatest combining power are

verypl'Obablyletters of the key. A still later solution, by Lieut. Commander Smith, is perhaps

thetn08t lucid and systematized of the three. He sets forth in definite language certain considerations which the other two writere certainly entertained but failed to indicate. .

c~ The following details have been summarized from Commander Smith's solution:

(1) The Playfair cipher may be recognized by virtue of the fact that it always contains an

even number of letters, and that when divided into groups of two letters each, no group contains

a-repetition of the same letter,-as NNor EE. Repetitions 'of digraphs, trigraphs, and polygraphs

will be evident in fairly long messegee.

(2) Using the square 8 shown in Fig. 25a, there are two general cases to be considered, as

regards the results of encipherment: . l i

~-

1111111 I
N F W P X

I-'-------IR H Z T L

!---- --- I...............

U I Y Q M

1--:"'- (

E V B D .A

I-'-------1"':"-

C 0 K G S

FIGUBII.2Sd.

A E V B D

I-----I---I---

S C 0 K G

I---------- X N F W P

I----------- L R H Z T

I----- M U I Y Q

0 K G S C

I----------- H Z T· L 'R

-------- V B D A E

F W P X .N

I---

I Y Q M U

Z T L R H

- -------- Y 'Q M u I

----r-'-

B D A E V "

K ..G. S C 0

I-'-piX- - W N F

(2) In the foregoing square practically all indications that the square has been developed

from a keyword have disappeared. The principal disadvantage of such an arrangement is that

it requires more time to locate the letters desired, both in cryptographing and dee'l'yptogtaphing,

than it usually does when a semblance of normal alphabetic order is preserved in the square.

(3) Note the following three squares:

·The Pilloyfair Square is as folloWs:

86

IIAftersuch combinatiOns as ERp, ORp, and ENphave been assumed or determined, the above

rule may be of use in discovering additional digraphs and partial words." 9

RULE III. In the equation 1.2=3.4, 1 and 3 can never be identical, nor can 2 and 4 ever be

identical. Thus ANpcould not possibly be represented by AYe' nor could ERpbe represented by KRe.

This rule is useful in elimination of certain possibilities when a specific message is being studied.

RULE IV. In the equation 1.2p=3.4e, if 2 and 3 are identical, the letters are all in the same

row or column, and in the relative order 124. In the square shown, ANp=NKe and the- absolute

order is ANK.. The relative order 124 includes five absolute orders which are cyclic permutations

of one another. Thus: ANK .. , NK .. A, K.. AN, •. ANK, and .ANK.•

RULE V. In the equation 1.2p=3.4e, if 1 and 4.are identical, the letters are all in the same

row or column, and in the relative order 243. In the square shown, KNp=RKe and the absolute

order is NKR. The relative order 243 includes five absolute orders which are cyclic permutations

of one another. Thus NKR .. , KR .. N, R.. NK, .. NKR, and •NKR ..

RULE VI. IlAnalyze the message for group recurrences. Select the groups of greatest

recurrence and assume them to be high-frequency digraphs. Substitute the assumed digraphs

throughout the message, testing the assumptions in their relation to other groups of the cipher.

The reconstruction of the square proceeds simultaneously with the solution of the message and

aids in hastening the translation of the cipher."

d. (1) When solutions for the Playfair cipher system were first developed, based upon the

fact that ·the letters wereinseI'W in the cells in keyword-mixed order, cryptographers thought

it desirable to place stumbling blocks in the path of such solution by departing from strict,

keyword-mixed order. Playfair squares of the lattei-type are designed as "modified Playfair

squares." One of the simplest methods is illustrated in Fig. 25a, wherein it will be noted that

the last five letters of the keyword proper are 'inserted in the fourth row of the square instead

of the second, where they would naturally fall. Another method is to insert the letters within

the cells from left to right and top downward- Qui use a sequence that is a keyword-mixed sequence

developed by a columnar transposition based upon the keyword proper. Thus, using the keyword BANKRUPTCY:

21547968310

BANKRUPTCY

DEFGHILMOQ

SVWXZ

Sequence: A E V B D S C 0 K G X N F W P L R H Z T M U I Y Q ---- • There is an error in this reasoning. Take, for example, the 24 equations having F as an initial letter:

Case Case CB88 CB88

1. FB.=DN" 2. FE=ED 2. F'l'=NII 1. FX=GW

2. FD =EH 1. FL=EM 2. FW=NT 1. F'R=HN

1. FI =DM 1. FP=ET 1. FK=GN 2. FH=EG

1. FU =DT 1. FV=EW 2. FG=EF 1. FQ=HM

1. FS =DW 2. FN=NW 1. FO=GM 1. FY=HT

1. FA =EN 2. FM=NF 1. FC=GT 1. FZ=HW

Here, the initial letter F. represents the following initial letters of plain-text digraphs:

DENGH

It is seen that F. represents D", N". G", H" 4 times each, and E", 8 times. Consequently, supposing that it has

been determined that FA.=EN", the probability that F. will representE; is not 1 in 5 but 8 in 24, or 1 in 3; but

supposing that it has been determined that FW.=NT ", the probability that F. will represent N"is 4 in 24 or 1 in 6.

The difference in these probabilities is occasioned by the fact that the first instance, FA.= EN" corresponds to a

Case 1 encipherment, the second instance. FW.=NT", to a Case 2 encipherment. But there is no way of knowing

initially, and without other data, whether one is dealing with a Case 1 or Case 2 encipherment. Only as an

approximation, therefore, may one say that the probability of F. representing a given a" is 1 in 5.
=1

~I

88 89

10 See Par. 44c.

FrOl1U 26.

(2) Without going through the l»reliminary tests in detail, with which it will be 8lIiIUm.ed

that the student is now familiar," the conclusion is reached that the cryptogram isdigraphic in

nature, and a digraphic frequency distribution is made (Fig. 26).

ABC 0 E F G H I K L II N 0 P Q R STU V W Y Z

i -I,

At first glance they all appear to be different, but closer examination shows them to be cyclic

permutations of one another and of the square in Fig. 256. They yield identical equivalents in

all cases. However, if an attempt be made to reconstruct the oriyinal keyword, it would be

much easier to do so from Fig. 256 than from any of the others, because in Fig. 256 the keywordmixed sequence has not been disturbed as much as in Figs. 25c, d,». In working with Playfair

ciphers, the student should be on the lookout for such instances of cyclic permutation of the

original Playfair square, for during the course of solution he will not know whether he is building

up the original or an equivalent cyclic permutation of the original square; only after he has

completely reconstructed the square will he be able to determine this point.

(4) It can readily be shown that the columns of a Playfairsquare may be cyclically permuted

(see subpar. d) to produce a first set of 25 squares all of which, though at first glance apparently

different, will yield identical equivalents; likewise, the rows of such a square may be cyclically

Permuted to produce a second set of 25 squares all of which will also yield identical equivalents.

T4us :there may bea total of 50 cyclic permutations composed of two sets of 25 each. The

ciph,er equivalents. yielded by Case 2 encipherments (letters in the same row or in the same

column) willbeIdentical for any two of these 50 different Playfair squares; but the cipher equivalents yielded by Case 1 encipherments (letters at diagonally opposite corners of a rectangle)

willbeidentical only for two squares belonging to the same set of 25 cyclic permutations.

,.~n !'he ~teps in the solution of a typical example of this cipher maybe useful. Let

the mesiage be tt& follows: .

.~ 1',' f, I ,. 8 10 11 11 11 1411 11 17 11 18 JO II 21 2lI • lIlI ill '11 2lI 2lI 10

A:. V ,T Q E U H I 0 FTC H X SeA K T V T R A Z E V TAG A E

B.O X· T Y II He R L Z Z T Q T 0 U II eye X C T GilT Y C Z U

C. S N 0 P 0 G X V X seA K T V T P K PUT Z P T W Z F N B G

D. P T R K X I X B P R ZOE PUT 0 L Z E K T T C S N H C Q II

E. V T RKM we F Z U B H T V Y A B G I P R Z K P C Q F N L V

F. 0 X 0 T U Z F A C X x C P Z X Hey NOT Y 0 L G X X I I H

G. T II S II X CPT 0 T C X 0 T T C Y ATE X H F A C X x C P Z.

H ...!-!! r c r X WL Z T S G P Z T V Y weE T WGee II B H II Q

J. Y X Z P W G R T I V U x PUll Q R K M W eXT II R S WG H B

K. X CPT 0 T C X 0 T II I P YON F G KIT COL X U E T P X

L. X F S R S U Z TO B H 0 ZIG X R K I X Z P P V Z IOU H Q

M. 0 T K T K C C H X X

A

B

C

o

E

F

G

H

I

K

L

II

N

o

P

Q

R

S

T

U

V

W

X

Y

Z

I I - - - - - - - - - - - - - - - - - - - - 2 2

2 1 J 2 I I I 5 I .. --I- - - I I I 2

- I I

2 I 2 I

- - - - - - - - I 2 - - - - - - - I I I I

f--- !-- - - - - - - - - - I I I I I

I- II I I 4

f--

I I

I-- - - - - I- - - - - II I I 2 I 2

1- - - I

3 I 6 2

I I 4 2 I I I 3

f-- - - - - - I I I

- - I 4 I I I ,---- - - - - I I 2 I J

c--- - - - - - ,- 3 I J 2 2 I I 2 I - - - - - - - - - - - - - - - - - - -

I I I 1 - - - - - - - - - - - - - - - -

5

c-- - - - - - - - - - - - - 2 I I - - - - - - - - - - - - - - - - - - - - I 5 I 3 2 2 I I

- - - - - - - - - - - - - - 2 3 I I

- - - - - I-- - - - - - - - - 1-- 1--'

2 2 I 2 3 2
92

98

occupy a row; and they may be combined by means of their common letter, T. According to

subpar. d (4), the two sequences may be inserted within a Playfair square in 25 different ways

by cyclically permuting and shifting the letters of one of these two sequences; and the same

two sequences may be again inserted in another set of 25 ways by cyclically permuting and

shifting the letters of the other of these two sequences. In Fig. 27 the diagrams labeled (1)

to (10), inclusive, show 10 of the possible 25 obtainable by making the HTOXN sequence one

of the rows of the square; diagrams (11) and (12) show 2 of the possible 25 obtainable by making

the HTOXN sequence one of the columns of the square. The entire complement of 25 arrangements for each set may easily be drawn up by the student; space forbids their being completely

set forth and it is really unnecessary to do so.

FIGURB '0.

(7) It is perhaps high time that the whole list of tentative equivalent values be studied in

relation to their consistency with the positions of letters in the Playfair square; moreover, by so

doing, additional values may be obtained in the process. The complete list of values is as follows:

A"umed tlaluu Deritled by Rule I

ATrCX. TArXC.

LlrPZ. ILp=ZP.

ONrXH. NOrHX.

THp=OT. HTp=TO.

IRp==UZ. Rlp==ZU.

DBp==FA. BDp=AF.

ECp=TE. CEp==ET.

TErPT. ETp=TP.

Elp==TC. IEp==CT.

RSp=YA. SRp=AY.

-Sp=SM. S-p=MS.

(8) By Rule V, the equation THp=OT. means that H, T, and 0 are all in the same row or column and in the relative order 2-4-3; similarly, C,E, and Tare in the same row or column and in the

relative order 243. Further E, P, and T are in the same row and column, and their relative

order is also 243. That is, these sequences must occur in the square:

(1) (2) (3)

H TO. • , or C E T • • , or E T P , or

TO. • H , or E T • • C , or T P • • E , or

o . . H T , or T • . C E , or P • • E T , or

• • H TO, or • • C E T , or . . E T P , or

• HTO. . CET. • ETP.

(9) Noting the common letters E and T in the second and third sets of relative orders, these

may be combined into one sequence of four letters. Only one position remains to be filled and

noting, in the list of equivalents that Elp=TCc, it is obvious that the letter I belongs to the CET

sequence. The complete sequence is therefore as follows:

C E T PI, or

E T PIC, or

T PIC E , or

PICET or

ICE T P

(10) Taking up the HTO sequence, it is noted, in the list of equivalents that ONp=XH., an

equation containing two of the three letters of the HTO sequence. From this it follows that

N and Xmust belong to the same row or column as mo. The arrangement must be one of the

following:

H T 0 X N

T 0 X N H

o X N H T

X N H T 0

N H T 0 X

(11) Since the sequence containing HTOXN has a common letter (T) with the sequence

CETPI, it follows that if the HTOXN sequence occupies a row, then the CETPI sequence must

occupy a column; or, if the HTO sequence occupies a column, then the CETPI sequence must

(1)

C - - - IE

- - - - - T 0 X N H - - - - P - - - II

(5)

C i--- - - IE - - - - - 0 X N H T - - - - -

P - - - - -

I

(9)

P ---I ---C

E ----

X N H T 0

148214-88--1

(2)

C - - - - IE - - - - - H T 0 X N - - - - - P

I---- - - - I

(6)

P - - - I - - - C

E - - - T 0 X N H

(10)

P - - - - -

I - - - - '-

C

I--- - - IE i--- - - 1-

0 X N H T

(3)

C - - - - - E

I---- - - -

N H T 0 X

I--- - - - P

I---- - - II

(7)

P i--- - - II - - - - - C - - E - - H T 0 X N

(11)

N

I--- H >---- - - - 1-

P I C E T

I--- - - 1-

0

I---- - - IX

(4)

C f--- - - IE

i--- - - IX N H T 0 - - - - - P - - - - II

(8)

P - - - - II - - - - - C - - - - - E - - - - - N H T 0 X

(12)

N

- - - - 1-

H

- - - - IT P I C E

I-- - - 1-

0 IX

______________l
,

.

•

~'

94

(12) Before trying to discover means whereby the actual or absolute arrangement may

be detected from among-the full set of 50 possible arrangements, the question may be raised: is

.it necessary? So far as concerns Case 2 encipherments, since anyone of the 50 arrangements

will yield the same equivalents as any of the remaining 49, perhaps a relative arrangement

will do.

(13) Let arrangement 8 be arbitrarily selected for trial.

P

I---------- I ---------- C

I--- -------- E --- N H T 0 X

FIOUBI:28G.

(14) mat additional letters can be inserted, using as a guide the list of equivalents in subparagraph (7)? There is ATp=CX:., for example. It contains only one letter, A, not in the

arrangement selected for trial, and this letter may immediately be placed, as shown."

P

I--

I

I---------- C A '-----------

E

I--------!-

N H T 0 X

FIOUBJ:2llIl.

Scanning the list for additional cases of this type, none are found. But seeing that several highfrequency letters have already been inserted in the square, perhaps reference to the cryptogram

itself in connection with values derived from these inserted letters may yield further clues. For

example, the vowels A, E, I, and 0 are all in position, as are the very frequent consonants Nand T.

The following combinations may be studied:

ANp=SX. ATp=CX. NArXS. TAp=XC.

ENp=ST. ETp=TPc NEp=TS. TEp=PT.

I Np=ST. ITp=CP. NIp=TS. TIp=PC.

ONp=XH. OTp=XO. NOp=HX. TOp=OXc

ATp(=CX.), TAp(=XC.), ONp(=XH.), TEp(=PT.) and ETp(=TP.) have already been inserted in the

text. Of the others, only OX.(=TOp) occurs two times, and this value can be at once inserted in

the text. But can the equivalents of AN, EN, or IN be found from frequency considerations?

10 The fact that the placement of A yields ATv=CX. means that the outline selected for experiment really

belongs to the correct set of 25 possible cyclic permutations, and that the letters of the NHTOX sequence belong

in a row, the letters of the PICET sequence belong in a column of the original Playfair square. If the reverse were the case, one could not obtain ATv=CX. but would obtain ATv=XC.. •

---------- -------------------------------------------------"" _,-W!"

95

Take ENp,for example; it is represented by STc' What combination of ST is most likely to represent ENpamong the following candidates:

KT. (4 times); by Rule I, NEp wouldeeTK, (no occurrences)

VT. (5 times); by Rule I, NEp would=TVo (2 times)

ZTc (3 times); by Rule I, NEp would=TZc (1 time)

VTc certainly looks good: it begins the message, suggesting the word ENEMY; in line H, in the

sequence PZTV would become LINE. Let this be assumed to be correct, and let the word ENEMY

also be assumed to be correct. Then EMp=QEo and the square then becomes as shown herewith:

P

I---------- I ---------- C A

I---------- V M E Q '----------- N H T 0 X

FIoUBJ: 28e.

(15) In line E is seen the following sequence:

Line E: VT RK MW CF ZU BH TV YA BG IP RZ KP CQ FN LV

EN RI NE RS PT E

The sequence ...RI .. NERS .. PT... suggests PRISONERS CAPTURED, as follows:

MW CF ZU BH TV YA BG IP RZ KP

P RI SO NE RS CA PT UR ED

This gives the following new values: SPp=CFc; SOp=BH.; CAp=BG.; URp=RZ.; EDp=KPeThe letters Band Gcan be placed in position at once, since the positions of Cand Aare already

known. The insertion of the letter Bimmediately permits the placement of the letter S, from the

equation SOp=BH.. Of the remaining equations only EDp=KPc can be used, Since E and Pare

fixed and are in the same column, Dand Kmust be in the same column, and moreover the Kmust

be in the same row as E. There is only one possible position for K,viz, immediately after Q. This

automatically fixes the position of D. The square is now as shown herewith:

P D ---------- I ---------- G S C B A ---------- V M E Q K --------IN H T 0 X

FIGUBE28d.
I

I

96

. (16) A review of all equations, including the very first ones established, gives the following

which may now be used: DBp=FAe ; RSp=YAe• The first permits the immediate placement of F'

the second, by elimination of possible positions, permits the placement of both R and Y. Th~ square is now as shown herewith:

P F D - - - - - Y I R

f-- G S C B A I-- - - r--

V M E Q K

I--- - - IN H T 0 X

PIon. 28e.

Once more a review is made of all remaining thus far unused equations. LIp=PZe now permits

the pl~cement of Land Z. IRp=UZe now permits the placement of U, which is confirmed by the

equation URp=RZe from the word CAPTURED.

L P F D

Z Y I U R

fG S C B A

IV M E Q K

I--- - - IN H T 0 X

PlG~ 7P/.

There is then only one cell vacant, and it must be occupied by the only letter left unplaced

viz; W. Thus the whole square has been reconstructed, and the message can now be decrypto:

graphed.

. (17) Is the squ~re just reCC?nstructed identical with the original, or is it a cyclic permutation of a keyword-IDlXed Playfair square of the type illustrated in Fig. 2561 Even though the

message can be read with ease, this point is still of interest. Let the sequence be written in five

ways, each composed of five partial sequences made by cyclicly permuting each of the horizontal

rows of the reconstructed square. Thus:

Row 1 Row 2 Row 3 Row 4 Row 5

(a) L W P F D Z Y I U R G S C B A V M E Q K N H T 0 X

(b) W P F D L Y I U R Z S C BAG ME Q K V H T 0 X N

(c) P F D L W I U R Z Y C BAG S E Q K V M T 0 X N H

(d) F D L W P U R Z Y I BAG S C Q K V M E o X N H T

(e) D L W P F R Z Y I U A G S C B K V M E Q XNHTO

97

By experimenting with these five sequences, in an endeavor to reconstruct a transpoSition

rectangle conformable toa keyword sequence, the last sequence yields the following:

PYACMN

DFIGBEH

LRUSKQT

W Z V X 0

By shifting the 0 from the last position to the first, and rearranging the columns, the following

is obtained:

2 5 :3 6 1 4 7

COMPANY

BDEFGHI

KLQRSTU

V W X Z

The original square must have been this:

A G S C B

I--- - - IK V M E Q

I,--

X N H T 0

I---

D L W P F - - - 1-

R Z Y I U.

j. Continued practice in the solution of Playfair ciphers will make the student quite expert

in the matter. and will enable him to solve shorter and shorter messages." Also, with practice

it will become a matter of indifference to him as to whether the letters are inserted in the square

with any sort of regularity, such as simple keyword-mixed order, columnar transposed keywordmixed order, or in a purely random order.

g. It may perhaps seem to the student that the foregoing steps are somewhat too artificial,

a bit too "cut and dried" in their accuracyto portray the process of analysis, as it is applied in

practice. For example, the critical student may well object to some of the assumptions and the

reasoning in step (5) above, in which the words THREE and ONE (Ist hypothesis) were rejected

in favor of the words THIRD and SECOND (2nd hypothesis). This rested largely upon the

rejection of REp and ERp as the equivalents of UZe and ZUe, and the adoption of IRp and RIp as

their equivalents. Indeed, if the student will examine the final message with a critical eye he

will find that while the bit of reasoning in step (5) is perfectly logical, the assumption upon which

it is based is in fact wrong, for it happens that in this case ERpoccurs only once and REp does not

occur at all. Consequently, although most of the reasoning which led to the rejection of the 1st

hypothesis and the adoption of-the 2nd was logical, it was in fact based upon erroneous assump11 The author once had a student who "specialized" in Playfair ciphers and became 80 adept that he could

solve messages containing as few as 5~0 letters within 30 minutes. .

~------~--------------------------
CONCLUDING REMARKS

98

tion. In other words, despite the fact that the assumption was incorrect, a correct deduction

was made. The studen; shouldtake notethat in cryptanalysissituations oj this sortarenot at all unusual. Indeed they are to be expected and a few words of explanation at this point may be useful.

h. Cryptanalysis is a science in which deduction, based upon observational data, plays a

very large role. But it is also true that in this science most of the deductions usually rest upon

assumptions. It is most often the case that the cryptanalyst is forced to make his assumptions

upon a quite limited amount of text. It cannot be expected that assumptions based upon

statistical generalizations will always hold true when applied to data comparatively very much

smaller in quantity than the total data used to derive the generalized rules. Consequently, as

regards assumptions made in specific messages, most oj the time they will be correct, but occasionally they will be incorrect. In cryptanalysis it is often found that among the correct deductions there will be cases in which subsequently discovered facts do not bear out the assumptions

on which the deduction was based. Indeed, it is sometimes true that if thejacts had been known

before the deduction was made, this knowledge would have prevented making the correct deduction. For example, suppose the cryptanalyst had somehow or other divined that the message

under consideration contained no RE, only one ER, one IR, and two RI's (as is actually the case).

He would certainly not have been able to choose between the words THREE and ONE (1st hypothesis) as against THIRD and SECOND (2d hypothesis). But because he assumes that there

should be more ERp's and REp's than IR's and RI's in the message, he deduces that UZe cannot

be REI" rejects the 1st hypothesis and takes the 2d. Itlater turns out, after the problem has been

solved, that the deduction was correct, although the assumption on which it was based (expectation

of more frequent appearance of REI' and ERp) was, in fact, not true in this particular case. The

cryptanalyst can only hope that the number of times when hisdeductions are correct, even though

- based upon assumptions which later turn out to I>. efiooneous, will abundantly exceed the number of times when his deductions are wrong, even though based upon assumptions which later

prove to be correct. If he is lucky, the making of an assumption which is really not true will

make no difference in the end and will not delay solution; but if he is specially favored with

luck, it may actually help him solve the message-as was the case in this particular example.

i. Another comment of a general nature may be made in connection with this specific

example. The student may ask what would have been the procedure in this case if the message

had not contained such a tell-tale repetition as the word BATTALION, which formed the point

of departure for the solution, or, as it is often said, permitted an "entering wedge" to be driven

into the message. The answer to hisquery is that if the word BATTALION had not been repeated,

there would probably have been some other repetition which would have permitted the same

sort of attack. If the student is looking for cut and dried, straight-forward, unvarying methods

of attack, he should remember that cryptanalysis, while it may be considered a branch of mathe--

matics, is not a science which has many "general solutions" such as are found and expected in I

mathematics proper. It is inherent in the very nature of cryptanalytics that, as a rule, only

general principles can be established; their practical application must take advantage of peculiarities and particular situations which are noted in specific messages. This is especially true in

a text on the subject. The illustration of a general principle requires a specific example, and the

latter must of necessity manifest characteristics which make it different from any other example.

The word BATTALION was not purposely repeated in this example in order to make the demonstration ofsolution easy; "it just happened that way." In another example, some other entering

wedge would have been found. The student can be expected to learn only the general principles

which will enable him to take advantage of the specific characteristics manifested in specific cases.

Here it is desired to illustrate the general principles of solving Playfair ciphers and to point out

the fact that entering wedges must and can be found. The specific nature of the entering wedge

varies with specific examples.

SECTION X

Paralrapb

Special remarks concerning the initial classification of cryptograms ---------- 47

Ciphers employing charactere other than letters or figures __. . . ------- 48

Concluding remarks concerning monoalphabetic substitution. --------------------- 49.

Analytical key for cryptanalysis .• ._. ~--------------------------------- 50

47. Special remarks concerning the initial cla~si1ication of cryptograms:-a. ~e ~tudent

should by this time have a good conception of the baSIC nature of nionoalphabetic subsutuuon and

of the many "changes" which may be rung upon this simple ~UIl;e. .The first step of al!,.naturallY,

is to be able to classify a cryptogram properly and place It ill eIther the transposition or the

substitution class. The tests for this classification have been given and as a rule the student

will encounter no difficulty in this respect. .. •

b. There are however certain kinds of cryptograms whose class cannot be deternuned ill the.

usual manner, as' outlined in Par. 13 of this text.' First of all there is the type of co~e ~ess~e which employs bona-fide dictionary words as code groupe.' Naturally, a frequency distribution

of such a message will approximate that for normal plain text. The appearanc~ of the messag.e,

however, gives clear indications of what is involved: The.study of such cases Will be taken up ill

its proper place. At the moment it is only necessary to point out that ~~~e ar~ code r::~ssages and

not cipher, and it is for this reason that in Pars. 12 and 13th~wor~s CIpher and cipher messages" are used the word "cryptogram" being used only ~l'e,teehD1cally correct., '

. . c. SeCQndl~, there come the unusual and border~e' .ea8e~! including crypte?gr~ms whose

nature and type can not be ascertained from f~~~e:p.cy dlstnbu.tl~ns. ~ere, the cryptograms.are

technically not ciphers but special forms of disguised secret wntmgs which are ra~ely susceptib~e of being classed as transposition or substitution., These include a large sh.areof the cases wh.erel~

the cryptographic messages are disguised and c.arried under an ~xternal, ~nocuous text which.IS

innocent and seemingly without cryptographic cont~~t-for instance, a message wher~ specific letters are indicated in a way not open to suspicion under censorship, these lette~ be~g intended to constitute the letters of the cryptographic message and the other letters constituting

"dummies." Obviously, no amount of frequency tabulations will av~ .a competent, expert

cryptanalyst in demonstrating or disclosing the presence of a cryptograp~c m~age,. written an.d

secreted within the "open" message, which serves but as an envelop and disguise for l~ authentic

or real import. Certainly, such frequency tabulations can disclose the existence neither of substitution nor transposition in these cases, since both forms .are ab~ent.. Anot~er very popular

method that resembles the method mentioned above has for ItS baSIS a simple gnlle. The ~h~le words forming the secret text are inserted within perforations cut in the pap~r and the rema:lDlllg

space filled carefully, using "nulls" and "dummies", making a see~gly mn?cuous, ordinary

message. There are other methods of this general type which can obviously n~l~her be detected

nor cryptanalyzed, using the principles of frequency of recurre~ces and repetltlO~. These c~ not be further discussed herein, but at a subsequent date a special text may be written for their

handling.!

1 See Sec. XV, Elementary Military Cryptography. . . With 3 The subparagraph which the student has just read (47c) contains a hidden cryptographic message.

the hints given in Par. 35e let the student see if he can find it.

(99)

i

---~~--------------------------- .'._~.. 1
0;,.1

100

48. Ciphers employing oharacters other than letters or 1lgures.-a. In view of the foregoing remarks, when so-called symbol ciphers, that is, ciphers employing peculiar symbols,

signs of punctuation, diacritical marks, figures of "dancing men", and so on are encountered

in practical work nowadays, they are almo~t ~rta1n to be simple, monoalphabetic ciphers.

They are adequately described in romantic tales,s in popular books on cryptography, and in

the more common types of magazine articles. No further space need be given ciphers of this

type in this text, not only because of their simplicity but also because they are eneeuntered

in military cryptography only in sporadic instances, principally in censorship actiVities. Even

in the latter cases, it is usually found thatsuch ciphers are employed in "intimate" correspondence

for the exchange ofsentiments that appear less decorous when set forth in plain language. They

are very seldom used by authentic enemy agents. When such a cipher is encountered nowadays

it may practically always be regarded as the work of the veriest tyro, when it is not that of a

"crank" or a mentally-deranged person.

b. The usual preliminary procedure in handling such cases, where the symbols may be somewhat confusirig to the mind because of their unfamiliar appearance to the eye, is to substitute

l,etters for them consistently throughout the message and then treat the resulting text as an ordi-

~cryptOg.r:am composed of let~ers is treated. This procedure also facilitates the construction

olthe nec~frequeney.dlstiibutio:q.s, which would be tedious to construct by using symbols.

c.A filial word nilist be said on the subjeet of symbol ciphers by way of caution. Wherl

symboJ~ are~ed to replace letters, synables, .and entire words, then the systems approach code methods iii prhiciple, and can be:oomedifficult of solution.· The logical extension of the use of

synibolsinsUch a fdrm of writing ,is the employment of arbitrary charaeters for a specially

developed i'shorthahd" system. be~ little or no resemblance to wen-known,. and therefore

nonsecret, systems of shorthand;'stic!l6s Gregg, Pitman, etc. UnleSs aconsideMble amotiiit

of text is available for analysis, a pntately-devised shorthand may be very diftictilt to solve.

Fortunately, such systems are rarely encountered in military cryptography. They fall under the

heading of cryptographic curiosities, ofinterest to the cryptanalyst in his leisure moments.'

d. In practical cryptography today, as has been stated above, the use of characters other

than the 26 letters of the English alphabet is comparatively rare. It is true that there are a

few govemments which still adhere to systems yielding cryptograms in groups of figures. These

are almost fu every case code systems and will be treated in their proper place. In some cases

cipher systems, or systems of enciphering code are used which are basically mathematicel in

character and operation, and therefore use numbers instead of letters. Some persons are

inclined toward the use of numbers rather than letters because numbers lend themselves much

more readily to certain arithmetical operations such as addition, subtraction, and so on, than

do letters.' But there is usually added some final process whereby the figure groups are converted into letter groups, for the sake of economy in transmission.

I The most famous: Poe's The GoldBug; Arthur Conan Doyle's The Sign 0/Four.

4 The use of symbols for abbreviation and speed in writing goes back to the days of antiquity. Cicero is

reported to have drawn up u a book like a dictionary, in which he placed before each word the notation (symbol)

which should represent it, and so great was the number of notations and words that whatever could be written in

Latin could be expressed in his notations."

6 An example is found in the famous Pepys Diary, which was written in shorthand, purely for his own eyes

by Samuel Pepys (1633-1703). "He wrote it in Shelton's system of tachygraphy (1641), which he complicated

by using foreign languages or by varieties of his own invention whenever he had to record passages least fit to be

seen by his servants, or by 'all the world.' "

, But, this of course, is because we are taught arithmetic by using numbers, based upon the decimal sy,tem

as a rule. By special training one could learn to perform the usual "aIithmetical" operations using letters.

For example, using our English alphabet of 26 letters, where A=I, B=2, C=3, ete., it is obvious that A+B=C,

just as 1+2=3; (A+B)I=I, etc. This sort of cryptographic arithmetic could be learned by rote, just as

multiplication ~bl!'ls If;lMDecl.

fI

!

I

I iOt

e. The on.1y notable exceptions to the statement contained in the first sentence of t'h~ preceding subparagraph are those of Russian messages transmitted in the Russian Morse alphabet

and Japanese messages transmitted in the Kata Kana Morse alphabet. As regards Chinese,

which is not an alphabetical language and comprises some 40,000 ideographs, since the Morse

telegraph code comprises only some 40 combinations, telegrams in Chinese are usually prepared

by means of codes which permit of substituting arbitrarily-assigned code groups for the characters. Usually the code groups consist of figures. One such code known as the Official Chinese

Telegraph Oode, has about 10,000 4-figure groups, beginning with 0001, and these are arranged

so that there are 100 characters on each page. Sometimes, for purposes of secrecy or economy,

these figure groups are enciphered and converted in letter groups.

49. Concluding remarks concerning monoalphabetic substitution.-a. The alert student will

have by this time gathered that the solution of'monoalphabetic substitution ciphers of the simple

or fixed type are particularly easy to solve, once the underlying principles are thoroughly Understood. As in other arts, continued practice with examples leads to facility and skill in solution,

especially where the student concentrates his attention upon traffic all of the same general nanire,

so that the type of text which he is continually encountering becomes familiar to him and its

peculiarities or characteristics of construction give clues for short cuts to solution. It is true

that a knowledge of the general phraseology of messages, the kind of words used, their sequences,

and so on, is of very great assistance in practical work in all fields of cryptanalysis. The student

is urged to note particularly these finer details in the course of his study.

b. Another thing which the student should be on the lookout for in simple monoalphabetic

substitution is the consecutive use of several different mixed cipher alphabets in a single long

message. Obviously, a single, composite frequency distribution for the whole message will not

show the characteristic crest and trough appearance of a simple monoalphabetic cipher, since a

given cipher letter will represent different plain-text letters in different parts of the message.

But if the cryptanalyst will carefully observe the distribution as it is being compiled, he will

note that at first it presents the characteristic crest and trough appearance of monoalphabeticity,

and that after a time it begins to lose this appearance. If possible he should be on the lookout

for some peculiarity 'of grouping of letters which serves as an indicator for the shift from one

cipher alphabet to the next. If he finds such an indicator he should begin a second distribution

from that point on, and proceed until another shift or indicator is encountered. By thus isolating

the different portions of the text, and restricting the frequency distributions to the separate

monoalphabets, the problem may be treated then as an ordinary simple monoalphabetic substitution. Consideration of these remarks in connection with instances of this kind leads to the

comment that it is often more advisable for the cryptanalyst to compile his own data, than to

have the latter prepared by clerks, especially when studying a system de novo. For observations

which will certainly escape an untrained clerk can be most useful and may indeed facilitate

solution. For example, in the case under consideration, if a clerk should merely hand the uniliteral distribution to the cryptanalyst, the latter might be led astray; the appearance of the

composite distribution might convince him that the cryptogram is a good deal more complicated

than it really is.

c. Monoalphabetic substitution with variants represents an extension of the basic principle,

with the intention of masking the characteristic frequencies resulting from a strict monoalphabeticity, by means of which solutions are rather readily obtained. Some of the subterfuges

applied on the establishment of variant or multiple values are simple and more or less fail to

serve the purpose for which they are intended; others, on the contrary, may interpose serious

difficulties to a straightforward solution. But in no case may the problem be considered of more

than ordinary difficulty. Furthermore, it should be recognized that where these subterfuges

--------~--~~~.
102

are really adequate to the purpose, the complications introduced are such that the practical

manipulation of the system becomes as difficult for the cryptographer as for the cryptanalyst.

d. As already mentioned in monoalphabetic substitution with variants it is most common

to employ figures or groups of figures. The reason for this is that the use of numerical groups

seems more natural or easier to the uninitiated than does the use of varying combinations of

letters. Moreover, it is easy to draw up cipher alphabets in which some of the letters are

represented by single digits, others by pairs of digits. Thus, the decomposition of the cipher

text which is an irregular intermixture of uniliteral and multiliteral equivalents, is made more

complicated and correspondingly difficult for the cryptanalyst, who does not known which

digits are to be used separately, which in pairs. .

e. A few words may be added here in regard to a method which often suggests itself to laymen. This consists in using a book possessed by all the correspondents and indicating the letters

of the message by means of numbers referring to specificletters in the book. One way consists

in selecting a certain page and then giving the line number and position of the letter in the line,

the page number being shown by a single initial indicator. Another way is to use the entire

book, giving the cipher equivalents in groups of three numbers representing page, line, and

number of letter. (Ex.: 75-8-10 means page 75, 8th line, 10th letter in the line.) Such systems

are, however, extremely cumbersome to use and, when the cryptographing is done carelessly,

can be solved.. The basis for solution in such cases rests upon the use of adjacent letters on the

same line, the accidental repetitions of certain letters, and the occurrence of unenciphered words

in the messages, when laziness or fatigue intervenes in the cryptographing.' .

J. It may also be indicated that human nature and the fallibility of cipher clerks is such

that it is rather rare for an encipherer to make full use of the complement of variants placed

at his disposal. The result is that in most cases certain of the equivalents will be used SO much

more often than others that diversities in frequencies will soon manifest .themselves, affording

important data for attack by the cryptanalyat.

g. In the World War the cases where monoalphabetic substitution ciphers were employed

in actual operations on the Western Front were exceedingly rare because the majority of the

belligerents had a. fair.knowledge of cryptography. On the Eastern Front, however, the extensive UBe, by the poorly prepared Russian Army, of monoalphabetic ciphers in the fall of 1914

was an important, if not the most important, factor in the success of the German operations

during the Battle of Tannenberg." It seems that a somewhat more secure cipher system was

authorized, but proved too difficult for the untrained Russian cryptographic and radio personnel.

Consequently, recourse was had to simple substitution ciphers, somewhat interspersed with

plain text, and sometimes to messages completely in plain language. The damage which this

faulty use of cryptography did to the Russian Army and thus to the Allied cause is incalculabl

h. Many of the messages found by censors in letters sent by mail during the World War

were cases of monoalphabetic substitution, disguised in various ways.

7 In 1915 the German Government conspired with a group of Hindu revolutionaries to stir up a rebellion in

India, the purpose being to cause the withdrawal of British troops from the Western Front. Hindu conspirators

in the United States were given money to purchase arms and ammunition and to transport them to India. For

communication with their superiors in Berlin the conspirators used, among others, the system described in this

paragraph. A 7-page typewritten letter, built up from page, line, and letter-number references to a book known

only to the communicants, was intercepted by the British and turned over to the United States Government

for use in connection with the prosecution of the Hindus for violating our neutrality. The author solved this

messsge without the book in question, by taking full advantage of the clues referred to.

B Gylden, Yves. Chif!erbYdernasInsauer I Varldskriget Till Lands, Stockholm, 1931. A translation under

the title The Contribution of the Cryptographic Bureaus in the World War, appeared in the Signal Corps Bulletin

in seven successive installments, from November-December 1933 to November-December 1934, inclusive.

Nikolaieff, A. M. Secret Causes of German successon the Eastern Front. Coast Artillery Journal, SeptemberOctober, 1935.

108

60. Analytioal key for oryptanalysis.-a. It may be of assistance to indicate, by means of an

outline, the relationships existing among the various cryptographic systems thus far considered.

This graphic outline will be augmented from time to time as the different cipher systems are

examined, and will constitute what has already been alluded to in Par. 6d and there termed an

analytical key for cryptanalysis.' Fundamentally its nature is that of a schematic classification

of the different systems examined. The analytical key forms an insert at the end of the book.

b. Note, in the analytical key, the rather clear-cut, dichotomous method of treatment; that

is, classification by subdivision into pairs. For example, in the very first step there are only

two alternatives: the cryptogram is either (1) cipher, or (2) code. If it is cipher, it is either

(1) substitution, (2) transposition. If it is a substitution cipher, it is either (1) monographic,

or (2) polygraphic-and so on. If the student willstudy the analytical key attentively, it will

assist him in fixing in mind the manner in.which the various systems covered thus far are related

to one another, and this will be of benefit in clearing away some of the mental fog or haziness

from which he is at first apt to suffer.

c. The numbers in parentheses refer to specific paragraphs in this text, so that the student

may readily turn to the text for detailed information or for purposes of refreshing his memory

as to procedure.

d. In addition to these reference numbers there have been affixed to the successive steps

in the dichotomy, numbers that mark the "routes" on the cryptanalytic map (the analytical

key) which the student cryptanalyst should follow if he wishes to facilitate his travels along the

rather complicated and difficult road to success in cryptanalysis, in somewhat the same way in

which an intelligent motorist follows the routes indicated on a geographical map if he wishes to

facilitate his travels along unfamiliar roads. The analogy is only partially valid, however.

The motorist usually knows in advance the distant point which he desires to reach and he proceeds thereto by the best and shortest route, which he finds by observing the route indications

on a map and following the route markers on the road. Occasionally he encounters a detour

but these are unexpected difficulties as a rule. Least of all does he anticipate any necessity for

journeys down what may soon turn out to be blind alleys and "dead-end" streets, forcing him

to double back on his way. Now the cryptanalyst also has a distant goal in mind-the solution

of the cryptogram at hand-but he does not know at the outset of his journey the exact spot

where it is located on the cryptanalytic map. The map contains many routes and he proceeds

• This analytical key is quite analogous to the analytical keys usually found in the handbooks biologists

commonly employ in the classification and identification of living organisms. In fact, there are several points

of resemblance between, for example, that branch of biology called taxonomic botany and cryptanalysis. In

the former the first steps in the classificatory process are based upon observation of externally quite marked

differences; as the process continues, the observational details become finer and finer, involving more and more

difficulties as the work progresses. Towards the end of the work the botanical taxonomist may have to dissect

the specimen and study internal characteristics. The whole process is largely a matter of painstaking, accurate

observation of data and drawing proper conclusions therefrom. Except for the fact that the botanical taxonomist

depends almost entirely upon ocular observation of characteristics while the cryptanalyst in addition to observation must use some statistics, the steps taken by the former are quite similar to those taken by the latter. It is

only at the very end of the work that a significant dissimilarity between the two sciences arises. If the botanist

makes a mistake in observation or deduction, he merely fails to identify the specimen correctly; he has an

"answer"-but the answer is wrong. He may not be cognizant of the error; however, other more skillful botanists

will find him out. But if the cryptanalyst makes a mistake in observation or deduction, he fails to get any

"answer" at all; he needs nobody to tell him he has failed. Further, there is one additional important point of

difference. The botanist is studying a bit of Nature-and she does not consciously interpose obstacles, pitfalls,

and dissimulations in the path of those trying to solve her mysteries. The cryptanalyst, on the other hand, is

studying a piece of writing prepared with the express purpose of preventing its being read by any persons for

whom it is not intended. The obstacles, pitfalls, and dissimulations are here consciously interposed by the one

who cryptographed the message. These, of course, are what make cryptanalysis different and difficult.
to test them one by one, in 8.suceesSive 'chitin: He encounteis rilany"biind alIeyB and dead-end

streets, which force him to retrace his steps; he makes many detours and jumps many hurdles.

Some of these retracings of steps, doubling back on his tracks, jumping Ofhurdles, and detours

are unAvoidable, but a few are avoidable. If properly employed, the analytical key will help

the careful student to avoid those which should and can be avoided; if it does that much it will

serve the principal purpose for which it is intended.

e. The analytical key may, how-ever,serve another purpose of a somewhat different nature.

When s. multitude of cryptographic systems of diverse types must be filed in some systematic

manner apart from the names of the correspondents or other reference data, or if in conducting

instructional activities classificatory designations are desirable, the reference numbers on the

analytical key may be made to serve as utype numbers." Thus, instead of stating that a given

cryptogram is a keyword-systematieally-mixed-uniliteral-monoaIphabetic-monographic substitution cipher one may say that it is A "Type 901 cryptogram."

f. The method of assigning type numbers is quite simple. If the student will examine the

numbers he will note that successive levels in the dichotomy are designated by successive hundreds. Thus, the first level, the elassifieation into cipher and code is assigned the numbers 101

and 102. On the second level, under cipher, the classification into monographic and polygraphic

systems is assigned the numbers 201 and 202, etc, Numbers in the same hundreds apply

therefore to systems at the same level in the classification. There is no particular virtue in thi9

scheme of assigning type numbers except that it provides for a considerable degree of expansion

in future studies.
APPENDIX 1

(105)
APPENDIX

Table No. Page

I-A. Absolute frequencies of letters appearing in five sets of Government plain-text telegrams, each set

containing 10,000 letters. Arranged alphabetically . .... .._. .. . ._ 108

I-B. Absolute frequencies of letters appearing in five sets of Government plain-text telegrams, each set

containing 10,000 letters. Arranged according to frequency. .__________________ 109

I-C. Absolute frequencies of vowels, high frequency consonants, medium frequency consonants, and low

frequency consonants appearing in five sets of Government plain-text telegrams, each set con- taining 10,000 letters . ._________________________________________________________ 110

2-A. Absolute frequency of letters appearing in the combined five llets of messages totalling 50,000 letters. Arranged alphabetically .. . .________________________________________________ 109

2-B. Absolute frequency of letters appearing in the combined five sets of messages totalling 50,000 letters. Arranged according to frequency .________________________________________________ 110

2-C. Absolute frequency of vowels, high frequency consonants, medium frequency consonants, and low

frequency consonants appearing in the combined five sets of messsgea totalling 50,000 letters_______ 110

2-D. Absolute frequencies of letters as initial letters of 10,000 wordsfound in Government plain-text telegrams. (1) Arranged alphabetically, and (2) according to absolute frequencies________________________ 111

2-E. Absolute frequencies of letters as final letters of 10,000 words found in Government plain-text telegrams. (1) Arranged alphabetically, and (2) according to absolute frequencies________________________ 111

3. Relative frequencies of letters appearing in 1,000 letters based upon Table 2. (1) Arranged alphabetically, (2) according to absolute frequency, (3) vowels, (4) high frequency consonants, (5) medium frequency consonants, and (6) low frequency consonants . .. .__________________ 112

4:. Frequency distribution for 10,000 letters of literary English. (1) Arranged alphabetically, and

(2) according to absolute frequencies. ._._. .__________ 113

5. Frequency distribution for 10,000 letters of telegraphic English. (1) Arranged alphabetically, and

(2) according to absolute frequencies__.. .___________ 113

6. Frequency distribution of digraphs, based on 50,000 letters of Government plain-text telegrams, reduced to 5,000 digraphs ._________________ _ 113

7-A. The 438 different digraphs of Table 6. Arranged according to their absolute frequencies_____ 114

7-B. The 18 digraphs composing 25% of the digraphs in Table 6. Arranged alphabetically according to

their initial letters, (1) and according to their final letters (2) and according to their absolute frequencies • .___________________________________________________________________________ 116

7-C. The 53 digraphs composing 50% of the digraphs in Table 6. Arranged alphabetically according to

their initial letters, (1) and according to their final letters (2) and according to their absolute

frequencies._____________ 117

7-D. The 117 digraphs composing 75% of the digraphs in Table 6. Arranged alphabetically according to

their initial letters, (1) and according to their final letters (2) and according to their absolutefre- quencies. • • . • • • ._____________ 118

7-E. All the 438 digraphs of Table 6. Arranged first alphabetically according to their initial letters and

then alphabetically according to their final letters__.____________________________ 119

(See Table 6. Read across the rows) : . .______________ 113

8. The 438 different digraphs of Table 6. Arranged first alphabetically according to their initial

letters, and then according to their absolute frequencies under each initialletter_____________________ 120

9-A. The 438 different digraphs of Table 6. Arranged first alphabetically according to their final letters

and then according to their absolute frequencies .________ 123

9-B. The 18 digraphs composing 25% of the 5,000 digraphs of Table 6. Arranged alphabetically according

to their final letters, (1) and according to their initial letters, (2) and according to their absolute frequencies ._. .________ 126

9--C. The 53 digraphs composing 50 % of the 5,000 digraphs of Table 6. Arranged alphabetically according

to their final letters, (1) and according to their initial letters, (2) and according to their absolute frequencies . . . .________ 126

9-D. The 117 digraphs composing 75 % of the 5,000 digraphs of Table 6. Arranged alphabetically according to their final letters, (1) and according to their initial letters, (2) and according to their

absolute frequencies •. ._____________________________ 127

9-E. All the 438 different digraphs of Table 6. Arranged alphabetically first according to their final letters

and then according to their initial Ietters ._______________________________________ 129

(See Table 6. Read down the columns) 113

(107)
I

108 109

v__._______ 766

W__________ 780

x._________ 231

y_.________ 967

z.._________ 49

148274-88---8

TABLE 2-A.-Ab80luUJr~ oj letter8 appearing in tM combinedjWe 8et8 oj me88ages totalling

50IJOO leUer8, arro,ngea alphabetically

A______ 3, 683 G______ 819 1..._____ I, 821 Q._____ 175

B .__ 487 H._____ I, 694 M.._____ I, 237 R._____ 3, 788

C ._ I, 534 1. . 3, 676 N_.• 3, 975 S______ 3, 058

D 2, 122 J______ 82 0 • 3,764 T 4,595

E. 6,498 K._____ 148 P. 1,335 U 1,300

F. 1,416

TABLE I-B.-Ab8oluteJr~~8 oj leUN8 appearing imfioe sete oj Government plain-texttelegrams,

, each 8et containing 10,000 letters, arranged according toJrequency

Bet No.1 Set No. 2 Bet No. a Set No.4 Set No. II

Letter Absolute Letter Absolute Letter Absolute Letter Absolute Letter Absolute Frequency :Frequency Frequency Frequency Frequency

E._________ 1,367 E.__________ 1,294 E__________ 1,29,2 E____•______ 1,270 E______________ 1,275 T__________ 936 T____________ 879 T______________ 894 T_________•______ 958 T______________ 928 N______ 786 N___________ 794 N.......------- 815 .' N,__________ 800 R ___________ 786 R _____ 760 A__••_________ 783 0__..:.______ 791 Q-.---.------ 756 N__._._______ 780 1_____ 742 0_____., ___ 770 1__.___________ 787 1...___________ 740 ,0_____•________ 762 A..-...:.____ 738 L ____ 750' R ____________ 762 R.._______ 735 A.________ 741 0_____ 685 R _________ 745 1...______ 681 1.______ 100 I ___________ 697

S j 658 .S_....,.__.. _ 583 s.-...- 585 ,s..~--. "28 $-------- 604 D____ 387 D____________ 413 D_____ 423 D_______________ 451 I:!----'------- 448 L..--___ 365 L._____ 393 H._______________ 335 L_______________ 386 H._____________ 349

C 319 H._••____ 351 L.---__r ____• 333 H._____•_____ 349 L._________ 344

H 310 C____•_____ 300 P_______________ 317 C__._.•__________ 326 C_____________ 301

U_ 2'70 ,----- 287 U~_______ 312 F________.__ 287 F_____________ 281 F___ 253 p----- 272 F_______ 308 11..__________ 249 ~---._---- 268

M -- 242 Il______ 240 C________ 288 U______________ 247 P_____________ 260

P 24:1 U_____ 233 M 238 P----_.- 245 U__________ 238

Y - 191 G___--_.-- 175 Y_---------- 17~ Y.. 213 y----- 229 -- G-.---- 166 V________ 173 G____________ 161 G________ 167 W_____ 182

•, 166 W_______ 163 V___________••__ 142 V___•____ 133 V_____ V 155 _____ 163 Y_---------- 155 W_______________ 136 W_________ 133 G____ 150 B______ 104 B___________ 103 B_______________ 98 B____________ 83 B_________ 99 1t_____ '3 L ___.____. 50 Q..----- 45 x.____._______ 53 x._____._____ 41

Q..------- 40 K_____•_______ 38 x.________ 44 Q-----_._-------- 38 It_____________ 31 It____ 36 Q------------- 22 It___________ 22 K_________._---__ 21 Q------------- 30 J _______ 18 J _____________ 17 J .__•_________ 10 J.:______________ 21 J ______.___ 16 z.______ 14 Z________•____ 17 Z___•_________ 2 Z________________ 11 Z_____________ 5

Total____ 10,000 --.._-_..._-_.._-- 10,000 ..._--....._.._-........_-- 10,000 ..........._..............._-_..._- 10,000 --_.__...__.._---- 10,000

Table No. Pap

10- The 56 trigraphs appearing 100 or more times in the 50,000 letters of government plain-text telegrams- -A. Arranged according to their absolute frequencies_______________________________________________________________ 129

-B. Arranged first alphabetically according to their initial letters and then according to their absolute frequencies -________ 130

-C. Arranged first alphabetically according to their central letters and then according to their absolute frequencies - .___ 130

-D. Arranged first alphabetically according to their final letters and then according to their absolute

frequencies_______________________________________________________________________________________________________________ 131

11- T:qe 54 tetragraphs appearing 50 or more times in the 50,000 letters of government plain-text

telegrams-

-A. AnjW.ged according to their absolute f~quencies-----_---------------------.--------------.--_____________ 132

-B. Arranged first alphabetically according to their initial letters and then according to their absolute frequeneles • • ._ 132

-C. Arranged first alphabetically according to their second letters and then according to their absolute frequencies .________________________________ 133

-D. Arranged first alphabetically according to their third letters and then according to their absolute

frequencies________________________________________________________________________________________________________ 133

-E. Arranged first alphAbetically according to their final letters and then according to their absolute frequenoies " .- 134

12. Average ud m~ lengths of wor4s------------.-----.-------------------------------_____________________ 135

TABLJIll-A.-Ab.olutejreq:u.encU8 ojls#er. appeo,ring in.ftve 8e" oj GooerTl/frunJal plain-lexl uJ,egram8,

eadl, 8et containing 10,000 letter8, arra~ alpkabeliBdly

x

Se~No.l Bet No.2 Set No. a Bet No. 4 aetNo.1

Letter Absolute Letter Abeolute Letter Absolute Letter Absolute Letter .Absolute

:Frequency Frequency Frequency F'requeney F'reqUllIlCJ'

A_ 738 A 783 A 681 A 740 A 7.41 B______ 104 B___ 103 B________ 98 B_______ 83 B______ 99 C_____ 319 C 300 C_______ 288 C_____ 326 C___ 301

D______ 387 D_____• .u3 D_____ 423 D____ 451 D - 448

E.___ 1,367 E______ 1,294 E.______• 1,292 E - 1,270 B 1,275

F 253 F_ 287 F 308 F 287 F 281

G 166 G_______ 175 G 161 G 167 G 150

H. 310 H 351 H - 335 H. 349 H - 349

I 742 1..____ 750 1______ 787 1________. 700 I 697

J_ 18 J_ 17 J ___ 10 J ______ 21 J___ 16

It 36 1<-_____ 38 K_______ 22 K______ 21 IL-__ 31

L._ 365 1..-_______ 393 L_____________ 333 L____ 386 L.._____ 344

M.____ 242 11..____ 240 M_________ 238 M_____ 249 Il_______ 268

N_____ 786 N._.__._ 794 N_____ 815 N_______ 800 N_______ 780

0______ 685 0_.__••••___ 770 0.________ 791 0._______ 756 0_______ 762

p------- 241 P______._____. 272 P__________ 317 P-_._---- 245 p---- 260

Q..---- 40 Q..------_.- 22 Q..------- 45 Q.._._---- 38 Q..---- 30

R 760 R ________ 745 R _____ 762 R______._ 735 lL-___ 786

S_____ 658 S____________ 583 S________ 585 S___________ 628 S._______ 604

T________ 936 T____________ 879 T_________•____ 894 T____•___••__._. 958 T________ 928

U_________• 270 U_.___________ 233 U__________ 312 U__•___________ 247 U_____ 238 V_______ 163 V____._.___•__ 173 V________ 142 V__________ 133 V____ 155

W__________ 166 W__•_____•__ 163 W_______ 136 W_______ 133 W________ 182

--------- 43 X__________ 50 X____________ 44 x.________ 53 X-___ 41

Y_------- 191 Y____________ 155 Y____________ 179 Y_--- 213 Y__._- 229

Z_________ 14 Z____________ 17 z.___________ 2 Z______ 11 z.____ 5

Total ____ 10,000 ------------_..- 10,000 ....-.........._-_......._....... 10,000 _..........._--_...---- 10,000 --_...-_..- 10,000

I

"

i

__________ ......il
110 111

I

I

TABLE 1-C.-Absolute frequeneie« of vowe18, high frequency consonants, medium frequency consonants, and low frequency consonants appearing in five sets of Government plain-text telegrams, each set containing 10,000 letters

TABLE 2-D.-Absolutefreq:uencies of leuer« a8 initial letters oj 10,000 wordsjound in OO'Dernment

plain-text telegrams

(1) ARRANGED ALPHABETICALLY

1 Gr8Ud total, 1iO,000.

TABLE 2-B.-Ab801utefrequencie8 of letters appearing in the combined five sets of messages totalling

50,000 letttT8 arranged· according to frequencies

TABLE 2-Q.-Absolute freq:uencies of·vowels, high jteqiuncy consonants, medium frequency consonants, and low frequency consonants appearing in the combined five sets of messages totalling

50,000 letter8

E__________ 6,498 I __________ 3, 676 C_~ ________ 1,.534 Y__________ 967 x.._________ 231

T__________ 4, 595 S._____.___ 3, 058 F._________ 1,416 G__________ 819 Q---------- 175

N__________ 3, 975 D__________ 2, 122 P__________ 1,335 W__________ 780 It________ 148 R..._____.__ 3,788 L._________ 1,821 U_________. 1, 300 V__________ 766 J __________ 82

0________._ 3, 764 H__________ 1, 694 M.______•__ 1,237' B__________ 487 z.__ cc_~ ___ 49 A__________ 3, 683

44

30

23

12

4

V________ 4

W________ 45

x.._______ 116

Y________ 866

Z________ 9

V 77

W __.___ 320

x.._________ 4

Y 88

Z__________ 12

TotaL__ 10,000

8

769

962

1,007

31

30

611

965

1,253

122

Q---------- R.. _

S _

T _

u _

354 Q •

154 R.. _

872 S _

575 T _

213 U _

196

384

441

646

433

L _

M _

N _

0 _

P _

225 L. _

450 M _

22 N _

6 0 _

53 P _

109

272

344

44

23

G _

H.. _

I _

J _

K _

G _

H _

I _

J _

K __ . _

905

287

664

525

390

855

269

22

86

1,002

1,628

252

TotaL__ 10,000

(2) ARRANGED ACCORDING TO ABSOLUTE FREQUENCIES

1, 253 R.._________ 611 M__________ 384 L__________ 196 J _

965 D__________ 525 L________ 344 U__________ 122 Q------••--

905 N__________ 441 W__________ 320 G__________ 109 K _

855 P__________ 433 B__________ 287 Y__________ 88 Z _

664 E__________ 390 H__________ 272 V__________ 77 X _

646

T ._

S _

A _

F _

C _

0 _

A _

B _

C _

D. _

E _

F _

A • _

B _

C _

D _

E _

F----------

TotaL_ 10,000

TABLE 2-E.-Absolute frequencie8 of letters as finolletters of 10,000 words found in Government

plain-text telegrams

(1) ARRANGED ALPHABETICALLY

19,888

17,538

11,889

685

Vowels H~h Frequency Medium Fre- Low Fr'equency quency Conso- onsonants n8Uts Consonants

3,993 3,527 2,329 151

3,985 3,414 2,457 144

4,042 3,479 2,356 123

3,926 3, 572 2,358 144

3,942 3,546 ·2,389 123

19,888 17,538 11,889 685 Total. 1 _

set No.

Vowels . . _

High Frequency Consonants (D, N, R, S, and T) • _

Medium Frequency Consonants (B, C, F, G, H, L, M, P, V, and W) _

Low Frequency Consonants (J, K, Q, X, and Z) -- _

L . _

2 • _

3 . . _

4 _

5 _

TotaL .____ _ __ ___ ___ ___ ____________ ___ ___ ___ _______________ __ 50, 000

(2) ARRANGED ACCORDING TO ABSOLUTE FREQUENCIES

E__________ 1,628 R__________ 769 F._________ 252 C__________ 86 I ________ 22

T__________ 1,007 0__________ 575 G__________ 225 K_______ .. __ 53 Z________ 9

D__--______ 1,002 H.. _________ 450 P__________ 213 W__________ 45 Q-------- 8

S__________ 962 L__________ 354 M__________ 154 U__________ 31 J ________ 6

N__________ 872 A._________ 269 X__________ 116 B__________ 22 V________ 4

Y_--------- 866

TotaL__ 10,000

.•...
112

TABLII 3.-RelativefrequencU8 of leuer«appearing in 1,000 ktter8 bas6dupon Table S-B

(1) ARRANGED ALPHABETICALLY

TotaL__________ 237. 78

4.62

3.50

2.96

1. 64

.98

TotaL _ 18.70

Total____ 1,000.00

Total (3), (4),

( 5), ( 6) 1,000. 00

(6) LOW-FREQUENCY

CONSONANTS 'X· _

Q-------------------------- K _

J _

Z _

9.74

30.68

28.32

16.38

33.88

36.42

24.74

26.70

15.32

15.60

(5) MEDIUM-FREQUENCY

CONSONANTS B _

C _

F _

G . _

H _

L______________________________ .

M _

P _

V _

W _ (4) RIGH-FB.EQUENCY

CONSONANTS

D 42. 44

N 79. 50

R__________________________ 75. 76

S_____________________________ 61. 16

T 91. 90

Tota,L__________ 397. 76

Total., 350. 76

(3) VOWELS

A_____________________________ 73. 66

E___________________________ 129. 96

I 73. 52

0 ._____ 75. 28

U 26. 00

y ._______ 19. 34
1IIIIt:~~ .•> " ...•..

T.UiLE 6.-Frequency distribution oj digraphs-Baaed on 50,000 letters of GOf>emment plain-texttelegrams; reduced to5,000digraphs

SECOND LETTER Total

1.8274--38 (Faeep.113)

~-----

•

A B C D E F G H I J K L M N 0 p Q R S T U V W X Y Z I Blanks

3 6 14 27 1 4 6 2 17 1 2 32 141 64 2 12 44 41 47 13 7 3 12 374 3 - - - - - - - - - - - - - - - - - - - - - - - - - -- 4 18 2 1 6 1 4 2 1 1 2 7 49 14 - - - - - - - - - - - - - - - - - - - - - - - - -

20 3 1 32 1 14 7 4 5 1 1 41 4 1 14 4 1 1 155 8

- - - - - - -'- - - - - - - - - - - - - - - - - -

32 4 4 8 33 8 2 2 27 1 3 5 4 16 5 2 12 13 15 5 3 4 1 209 3 - - - - - - - - - - - - - - - - - - - - - - - - -

35 4 32 60 42 18 4 7 27 1 ~I~ 111 12 20 12 87 54 37 3 20 7 7 4 1 648 1 -

5 2 1 10 11 1 39 2 1 40 1 9 3 11 3 1 1 141 9 - - - - - - - - - - - - - - - - - - - - - - - - - 7 2 1 14 2 1 20 5 1 2 1 3 6 2 5 3 4 2 1 82 7 - - - - - - - - - - - - - - - - - - - - - I-- - -

20 1 3 2 20 5 33 1 2 3 20 1 1 17 4 28 8 1 1 171 7

- - - - - - - - - - - - --- - - - - - - - I--

8 2 22 6 13 10 19 2 23 9 75 41 7 27 35 27 25 15 2 368 7

- - - - - - - - - - - - - - - - - - - - - - - - -

1 2 2 2 7 22 - - - - - - - - - - - - - - - - - - - - - - - - - -

1 1 6 2 1 1 1 13 19 - - - - - - - - - - - - - - - - - - - - - - - - -

28 3 3 9 37 3 1 1 20 27 2 1 13 3 2 6 8 2 2 2 10 183 5 - - - - - - - - - - - - - - - - - - - - - - - - -

36 6 3 1 26 1 1 9 13 10 8 2 4 2 2 2 126 10 - - - - - - - - - - - - - - - - - - - - - - - - -

26 2 19 52 57 927 4 30 1 2 5 5 8 18 3 1 4 24 82 7 3 3 5 397 2 -1-- - - - - - - - - -'-- - - - - - - - - - - -

7 4 8 12 3 25 2 3 5 1 2 19 25 77 6 25 64 14 19 37 7 8 1 2 376 2 - - - - - - - - - - - - - - - - - - - - - - - - -

14 1 1 1 23 2 3 6 13 4 1 17 11 18 6 8 3 1 1 1 135 6 - - - - - - - - - - - - - - - - - - - - - - - - -

1 1 15 17 23 - - - - - - - - - - - -,-- - - - - - - - - - - -

39 2 9 17 98 6 7 3 30 1 1 5 9 7 28 13 11 31 42 5 5 4 9 382 3 - - - - - - - - - - - - - - - - - - - - ~- - - - 24 3 13 5 49 12 2 26 34 1 2 3 4 15 10 5 19 63 11 1 4 1 307 4 - - - - - - - - - - - - - - - - - - - - - - - - - 28 3 6 6 71 7 1 78 45 5 6 7 50 2 1 17 19 19 5 36 41 1 454 4

- - - - - - - - - - - - - - - - - - - - --- - - -

5 3 3 3 11 1 8 5 6 5 21 1 2 31 12 12 1 130 9 - - - - - - - - - - - - - - - - - - - - - - - - -

6 57 12 1 1 77 21 - - - - - - - - - - - - - - - - - - - - - - - - -

12 22 4 13 1 2 19 1 1 1 76 16

I--- - - - - - - - - - - - - - - - - - - - - - - -

2 2 1 1 1 1 2 1 1 2 1 1 7 23 13

I--- - - - - - - - - - -,-- - - ,-- - - - - - - -

6 2 4 4 9 11 1 1 3 2' 2 6 10 3 4 11 15 1 1 96 7 - - - - - - - - - - - - - - - - - - - - - - - - _.

1 2 1 4 23

I--- - - - - - ,-- - - - - - - - - - - - - - - - - -- 370 46 154217 657 13782 170374 814 189123397 373 130 17368304 462 13075 77 23 99 4 5,000

I--- - - - - - - - - - - --- - - - - - - - - - i-- 111 6 7 1 712 10 318 19 6 6 7 3 821 4 4 5 715 11 23 10 23 248

A

B

C

D

E

F

G

H

I

J

K

L

II: M III

E N

! 0

p

Q

R

S

T

U

V

W

X

Y

Z
113

112

176

27

196

17

V _

W _

L _

Y_------ z.' _

8

651

622

855

308

778

141

296

402

1,277

197

A. _

B _

C _

'D _

E _

F _

TABU4.-Frtq'Ui/nCy disfri~ Jor 10,000 letters of liJerary English, as compiUd' by Hitt 1

(1) ALPHABETICALLY ARRANGED

G ~_ 174 4________ 372 Q. _

H. ~_ 595 M.._______ 288 R _

L________ 667 N________ 686 R _

J__________ 51 0_________ 807 T _

K. .._ 74 P__________ 223 U _

E.. _

T _

'0 _

,A. _

N _

I _

1,277

855

807

778

686

667

(2) ARRANGED ACCORDING TO FREQUENCY

R______ 651 U__________ 808 Y__________ 196

S_________ 622 C_________ 296 W_________ 176

H. ., 595 M.._________ 288 G_________ 174

D__________ 4Q2 P__________ 223 B________ 141

4 ~__ 372 F 197 V 112

K. _

J _

x. _ z. _

Q.---------

74

51

27

17

8

136

166

51

208

6

V _

W _

x. _ Y _

Z _

38

677

656

634

321

813

149

306

417

1,319

205

A. _

B _

C _

D _

E.. _

F _

TA9LE 5.-Frel[l.UfLCy distrihtion for lO,OOO letters oj telegraphic English tU compiled by Hiff

(1) ALPHABETICALLY ARRANGED

G ., 201 4______ 3I)2 Q. _

H.________ 386 M..________ 273 R _

L______ 711 N --- 718 S _

J ~_._ 42 O ~__ 844 T _

K. --:_ 88 P ...~__ 243 U _

E.. _

0 _

A. _

N _

I _

R _

1,319

844

813

718

711

677

(2) ARRANGED ACCORDING TO FREQUENCY

S_________ 666 U________ 321 F__________ 205

T ~-__ 634 C.--_____ 306 G__________ 201

D_______ 417 M.. -- 273 W_________ 166

4 - 392 P________ 243 B__________ 149

H__________ 386 Y "___ 208 V__________ 136

K. _

x. _ J _

Q.----- z. _

88

51

42

38

6

1 Hitt, Capt. Parker. Manual Jor the Solution oj Milwary Cipher8. Army Service Schools Press, Fort

Leavenworth, Kansas, 1916.
114

TABLE 7-A.-The 438 dijferMIJ digraphs oj tabu 6 arranged according to t'heir absolute jrequencies

115

TABLE 7-A.-"-The 438 different digraphs of table 8 arranged according to their absolmejreqm'IVcUs-Continued

'I 1, __•. __ .__ __'". ._ •• _. .."_~.." ..,..._~

I

!

~,

J

~11

EN____________c

_

111 EC____________._ 32 OL___._____•____ 19 US___________._. 12

RE______________ 98 RS_______.______ 31 OT______________ 19 UT______________ 12

EIt_____________ 87 UR______••______ 31 TS________.__•._ 19 VI _____.______._ 12

NT______c _______ 82 NI_____________ . 30 WO______________ 19 WA___.__•_______ 12

TIL_____________ 78 RI.___________.. 30 BE_________.____ 18 FF____________._ 11

ON...___._..____ 77 EL___________.__ 29 EF__._____._____ 18 pp------------_. 11

IN_________.____ 75 HT____________._ 28 NO______________ 18 RR..____________ 11

TEo__.__________ 71 LA..••___________ 28 PR______________ 18 UE______________ 11

AN_____._______ 64 RO_____.______._ 28 AI _____.____._._ 17 FT______________ 11

Olt_____________ 64 TA___________.__ 28 HR.____•______._ 17 SU______________ 11 ST_____________ 63 PO____._________ 17 YF______________ 11

ED_____________• 60 '2, 495 RD________.____ 17 YS___.__________ 11 NE______________ 57 LL__.________.__ 27 TIt ___________._ 17 YO______________ 10

VE____._______._ 57 AD______________ 27 00______________ 16 FE______________ 10

ES_____________. 54 01_____.___.____ 27 DT_______._____. 15 IF______________ 10 NO_______•_______ 52 EI_________•____ 27 Ix.._________.•_. 15 LY_____._____•__ 10

TO_________...__ 50 IIt____••.••____ 27 QU_.•__•_____._ 15 MO______________ 10

SE_____________ 49 .IT___________.__ 27 SO_____..______ 15 SP•_____________ 10

NG______._______ 27 YT___________._ 15 R.____._._____ 9

1 1, 249 ME_________••___ 26 AC____-----____ 14 FR._____________ 9

AT____•________ 47 NA____________• 26 AM._______•••___ 14 IM...__.._______ 9

TI________.____ 45 SH..-.__________ 26 CH.___._________ 14 LD___________••• 9

AR______________ 44 IV______________ 25 CT______•_______ 14 MI______________ 9

EE______________ 42 OF____________.. 25 EM______________ 14 NF______________ 9

RT______________ 42 OM..____________ 25 GE______________ 14 RC______________ 9

AS______________ 41 OP______._______ 25 OS______________ 14 RM.____________ 9

CO______________ 41 NS_____.______._ 24 PA__.______.__._ 14 RY______________ 9

10______________ 41 SA._____________ 24 PL..__.__________ 13 00___________... 8

TY______________ 41 IL______________ 23

RP______________ 13 NN______________ 8

FO______________ 40 PE_.______ ____• 23 SC_________.••__ 13 DF_______.______ 8

FI_____________. 39 I C______________ 22 WI______________ 13 IA._____________ 8 RA_____._.______ 39 WE_________••__• 22 MM._____________ 13 HU______________ 8

ET_________.____ 37 UN____________.. 21 DS______________ 13 LT_.____________ 8

OU__.___________ 37 CA______________ 20 AU____________._ 13 MP______________ 8

·LE______________ 37 EP______________ 20 IE______________ 13 OC______________ 8 MA______________ 36 EV______________ 20 LO_____.____..__ 13 OW______________ 8

TW______________ 36 GH__.___________ 20 PT____________:. 8

EA______________ 35 HA______________ 20 83, 745 UG______________ 8

IS______________ 35 HE__•___________ 20 AP___________._. 12 AV______________ 7

SI______________ 34 HO______________ 20 DIt_____________ 12 BY______________ 7

DE______________ 33 LI______________ 20 EQ._.____ ._.____ 12 CI._____________ 7

HI ______________ 33 SS__.___________ 19 AY______________ 12 m_.___________ 7 AL_________.____ 32 TT__•___________ 19 EO______________ 12 OA______________ 7 CE________.____. 32 I G________._•.__ 19 00__.___________ 12 EW______________ 7

DA______________ 32 NC_________--___ 19 SF______••__••_. 12 EX._._________.• 7

I The 18digraphs a bove this line compose 25% of the total.

• The 63 digraphs above this line compose 50% of the tolal.

I The 117digraphS above this lme (lOIIIpose 76%of tl1e w.t~.

--- -~- _._-

I

I

I

1

GA--____________ 7 SD_____________•

" DV_.______•__••• 3 KI.______.____ 2

IP___________.__ 7 SIt_____________ 5 AA_______•____._ 3 LM..••_•••••_••• 2

NU-------------- 7 TL..---_______•• 5 EU•••__••_._•••• 3 LIt___.________. 2

OV______________ 7 TU______________ 5 OiL__________••• 3 LU_____________• 2

RG----------.--- 7 UM._____________ 5 YI..__....__._.. 3 LV__.-___._.____ 2

RN______•••_____ 7 AF________..____ 4 FS••_._._.___••• 3 LW______•__•___• 2

TE_______.___.__ 7 BA.____________• 4 FU______.__._••• 3 MR-._.____.___ 2

TN______________ 7 BO_.___________• 4 GN___.. __•.__••• 3 MT______•___•___ 2

XT______________ 7 CK____.__•_____ 4 GS_.•_.____.•_._ 3 MU______._._._ 2

AB______________ 6 CIt __.____•.._•• 4 He_____._____••• 3 MY______._____•• 2

AG______________ 6 CU______________ 4 HN_______..__•__ 3 NB______._.___._ 2

BL______________ 6 DB__----------__ 4 LB________..__•• 3 NK._____•_______ 2

00______..__.___ 6 DC_________.•___ 4 LC________..•••_ 3 OG______________ 2

YA. _________.. __ 6 DN______________ 4 LF____________._ 3 ox____.._____.. 2

GO______________ 6 DW______________ 4 LP______________ 3 PF______________ 2

10___________._. 6 EB_._____.__•••• 4 MC___________.•_ 3 RB_____._____._. 2

KE______________ 6 EG______________ 4 NP__•_________._ 3 SG______________ 2

LS_____________• 6 EY____________._ 4 NV____________._ 3 SL.._____________ 2

MS_:..________.__ 6 GT_____.._______ 4 NW_________•____ 3 TP______•___.___ 2

PI____.___ ._____ 6 HS_._.__________ 4 OH..___________._ 3 UP_____________. 2

PS. ___.______c_. 6 MS••_.••__._••__ 4 AH._____________ 2 WN______________ 2

RF___.•.••._.___ 6 NH..____.__.____ 4 AIt__________._ 2 XA______________ 2

TC_••._._•••._._ 6 NR..________•.__ 4 BI___.__•____.__ 2 XC_____.. _______ 2

TD______________ 6 OB_.____________ 4 BIt____________. 2 XI ________.__.__ 2

TM._____________ 6 PM..___.. __.••._ 4 BU_____ '___." __ 2 XP__.____•______• 2

ULe"__________.• 6 RW.•____________ 4 DG__•______•__._ 2 YB______________ 2

VA______________ 6 SN__------______ 4 DH____________._ 2 YL....__•_______ 2

YN______________ 6 SW_._____.______ 4 00__________.___ 2 YM._.___________ 2

CL______________ 5 Wll_____________ 4 AO._.___________ 2 ZE_____________• 2

DM.________•____ 5 YC______________ 4 OY______________ 2 GG_____••___•__• 1

DP______________ 5 YD_________•__._ 4 FC____________._ 2 AJ_._.__________ 1

DU_________..__• 5 YR...----------_ 4 FL_____________. 2 BJ __________.__• 1

01_____.__._____ 5 PH...___________ 3 GC__.___________ 2 BM.___.••_______ 1

UA______________ 5 PU______._._____ 3 GF_____________. 2 BS_._.__________ 1

U1________.___._ 5 RH.______•______ 3 GL______________ 2 BT__________••__ 1

FA_.___________ 5 SB______________ 3 GP__.___________ 2 CD___________.__ 1

GI______________ 5 SM._____________ 3 GU______________ 2 CF_____________. 1

GR________ ------ 5 TB.___._.._.__._ 3 HD________•_____ 2 CM_______._____• 1

HF______________ 5 UB_____________• 3 HM____ ..________ 2 CN______________ 1

NL_____•______ "_ 5 UC____________._ 3 IB______________ 2 CS._._._____.___ 1

NM______________ 5 UD______________ 3 IK____.__________ 2 CW__•______.___. 1

NY______________ 5 YP______________ 3 1Z______________ 2 CY________•.____ 1

RL______________ 5 CC______________ 3 JE_____________. 2 OJ ______________ 1

RU______________ 5 AW______________ 3 JO______________ 2 DY___________••_ 1

RV___..__________ 5 DL.-.------_.--- 3 JU___.. ______.__ 2 E.l---."."---.""- 1

I 1"11111"11111"11111"11111"11111"11111"11111"11111"1111IUIIII 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 IUIIII 1"1111 1"1111 1"1111 1"1111
TA:BLB 7-A.-The 1~ different dtgraph8 uj table 6 arraft,(Jed aecM'tli,., 16 lMir ahsohdeJrefJ.'Ue1/tcUI-Continued

111

TA:BLJl7:...c.-TM68tligrapMco~ng6Q%f)JfAt 6,()(}()digf'ttpM tI} Tdle (Ji l1Jt'rtl/nfledalpAa6~1J

aaM'tlfng If} lheir miIial UfW3

AE________•••• 1 HY__________ 1 PD___________• 1 WL_______•___... 1 (1) AND ACCORDING TO THEIR FINAL (2) AND-ACCORDING TO THEIR ABSOLUTE UO____._••_._ 1 JA.__•___..... 1 PN.___•____.... I WR..__________• 1 LETTERS FRli!QUENCIES YU__.____..•.•. 1 KA...__._.___•• 1 PV.__.____._... 1 is_..__._.__..__ 1 AL.____•___._•• 32 MA.__________••_ 36 AN...____________ 64 MA.______.____._ EZ.________••_. 36 1 KC__.____••.• 1 PW________... 1 WY__________•••• 1 AN_---...--••- 64 AT___.___•_____• FD_____.__••_. 47 1 KL._________• 1 py----------••• 1 XD_._.___.__•••• t AR.....___._.__• 44 ND_______• 52 AR.---.--.--.., 44 NT_______._••••_ FG________._ 82 1 KN••_.__._••••_ 1 QIl-------_.._. 1 XI____.______... 1 AS___________ 41 NE._________ 57 AS__________• ~. NE..___________• 57 FIl_._._••__•••• 1 KS_________•••• 1 QIl-------_._. 1 XV••__••_._____• 1 AT~__________ 47 NL...___... 30 AL.___•________ 32 Nl).-----_______ FP___•____•• 52 1 LG____•____•••• 1 RJ__________•• 1 m.________.... 1 NT______.____ FI___________... 82 NI--..- ..----- 30 1 LH.____•__••• 1 RK.____•••••_. 1 XN___•______•__• 1 CE.....__________ 32 CO.___________ 41

.' FY••___•____• 1 LN_________•••• 1 SIt__________ 1 XO________•___._ 1 CO._________._. 41 ON_.....___._•• 77 CE._.__.....____ GD___________ 32 ON...------____ 77 1 MD__________•••• 1 SV_________._. 1 XR..._.___•••••• 1 OR.-.._________• 64 OR.__•••______ GJ__________._•• 64 1 MF________.•••• 1 ST__._.......... 1 XS___... ___.___• 1 DA..__________ 32 OU____________ 37 DE-__•___•______ 33 OU______.__..___ GIl_._____._ 37 1 MH.______••_. 1 TG.________••• 1 YG._______••___• 1 DL---__•___• 38 DA..___________ GI_________• 32 1 NJ__________ 4

1 TQ.____________ 1 YH._.____.__••_. 1

I

RA._________.__ 39 RE.___________• HB______ 98 1 NQ.________•••• 1 Tz..__••_.____•• 1 Y1f____________• 1 EA._____•___•___ 35 RE...._.__•_____ 98 EN_____________ RT________._____ 42 HL...__....__•• 1 0.1.______._•• 1 OF___________••• 111 I ZA___________._. 1 EC_________•__. 32 RI _____________ 30 ER.._____________ 87

RA.________•____ HP______ 39 1 01._________._. 1 UV__________._. 1 ZI__________.___ 1 ED______•_____ 60 RO____.______e. 28 ED______________ 60

RS••_._______•__ HQ.____ 31 1 PB__________•••• 1: VO__••__••___• 1 --- RS.._.________ 31 RI ____________ EE."______•_____ 42 ES_••_._._____.• 30 HI 54 __.____._ 1 PC_____•____' 1 VT___________• 1 TotaL_.__ 5,000 Et...____•__._._ 29 RT_.__•______ 42 EE..________".__ 42

RO______________ 28 ;

I TABLE 7-B.-The 1.8digra~ composing t5% oj '''''digraphs in TahU6 arranged alphabdicallr

"

EW________••• 111 ET_____________ 37

according to their initialletter8 ER..___•••_•• 87 sa,------------ 49 EA._._______._. 35 gr----------_.- 63

1 ES________ U 51______._.. 3,( EC______.______ 32

SE.____________ 49

(1) AND ACCORDING TO' THEIR FINAL (2) AND ACCORDING TO THEIR ABSOLUTE B E'J______ 37 ST_.________•• 63 51.___________• "", EL.___________ 34 j.~ 29 LETTERS FREQUENCIES r;

""!;, TL.__......_ 28 TH..____________ AN___ 78 64 ON_.______•____ 77 AN__________•__ H- FI_________ 39 FO____________ 64 ON.••__________• 77 '~t TE.__________ 40 71 TE.___•_______._ OR.___________• 71 64 OR._____________ FO_____•__• 40 FI...._._____._ 64 TIi.______ 39 78 TO____________ 50 '>. TL._________ 45 T1._____________ ED________._.__ 45 60 RE.____••••_____ 98 EN______._••_. 111 RE.._____________ 98 HI________• 33 TO_.___________., 50

HI___________ 33 TY.____________• EN______________ 41 111 ER..•_______••_. 87 HT._._...____• 28 TW____________ 36

HT.______•____ 28 TW___._________ ER_____________ 36 87 SE._____________ 49 ED_________.__ 60 SE__________.___ 49 TY____________._ 41 TA.__.__________ ES_________.__•• 28 54 ST•_____________ 63 ES__•__•________ 54 ST______________ 63 IN____••__•__•__ 75 IN______•___••.• 75 10___._______ 41 UR.__________._ 31 IO___._._.______ 41 UR. ____________ TE..__________.__ 31 71 TH.___________._ 78 IS_______••••__ 35 IS______________ IN__________ 35 75 Tlt___________ 78 IN._._._________ 75 TE._____________ 71 VE.__________• 57 VE._.__________ TO____._____••__ 57 50 TO_________.••__ 50 LA_____-__ 28 LE..___.______._. 37

NO___.__._._.___ VE-____.______._ 57 NT___._..____.__ LE-________ 37 TotaL•••• 2,495 LA._______••_.__ 28 TotaL____ 2,495 52 82 VE..._.._______• NE 57 ______________ 57 NE..____._._____ 57

NT-•••--.----•• 82 TotaL____ 1, 249 NO.------.•----- 52 TotaL_._ 1, 24'

---------------,----------
i

·,

118

TABLE 7-D.-The 117 digr4phB composing 75% of the 5,000 digraphB of Table 6, arranged alphabetically according to their initialletters---

119

TABLE 7-D, Concluded.-The 117 digraphB compriBing 75% ofthe 5,000 digraphB of Table 6,

arranged alphabetically according to their initialletters--

rn AND ACCORDING TO THEIR FINAL LETTERS (2) AND ACCORDING TO THEIR ABSOLUTE FREQUENCIES

AC______________ 14 EP______________ 20 LO______________ 13 RI______________ 30 AN______________ 64 EL____________ 27 MA______________ 36 RI______________ 30

!

AD______________ 27 ER______________ 87 RO•.____________ 28 AT______________ 47 EP______________ 20 ME______________ 26 RO______________ 28

• AI ______________ 17 ES______________ 54 MA______________ 36 RS..____________ 31 AR______________ 44 EV______________ 20 RD______________ 17

· AL______________ 32 E'l'______________ 37 ME______________ 26 RT._.___________ 42" AS______________ 41 EF______________ 18 NT______________ 82 AM._____________ 14 EV______________ 20 AL_________.____ 32 EM.._____________ 14 NE___________•__ 57 ST______________, 63 AN______________ 64 NA______________ 26 SA__________.___ 24 AD______________ 27 NO______________ 52 SE______________ 49 AR._____________ 44 FI______________ 39 NC______________ 19 SE______________ 49 AI ______________ 17 FO_____________. 40 NI ______________ 30 SI______________ 34 AS______________ 41 FO______________ 40 NO______________ 52 SH..~___________. 26 AC______________ 14 FI______________ 39 NG______._______ 27 SR_____________ 26 AT______________ 47 NE.~____________ 57 sr______________ 34 AM.__________._. 14 NA______________ 26 SA_____________• 24 AU______________ 13 GE______________ 14 NG______________ 27 SO______________ 15 AU______________ 13 GH______________ 20 NS______________ 24 SS______________ 19 GR____________. 20 Nt _____________. 30 SS____._________ 19 GE______________ 14 NC______________ 19 SO______________ 15

BE____._______._ 18 NO______________ 18 ST______________ 63 BE.____________. 18 NO"_____________ 18 HA______________ 20 NS______________ 24 HI ______________ 33

CA._____________ 20 HE..__________._ 20 NT______________ 82 TA.,,____________ 28 HT____'__________ 28

TH______________ 78

CE...____________ 32 HI______________ 33 TE______________ 71

CO______________ 41 HA______________ 20 ON______________ 77 TK_____________ 71

CR________ "____ 14 HO______________ 20 OF______________ 25 TH._____________ 78 CE______________ 32 HE______________ 20 OR._____________ 64 TO______________ 50

CO______________ 41 HR._____________ 17 OL______________ 19 TI_".__.___.____ 45 CA_____________. 20 HO______________ 20 OU______________ 37 TI______________ 45

CT_.. __._.______ 14 HT_____________• 28 OM______________ 25 TO______________ 50

CR_____________ 14 HR._____________ 17

OF______________ 25 TY______________ 41

ON______________ 77 TR.••_••________ 17 CT_..._._.___.,. 14 011._____________ 25 TW______________ 36

DA___.__________ 32 IC______________ 22 OP_____________. 25 TS_________...__ 19 IN______________ 75 OP______________ 25 TA______________ 28

DE______... _____ 33 IE__________---- 13 OR______________ 64 TT______________ 19 DE______________ 33 IO______________ 41 OL______________ 19 TS______________ 19

DI ______________ 27 IG______________ 19 OS______________ 14 T'I___..________ 36 DA______________ 32 IS______________ 35 OT______________ 19 TT______________ 19

00______________ 16 IL______________ 23 OT______________ 19 TY_____._._____ 41 01._____________ 27 IR. _____________ 27

OS______________ 14 TR._____________ 17

OS______________ 18 IN______________ 75 OU______________ 37 00______________ 16 IT______________ 27

DT_____________• 15 IO______________ 41 UN___•.________ 21 DT______________ 15 IV"_____________ 25 PE______________ 23 UR______________ 31

IR. ____________. 27 PA__________.__. 14 UR..__._.__...._ 31 OS______________ 13 IL_.____________ 23 PR._____________ 18 UN______________ 21

EA_____________• 35 IS______________ 35 PE______________ 23 I C______________ 22 PO______________ 17

EC______________ 32 IT______________ 27 PO_______.______ 17 VE ...._--.....__......- 57 EN______________ 111 IG._____________ 19 PA______________ 14 VE_____________• 57 ED______________ 60 IV______________ 25 PR.___________._ 18 ER._____________ 87 IX______________ 15

EE______________ 42 IX______________ 15 WE______________ 22 ED______________ 60 IE______________ 13

EF______________ 18 QU______________ 15 WO_____________. 19 ES______________ 54 QU______________ 15 WK_____________ 22

EI______________ 27 LA______________ 28 EE______________ 42 LE______________ 37

WO______________ 19

EL______________ 29 LE______________ 37 RA______________ 39 YT..:.___________ 15 ET______________ 37 LA______________ 28 RE______________ 98

EM______________ 14 LI_____________ 20 RD______________ 17 EA____________•• 35 LL______________ 27 RT______________ 42 YT______________ 15

EN_____________ 111 LL______________ 27 RE---_______.-". 98 TotaL____ 3, 741) EC______________ 32 LI______________ 20 RA______________ 39

EL________.___._ 29 LO______________ 13 RS______________ 31 TotaL___ 3, 745

TABLE 7-E.-All the 438 digraphs of Table 6, arrangedfirst alphabetically according to their initial

letters and then alphabetically according to their final letters.

(SEE TABLE 6.-READ ACROSS THE ROWS)
j

-

100

TABLE 8.-TM 488 diJ!~r~nI digraphs of Table 6, arranged.fir81 alphabetically accoraling to their·

initial letters, and tMn according to their absoltde frefIlUncUs 'UruUr each initial letter 1

AN_.____________ 64 CT____________ 14 EO______________ 60 GH.._____________ 20 AT______________ 47 cr______________ 7 ES______________ 54 GE______________ 14 AIl_____________ 44 CL______________ 5 EE______________ 42 GA__________•___ 7

AS______________ 41 CK._____________ 4 ET______________ 37 GO______________ 6 AL_____________ 32 CR._____________ 4 EA______________ 35 GI_______________ 5 AO____________ 27 00__________.__ 4 EC___________•__ 32 GR._____________ 5

AI._._••________ 17 CC_____________ 3 EL______________ 29 GT______________ 4 AC_____________ 14 CO_____________ 1 EI___•__________ 27 GN____________._ 3 AM..___________ 14 CF____________ 1 EP______________ 20 GS______________ 3 AU____•_____ 13 CM._____________ 1 EV_____________• 20 GC___________._ 2 AP______•_____ 12 CN____________ 1 EF______________ 18 GF____________._ 2

AY__••_________ 12 CS______________ 1 EM.._____________ 14 GL______________ 2 AV____________• 7 CW__________••_ 1 EO__________.___ 12 GP______________ 2

AB____•__._.____ 6 CY______________ 1 EQ-_____________ 12 GU______________ 2 AG__________•___ 6 Eft_____________ 7 GO______________ 1

A1'-------------- 4 DE._____________ 33 EW______________ 7 00._____________ 1

M----------.--- 3 OA._____________ 32 EX.._____________ 7 GJ______________ 1 AW~_____________ 3 DL____________ 27 ss___.__________ 4 ~------------- 1 AH._____________ 2 00______________ 16 EG______________ 4 GW._____________ 1 AIt.__..____.___ 2 DT______________ 15 EY______________ 4 AO_________•__ 2 DS~------------- 13 EU____•_________ 3

~----------- 1 DR._____________ 12 EJ______________ 1

AJ_.__•______ 1 00______________ 8 EZ__________• __ I HI..------------- 33 OF______________ 8 HT______________ 28 BE____________ 18 DM._____________ 5 FO______________ 40 HA.._____________ 20 BY______________ 7 OP______________ 5 FI______________ 39 HE______________ 20 BL_________._ 6 ott_____________ I) FF____________ 11 00_____________. 20 BA________ 4 DB_••••_________ 4 FT______________ 11 HR._____________ 17 BO_____________ 4 DC_____________• 4 FE__________•___ 10 HU______________ 8 BI_______•___ 2 DN______________ 4 FR._____________ 9 HF______________ 5 BR._____________ 2 DW______________ 4 FA____••________ 5 HS______________ 4

BU______________ 2 04_____________ 3 FS______________ 3 He______________ 3 BJ______________ 1 OV______________ 3 FU____________._ 3 HN______________ 3 BM...___________ 1 OG______________ 2 FC__._._______._ 2 HO_____________• 2 BS____________ 1 OR______•______ 2 FL______________ 2 HM._____________ 2 BT._____________ 1 DQ-------------- 2 FD____________._ 1 HB___._.______• 1 OJ______________ 1 FG___•__________ 1 HL._____________ 1

CO______________ 41 DY_.____________ 1 FM._____________ 1 HP______________ 1 CE______________ 32 FP______________ 1 HQ______________ 1 CA______________ 20 EN__•__••____ ._ III FW______________ 1 HW_____________• 1

CH______________ 14 ER._________•___ 87 FY•_____________ 1 HY______________ 1

I For arrangement alphabetically first under intial letters and then under final letters, see Table 6.

,..

121

TABLE 8 Contd.-The 438 different digraphs of Tabu 6, arra;ngedfirst alphabetically acoording to

their'initial letters, and then according to their ab80ltde freg:u.encU8 'Under each initial letter 1

IN______________ 75 LI______________ 20 NE______________ 57 OA_____________• 7

IO_____________ 41 LO__________•___ 13 NO______________ 52 OV_______•______ 7

IS______________ 35 LY______________ 10 NI~------------- 30 00______________ 6

IR. __________•__ 27 LO______________ 9 NG______________ 27 OI______________ 5

IT_____________• 27 LT___________ 8 NA._____________ 26 OB___________• 4

IV______________ 25 LS._._________• 6 NS____________• 24 OE__________•••_ 3

IL______________ 23 LB_______•____ 3 NC____________ 19 OH.__________•__ 3

I C_____________• 22 LC_____________ 3 NO_____________ 18 00_____________ 2

IG______________ 19 LF______•______ 3 NF______________ 9 Olt __________._. 2

Ix..____________• 15 LP______________ 3 NN________•_____ 8 OY___________•__ 2

IE_________•____ 13 LM.._____________ 2 NU______________ 7 OJ_________•___ 1

IF______________ 10 LR._____________ 2 NL______________ 5 OX_________•____ 1

m _____________ 9 LU______________ 2 NM..___•____ 5

'IA___.________•• 8 LV______________ 2 NY_________•____ 5 PE___________••_ 23

IP_____________. 7 LW______•______ 2 NIt_____________ 4 PR._____________ 18

10_____________. 6 LG______________ 1 NR._____________ 4 PO______________ 17 .m _____________ 1 NP______________ 3 PA._____________ 14

[B______________ 2 LN____________ 1 NY_____________ 3 PL___________••_ 13

IK______________ 2 NW_____________ 3 PP________••_.__ 11

·IZ______________ 2 'MA.._____________ 36 NB____________._ 2 PT______________ 8

:ME..._._________ 26 ~------------- 2 PI_________._. 6

JE______________ 2 MM._____________ 13 NJ______________ 1 PS_______•____ 6

JO______________ 2 140______________ 10 NQ______________ 1 PM.._________ 4

JU______________ 2 MI_____________ 9 PR_________•___ 3

JA.____________• 1 MP_____________ 8 ON______________ 77 PU____________ 3

MB_____________ ·6 OR.__________.___ 64 PF_____________ 2

KE______________ 6 MS_____•____._ 4 OU_____________ 37 PB___________ 1

XI______________ 2 MC___________ 3 OF______________ 25 PC___________ 1

KA________••____ 1 ,MR__________ 2 OM.._____________ 25 PO____________ 1

lKC______________ 1 :MT_____________• 2 OP______________ 25 PN__________•• 1

KL______________ 1 W ______________ 2 OL_____________ 19 PV____________ 1

KN______________ 1 MY______________ 2 OT____________•• 19 PW_____________ 1

KS______________ 1 MD________._._._ 1 OS______________ 14 PY_________•___ 1

MF______________ 1

LE__•___________ 37 Ml-t_____________ 1 00______________ 12 QU____________ 15

LA.________•___ 28 OC____•_________ 8 QM----_._---_._- 1

LL______________ 27 NT______________ 82 OW______________ 8 QR-------------- 1

1 For arrangement alphabetically first under initial letters and then under final letters, see Table 6.

" 'l':

_--,;1_'\ ~~~_~~~====='_'='_'=~~

I 1"11111"11111"11111"11111"11111"11111"11111"11111"1111IUIIII 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 1"1111 IUIIII 1"1111 1"1111 1"1111 1"1111
122

TABLE 8, Concluded.-The 438 different digraphs of Table 6, arrangedfirstalphabetically according

to their initial letters, and then according to their absolute frequencies under each initial letter 1

RE______________ 98 SR______________ 5 US______________ 12 XI ______________ 2

RT______________ 42 SN______________ 4 UT______________ 12 XP______________ 2

RA______________ 39 SW______________ 4 UE______________ 11 XD______________ 1

RS______________ 31 SB______________ 3 UG______________ 8 XE______________ 1

RI______________ 30 SM______________ 3 UL______________ 6 XF______________ 1

RO______________ 28 SG______________ 2 UA______________ 5 Xlt_____________ 1

RD______________ 17 SL______________ 2 UI______________ 5 XN______________ 1

RP______________ 13 SK______________ 1 UM______________ 5 XO___________.-- 1

RR______________ 11 SV______________ 1 UB______________ 3 XR._____________ 1

RC______________ 9 Sy______________ 1 UC______________ 3 XS______________ 1

RM______________ 9 00______________ 3

Ry______________ 9 TH______________ 78 UP______________ 2 YT______________ 15

RG______________ 7 TE______________ 71 UF______________ 1 YF______________ 11

RN______________ 7 TO______________ 50 UO______________ 1 YS______________ 11

,RF______________ 6 ,TI______________ 45 UV______________ 1 YO______________ 10

RL______________ 5 TY______________ 41 YE______________ 9 ,RU______________ 5 TW______________ 36 VE______________ 57 YA______________ 6

'RV______________ .5 TA______________ 28 ,VI______________ 12 YN______________ 6

'RW______________ 4 TS______________ 19 VA______________ 6 YC______________ 4 RH._____________ 3 TT______________ 19 VO______________ 1 YD______________ 4

RB______________ 2 TR._____________ 17 VT______________ 1 YR______________ 4

RJ______________ 1 TF______________ 7 yI______________ 3

RK.___________ 1 TN______________ 7 WE______________ 22 YP______________ 3

TC______________ 6 WO______________ 19 Y5-------------- 2

ST______________ 63 TO______________ 6 WI______________ 13 YL______________ 2

SE______________ 49 TM._____________ 6 WA______________ 12 ¥M______________ 2

51 ______________ 34 TL______________ 5 WH.._____________ 4 YG______________ 1

SH______________ 26 TU______________ 5 WN______________ 2 YH.._____________ 1

SA______________ 24 TB______________ 3 WL______________ 1 YU______________ 1

55______________ 19 TP______________ 2 WR._____________ 1 YW______________ 1

SO______________ 15 TG______________ 1 WS______________ 1

SC______________ 13 TQ______________ 1 WY______________ 1 ZE______________ 2

SF______________ 12 TZ~ _____________ 1 ZA______________ 1

SU______________ 11 XT______________ 7 ZI______________ 1

SP______________ 10 UR______________ 31 XA______________ 2

SD______________ 5 UN______________ 21 XC______________ 2 TotaL___ 5, 000

I For arrangement alphabetically first under initial letters and then under final letters, see Table 6.

123

TABLE 9-A.-The 438 different digraphs of Table 6, arranged first alphabetically according totheir

final letters, and then according to their absolute frequencies

RA______________ 39 EC______________ 32 RE______________ 98 GF______________ 2

MA______________ 36 lC______________ 22 TK_____________ 71 PF______________ 1

EA______________ 35 NC______________ 19 NE______________ 57 CF______________ 2

DA______________ 32 AC______________ 14 YE______________ 57 MF______________ 1

LA_________ .;____ 28 SC______________ 13 SK_____________ 49 UF______________ 1

TA______________ 28 RC______________ 9 EE______________ 42 XF______________ 1

NA______________ 26 OC______________ 8 LE______________ 37

SA______________ 24 'TC______________ 6 DE______________ 33

CA__________.: ___ 20 DC______________ 4 CE______________ 32 NG______________ 27

'HA_______.;______ 20 YC______________ 4 ME______________ 26 IG______________ 19

PA______________ 14 CC______________ 3 PE______________ 23 UG_____________ 8

WA_______.;______ 12 HC______________ 3 WE______________ 22 RG______________ 7

lA______________ 8 LC______________ 3 HE______________ 20 AG______________ 6

GA______________ 7 MC______________ 3 BE______________ 18 EG______________ 4

OA______________ 7 UC______________ 3 GE______________ 14 DG______________ 2

VA______________ 6 ,FC______________ 2 IE______________ 13 OG______________ 2

yA______________ 6 GC______________ 2 UE______________ 11 SG______________ 2

FA______________ 5 XC______________ 2 FE______________ 10 FG______________ 1

,UA______________ 5 KC______________ 1 YE______________ 9 GG______________ 1

;BA______________ 4 ,PC______________ 1 KE______________ 6 LG______________ 1

,AA______________ 3 OE______________ 3 TG______________ 1

XA______________ 2 JE______________ 2 YG______________ 1

JA_______.______ 1 ED______________ 60 ZE______________ 2

KA______________ 1 NO______________ 52 !E______________ 1

,ZA______________ 1 AD______________ 27 XE______________ 1

RD______________ 17 TH______________ 78

AB_______.,______ 6 OD______________ 12 SH______________ 26

ME______________ 6 LD______________ 9 GH._____________ 20

,DB._____________ 4 DD______________ 8 OF______________ 25 CH______________ 14

,EB_______ .;______ 4 ID______________ 6 EF______________ 18 EH______________ 7

DB______________ 4 TD______________ 6 SF______________ 12 NH______________ 4

LB______________ 3 SD______________ 5 FF______________ 11 WH______________ 4

SB________.;_____ 3 YD______________ 4 YF______________ 11 OH._____________ 3

TB______________ 3 00______________ 3 IF______________ 10 PH._____________ 3

UB._____________ 3 HD______________ 2 NF______________ 9 RI,L_____________ 3

IB______________ 2 CD______________ 1 DF______________ 8 AH._____________ 2

'NB______________ 2 FD______________ 1 TF______________ 7 DH._____________ 2

RB______________ 2 GD______________ 1 RF______________ 6 LH._____________ 1

,yB______________ 2 MD______________ 1 HF_________.____ 5 MH______________ 1

HB______________ 1 ,PD______________ 1 AF______________ 4 XH______________ 1

PB______________ 1 XD______________ 1 LF______________ 3 'YH______________ 1
-.,

124

TABLE 9-A, Contd.-The 488 dijfe1'em digraphs qj Table 8, arramgedfir8' alphabetically according

to theirjinalletter8, and then Q,CCordin(J to t/urir ab801llde jrefJ.1U'nCie8

125

TABLE 9-A, Co~clud~d.-:-Tk8 488 dijftrMt digraphs oj Tahl86, (l,rranged fir8t a1plUJl)e~ally accord'!,ng to the'!,rjinalletttr8, and then according to ,Mit' ahsol'l.de frequencies

TI______________ 45 LL.._____________ 27 AN______________ 64 RP_____________ 13 ES______________ 54 OT______________ 19 JU______________ 2 PW______________ FI_____________• 1 39 Ik_____________ 23 UN____________•. 21 AP____._.___•••• 12 AS______________ 41 TT______________ 19 LU______________ 2 YW______________ SI______________ 1 34 OL______________ 19 NN______________ 8 PP_________.____ 11 IS_______•______ 85 DT______________ 15 MU______________ HI ______________ 2 33 PL___._••_______ 13 RN______________ 7 5P__.______.____ 10 RS_______•______ 31 YT_.___________• 15 YU._____________ 1 IK.._____________ NI______________ 15 30 BL______________ 6 TN__________••• 1 MP_________••••• 8 NS_.____________ 24 CT______________ 14 EX.._____________ RI______________ 7 30 UL._____________ 6 YN______________ 6 IP_____•___•____ 7 85_.____________ 19 UT______________ 12 IV__________.___ 25 Ox._____________ 01______________ 1 27 CL_.___________• 5 ON_____________• 4 OP_____________ 5 TS______________ 19 FT______________ 11 EV______________ EI___•________._ 20 27 NL______________ 5 SN______________ 4: LP______________ 3 05______________ 14 LT______________ 8 AV______________ 7 Ty______________ J.,I--____________ 41 20 RL.____________ 5 GN______________ 8 NP_.____••_••___ 3 OS______________ 13 PT______________ 8 OV___-__________ 7 Ay______________ AI______________ 12 17 TL._____________ 5 HN______________ 3 YP__________•___ 3 US______________ 12 XT______________ 7 RV______________ 5 Ly______________ WI______________ 10 13 OL_____________• 3 WN______________ 2 GP___________•__ 2 yS______________ 11 GT______________ 4 OV______________ 3 RY______________ VI______••______ 9 12 FL______________ 2 CN___•__••___•__ 1 TP_________•____ 2 LS______________ 6 MT______________ 2 NV______________ 3 BY____--________ 141______________ 7 QL------------- 2 !<N--____________ 1 UP_____________• 2 PS______________ 6 BT______________ 1 LV______________ 2 NY______________ ,CI______________ 5 1 SL---__________ 2 LN______________ 1 XP____________ 2 HS______________ 4 VT______________ 1 PV______________ 1 EY______________ ,fI_••____._.____ 4 6 ,YJ,.--.-.-------- PN_____•________ 1 'FP______________ 1 MS______________ 4 SV______________ 1 MY______________ 2 ,GI--------_-"7"~, f) 'HL------------- :1 )[N-------------. l iiP____.______ 1 FS'-_____________ 3 OU______________ 37 UV__ ._-_________ 1 OY______________ ,01______________ 2 6 ~----_._-_._.- ·l EQ._____________ 12

G5______________ 3 QU______________ 15 CY______________ IUI___•__••._____ 1 6 WL.._____________ 1 ':TO______________ lSp DQ.________•____ 2

BS______________ 1 AU__________ __ 13 TW______________ 36 DY______________ YI_________-_-_- 1 "8 co_________.____ 4~ HQ._____•__•____ 1

CS._____________ 1 5U______________ 11 OW._____________ 8 FY._________.___ BI______________ 1 2 KS______________ 1 HU____•_______• 8 EW____••_______ 'OM..______.______ 25 IO_____________• 41 NQ.__•_________• 1 7 HY______________ ;KI_.________•___ 1 2 FO______________ TQ._____________ 1

WS______________ 1 NU______________ 7 DW______________ 4 PY_------------- 1

AM.._____________ XI ______________ 14 40 2 RO____•____._ XS______________ 1 DU______________ 5 RW______________ .4 SY______________ ZI______________ EM...-.---.•-- 14 28 1 1 MM._____________ 13 HO_____________• 20

ER._____________ 87 RU______________ 5 SW______________ 4 WY______________ 1

1'0______________ OR..____________ 64 NT______________ 82 TU______________ 5 AW______________ 3 IM.._____________ 1) 19 AR._____._______ 44 ST___.__________ 63 CU______________ AJ ______________ 4 NW______________ 1 RM._____________ 9 NO__•___________ 18 3 IZ-_____________ 2 BJ__________••__ 1 17

UR.____________ 31 AT______________ 47 EU______________ 3 LW______________ 2 EZ._____________ 1 TIl_____________ 6 PO_____________• IR. ________._. ~7 RT_____•_______• 42 OJ______________ FIJ._____________ 1 3 CW______________ 1 TZ______________ 1 DM..___________ 5 00_____________ 16 PR..••__••••_._ 18 ET___•__________ 37 EJ______________ PU______________ 1 50_____________• 3 FW______________ NM'..__________._. 5 15 HR._____________ 1

1'1 HT______________ 28 GJ BU______________ ___•_______.__ 1 UM.._____________ 5 LO________•___._ 13 '2 GW______________ 1 TotaL___ 5, 000 NJ_____________ 1

TR.___________ 17 IT______________ 27 GU______________ 2 HW______________ 1 PM.._____________ 4 EO______________ 12 OR._____________ OJ_____________ 12 1 SM___•_________ 3 MO______________ 10 RR.________•___ RJ______________ 1.1 1 m ____________. 2 YO______________ 10 FR.----_______ 'LM.._____________ 9 2 GO______•_______ 6 GR._________•___ CIt 5 _____________ 4 YM..____________ 2 00______________ 6 5R.______•______ AK. 5 _____________ 2 BM.___________._ 1 BO______________ 4 CR.________•____ 4 IK._____________ 2 CM.____________• 1 AO_______•_____• 2 HR._____________ N'K..____•_______ 4

2 FM._____________ 1 J 0_____________ 2 Ylt___._._______ OIt 4 _____________ 2 GM.._____________ 1 '00______________ 1 BR._____________ 2 ,R.K._____________ 1 QM.------------- 1 VO_____•________ 1 LR..____________ 2

.5K.-----------r 1 XO______________ 1 .MR.----____••_._ EN________••__ 111 QR..-----------_. 1 AL._____________ 32 ON______________ 77 OP_____________• 25 WR.__•_______._ 1 EL._____________ 29 IN__________._._ 75 EP•__._.________ 20 XR.__._••_••__•• 1

148274--38_9

_________________1 _
126 127

TABLE 9-B.-The 18 digrapluJ composing £6% oj tM 6~OOO digraph8 oj Table 6, arranged alphabetically. according to theirfinal letters-----

(1) AND ACCORDING TO THEIR INITIAL (2) AND ACCORDING TO THEIR ABSOLUTE

LETTlmS FREQUENCIES

3~

31

82

63

47

4~

37

28

NT _

ST _

AT _

RT _

ET _

HT _

50

41

41

40

28

TO _

CO _

IO _

FO _

RO _

m _

,

TABLE 9-D.......,The 117 digraphs composing 76% oj the 6,000 digraphs oj Table 6, arranged

, alphabetically accor4ing to theirfina1letter~ .. '

(l) AND ACCORDING TO THEIR INITIAL LETTERS

TABI!~ ,9-'C, Concluded.~17t.e63 digiVJ,p'h8 comporing 60% ,6J the 6,000 digrlUph, oj Table 8,

arranged alphabetically according wtheirjirwJ, letterB--

(2) AND ACCORDUWTO THEIR. ABSOLUTE FREQUENC~ES

39 LE._____________ 3'1 ON______________ 77 IS _

36 DE._____________ 33 IN______________ 75 RS- _

35 CE._____________ 32 AN______________ 64

32

28

28

~-------------- MA.. _

EA _

01. . _ LA _

TA. _

;rI-------------- 45 EC_________.-.-- 32 FJ;-------------- 39

Ep______________ 60

SI______________ 34

NO______________ 52

HI______________ 33

NI______________ 30 RE______________ 98 R!______________ 30

TE______________ 71

NE_____________ 57 AL______________ ~2

VE-7-~"·-------- 57 EL._____________ 2~ SE______________ 49

EE______________ 42 ''m_~____________ III

CA______________ 20 NO______________ 52 EF______________ 18 SI______________ 34

DA.____________• 32 RD______________ 17 OF_____________• 25 TI______________ 45

EA.._____________ 35

HA.._____________ 20 BE._____________ 18 IG______________ 19 AL______________ LA. 32 _____________ 28 CE______________ 32 NG____________ 27 EL._____________ 29

14A.------------- 36 DE______________ 33 IL______________ 23 NIL____________ 26 EE._________•___ 42 CIt_____________ 14 LL._____________ 27 PA..____________ 14 GE.___________._ 14 GH.._____________ 20 OL______________ 19 ~------------- 39 HE______________ 20 SH.___________ 26 sA..____________ 24 IE__________••__ 13 TH._____________ 78 AM._____________ TA.._____________ 28 LE______________ 37 14

ME______________ 26 AI______________ 17

EM._____________ 14 , DI ______________ ~7 OM.._____________ AC______________ 25 14 NE______________ 57

EC______________ 32 PE______________ 23 EI______________ 27

rc______________ 22 RE._____________ 98 FI______________ 39 AN______________ 64

NC______________ 19 SE______________ 49 HI______________ 33 EN______________ 111

TE_____________ 71 ~I-------------- 20 IN______________ 75

AI)..____________ 27 VE______________ 57 NI______________ 30 ON______________ 77

ED______________ 60 WE._____________ 22 RI ______________ 30 UN______________ 21

I

h

1

,

I

54

50

75

64

82

63

87

64

35

31

37

36

41

47

37

28

.82

42

63

TotaL____ 2, 495

TotaL 1,249

IN _

AN •

OU _

ER _

OR. • _

ES _

AT _

ET •

HT _ NT _

RT ._

ST _

'IS _

~S _

TW _

TY _

,TO _

,NT _

ST _

78

60

52

41

40

41

28

50

44

87

64

31

98

71

57

57

49

41

54

111

75

77

EN______________ III

ON______________ 77

ED _

NO _

TH. _

CO _

FO _

IO_: _

RO _

TO _

RE _

TE _

NE _

VE _

SE _

AS _

ES _

EN _

IN _

ON _

AR. _

ER _

OR. _

UR. _

75

77

54

50

78

87

64

82

63

32

29

98

49

71

57

39

33

30

30

34

45

64

ES _

TotaL 1, 249

IN _

ON _

TO _

TH _

AL _ EL _

NT _

ST _

FI _

HI _

NI _

RI _

SI _ TI _

AN _

ER. _

OR. _

RE _

SE _

TE _

'VE _

78

57

98

49

71

57

60

52

32

32

33

42

37

57

60

52

(1)

32

35

28

36

39

28

TABLE 9-C.~The 63 digraphs composing 60% oj the 6,000 digraphs oj Table 6, arranged

OJ,phabetically according to theirfinal letters--

AND ACCORDING TO THEIR INITIAL LETTERS

ED _ NO _

TH.. _

EC _

NE _

RE _

SE _

TE _

YE _

ED _

NO _

CE _

DE _

EE _

LE _

NE _

l:>A. _

'EA _ LA _

MA.. _

'RA. _

TA. _

AN . 64

'EN______________ 111
128

, :'(2) AND A.CCORDING T0'l'HEIR:4BSOLUTEFREi!t!TENCIJil41

TABL:m9-D, Oontd.-77w 111 j,i!1'a,hicom:fHJri1lfl 76%.oJ 1M 6,OOOlligrapA."Jfl'oJu ',arranged

al~l"fuoordi,.".·~ji'WiJlls#.r...-

(1) AND ACCORDINCl TO THEIR INITIAL LEJ'tTERS--,-Contlnued

M._____________ 39 TE____________ .71 m _____________ 78 ~--r_-------- 14

MA__:________\_~~ 3'6 'I mL__~~ __~~- 57 @'" "

.'26 !M.__ __________ .. .......----""":T--- . 14

EA______________ 35 VE________~~~_~2'· "~ ).\ G'lL__~~_~_~_:~~ 1,1 ,\\~O'

DA______________ 32 ~'

-SE~"••---•••.i--- ::i,9- CH-i.•---......_ 1+ EN______________ LA______________ 111 28 SE-------------- 42 TI _____________. 45 TA 01'1._____________ 77 ______________ 28 LE__________ ___ 37 MA______________ 2& D!______________ 33 FI_________•____ 3D IN-----;--.----- 76

SA______________ 24 CE______________ 32

SI______________ 34 Alt _____________ 64

CA______________ 20

.--------------

26

HI______________ 33

UN____________ U

HA._____________ 20 P!.._._---------- 23 HI_____________. 30

PL _____________ a WE____.:_________ 22 RI________.__.._ 30 TO._.___________ 50 HE______________ 20

01_____________. 27 CO______________ 41

Ee-------------- 32 EI___________._. 27 10______________ U IC_____.________ 22 IS!______________· 18

LI _________..__. 20 FO_______...__._ 40 NC______________ 19 Gl!:__•___•_______ 14

.AI______________ 17 RO______________ 28 Ac______________ 14 IE______________ 13 !L._____________ 39

HO______________ 20

ED______________ 60 EL._____________ 29 WO___._.______._ 19

NO______________ 52

or______._______ 25 laL-------------- ~7 NO______________ 18

!D._____________ 27

EP'___ __________ 18 IL______________ 23

PO______________ 17

RD______________ 17 Ok---_________. 19

00_______.______ 16

NG______________ 27 so______________ 15

RE______________ 98 lG____._._______ 19 OM______________ 25 LO______________ is

ErG-------------------------- 135

FIV--------:-----------:_____ 135- MJ!:N__________________________ 131

SEV .____ 131

ERS .•• ••• l~ 6

UND••• •• 125

NET • .118

PEIL________________________ 115

STA._________________________ 116

TER__________________________ 115

EQU .__. • 11.

REO__._______________________ 113

TED .____ 112·

ERI • 109

HXR._________________________ 106'

IRT ..•------..-.--- 106

DER .______ 101·

DREl.__.______________________ 100

TOP ._____ 174

NTH.. .____________ 17t

TWE. .___ 170

TWO_.________________________ 163

ATI_________________________ 160

THR. •__•__• 158

NTY__________________________ 157

HRE. .________ rss

WiN ._ 16a

FOU .__.___________________ 152

ORT. . .__.__ 146

REE__________________________ 146

SIL.__._. .___________ 146

ASH.________________________ 143

DAB__._______________________ 140

IGH. .____________________ 140

ERE. .____ 138

COM- .__ 136

ATE.. . • •• 136

'r ..,.

OP__•_______.___ 25 ES______________ 54 AT______________ 47 QU______________ .16 EP_________.__._ 20 AS____________._ 41 RT_______••••_._ 42 AU______________ 13 IS____._________ 35 ET__•.___._._••_ 37 RS______________ 31 HT______________ 28 IV_____________. 25 EIl_____________ 87 NS.____________ 24 IT______...........""_ 27 EV______________ 20

OR.___._..______ 64 $S-------------- 19 OT_______.._.__ 19 AR____________. 44 1'5_____________ 19 TT_______.....__ 19 TW______________ 36

UR._____________ 31 OS____________._ 14 DT_______.....__ 15 IX.__________.__ 115 IR.•••__._•••__• 27 DS______________ 13 YT_._____•••••__ 15

fR._. __.•______• 18 CT________._.___ 14 TY______________ 41

HR.••__••__••••• 17 NT______________ 82

'I'R._.__••______• 17 ST_____________ 63 OU__________••_ 37 TotaL____ 3, 7.i'

" '.' ',' '\. '. \1):,._' " ,

(2) AND ACCORDING TO THEIR ABSOLUTE FREQUENCIES-Continued

TA8LB9...D, Concludedj~:l1l41.t1' digrapM ,eompoling, 76% oj,the 61JOO digrdJph8~r'T~ IT;.'

arran-led 4lpMbetically~ng '0 theirfi'Nll kU,rs "

TABLE 9-E.-AU tht 481dijferem digraphs of Table 6 arranged alphabetically jirst according fa

theirfinal letters and thtn according totAtlr initial letters

($EE TABLE '6;-READ DOWN THE COLUMNS)';

TA8LE lQ-A.-Tht 66 trigraphs appearing 100 or more times in tht 60;000 letters of Govern1M'llJ

p14in-te:dltlegrams atTlJfI{Jed according to tMir ,absol'lde fNf.1Uncie8

ENT__________________________ 569

ION. • ._ 260

AND . ._ 228

ING.________________________ 226

lVE •• •• •• 22.5

1.10. . . --"___ 221

FOR- -- __.____ 218

OUR. .____________ 211

THI..------- ._________ 211

ONE._________________________ 210

NIN... • ._______________ 201

STO._________________________ 20:a

EEN'. . • 196

GHT" .•. .________ 196

INI!i.. .__._ 192

VEN•• 190

l!:VE_.__. .__. .______ 177

EST. ..._._________________ 176

TEE.._______________________ 17..

,'TotaL 3,74S •

YT_____________ 15

AU___________.._ 13

au-------------- 17

QU------------- 15

EV______________ 20 IV______________ 25

'tW________ _____ 96

;tx.------------- 15

'1'I______________ 41','!

cO_______.____._ 41 Alt_____________ 44 05______________ 14 DO______________ 16 '11l_____________ 17 XS______________ 36

FO_____________ - 40 tnt _____________ 81 1tS______________ 31

HO________"C____ 20 ER._____________ 87 10______________ 41 OR_____________ 64 AT______________ 4'1 LO________c_____ 18 PR_____________ 18 CT_________.____ 14

NO______________ 18 AIl_____________ 17 DT______________ 15

PO________.;__"__ 17 IR__.__________ 21 E'1'_____________. 81 kO______________ 28 M'l___________.__ !8

SO____________._ 15 AS______________ 41 ;r'i'______________ 27 TO______________ tid ss______________ 19 NT______________ 82

WO______________ 19 rs,_____________ ~9 OT______________ f9

s., DS______________ ,18 RT______________ 42

EP_________.____ 20 ES__•___________ 64 sf______________ ~a

OP________c;____ · , ,Is NS______________ 24 tIr______________ 19

I

~,_ I l i

II
1111111 1111111 1111111 1111111 1111111 1111111 1111111 1111111 1111111 1111111 1111111 1111111 1111111 1111111 1111111 1111111 III~III 1111111 1111111 1111111 1111111 1111111 111(11

1BO' 181

TA"IlLE 1Q-C.-The 56 ~aphs appearing 100 or more times in the 60,000 letur« of Govemmtnt.

-. plain-text telegram~ iairanged jir8t. alphabetically accord~ng to theit central letters and the~

: according to their abirolute jrequenc¥s

STA. . . .._ 115

OUR.. ... .__. 11

IVE . ._••_.... 225

EVE. . . 177

TWE-.--.-- ..__.__.________170

TWO__. ._.._._. .__ ' 163.

TER. .._. ... 11'5.

HIR .._.. .______ 106

DER . . .___ 101

ENT_.__.._•._. OM • 569

GHT .. ... . 196

EST •. 176

ORT . .__._._. . .146

NET ._._____________ 118

IRT .• .. 105

DAS.__ ._ 140

ERS_•... ._______ 126

FOU. .___________________ 152

EQU__________________________ 114

FIV__________________________ 135

SEV ._.._. .__.• 13.1

SIX- ._________ 146

NTY.- . .__________ 157·

DRE ._________________ 100

EST_._. .__________________ 176

ASH.__. .___ 143

STO__________________________ 202

NTH. • .• 171

ATL ._______ 160

NTY._________________________ 157

ATE . ._____ 135

TH!..________________________ 211

AT!..______________________ __ 160

ERI.•._•._.__________________ 109

COM-._______________ 136

IGH. ._______ 140

ION ._______ 260

NIN.. .. 207

EEN .____ 196

VEN__________________________ '190

WEN__________________________ 153

MEN__________________________ 131

TIO__________________________ 221

STO__.. . 202

TWO ._______________ 163

TOP.. • . .: 174

FOR ._. .___ 218

OUR .____________________ 211

THR_________________________ 158

PER_.__.. ._. 115

HRE ._.___________________ 153

o:R.T . .________ 146

EQU .. .__._. 114

ERE. . . 138

ERS_. ._. .__________ 126

ERL .__ .__ 109

IRT .____ 105

TABLE ~o-D.~The 56 trigraphs appearing 100 or more times in the 50,000 letier« oj Government

pla~n-text telegrama arrangedjirst alphabetically according totheirjinalletters and thenaccording

totheirab80lute jrelJ.'U6ncie8

TABLE IO-C, ConcJuded.~ The 66 trigrams app~ari'1/,fJ 100 or more time8 in the 60,000 letters' oj

Government plain-text telegrams arranged jir8t alphabetieallyaccording to their central letier«

and then according to their ab80lute frequenciee

IVE ._ 225

ONE•.. .__.__.___________ 21 0

lNE . .__.._.____ 192

EVE.. .__• 177

TEE.. ._..... 174

TWE_._. . •__.. 170

HRE_.________________________ 153

REE..._. .____________ 146

ERE. . .._.____________ 138

ATE.._________________________ 135

DRE.._._. . .. 100

STA. . ._ 115.

AND... .. 228

UND ••__••••_••_._.__. 125

RED :_______________ 113

TED__. . • 112

ING. . .__.. 226·

EIG_._.. .•. .. 135

NTH.•••• • . • 171

ASH.•.•__._••••_.•._.. ._._ 143

. I

202

146

13.1;

115

Hllt_.__..... fa 6

ENT~ ._•••• • • 569"

AND__. ::_______ 228·

lNG .__.; ·226:

ONE .________ 210

lNE_..._.: . . 192·

UND : • 12q

ION. . . 260

FOR ._.__.._.._. 218·

TOP.._.__._•••..•..__.._..... 174

FOU_.________________________ 152

COM-_________________________ 136

VEN ~____________________ 190

WEN. . .__. 153

REE.. . 146

_RED ".-~------------ ..--- 113

· UNO" ••._._·. . ._ 125

·STO _

,SIX- ""_"' .__

SEV .~c--.-- .. .•

.STA.. ~-----------------

TIO -------- 221'

THL .2_'-_________________ 21:1

·TEE ~l._L .---- 174 ..

·'TOP ._. . .-___ 174'

TWE_._.______________________ 170

. , TWOL ~~_~~c_. ~_"" __~~__ 1'63

THR...:L •__.________ 158

TER_________________________ 115

TED . . ...__ 112

.,

TIO... 221

NIN•. .._... 207

SIX-_________________________ 146

EIG ._ _. . 135

FIV._. . ._.__._.. 135

IGH._.____________ 140

THI_. ., .._.. . 211 , .

GHT•..:______________________ 196

THR ._.__. ._. . 158

IJEIt . ._._._.. 101;

HRE__________________________ 153

HIR_________________________ 106

ION •••• "----- 260

ING . .___ 226

IVE , ------..__----- 225

INE ,..._________________ 192

IGH. ,_~________________ 140

IRT. ~. c~---- 105

-MEN ~:~~ .:_~~_. 131

..OUR._. ': .'_~.~ __..•...' 211

ONE.. •••• • •••_._ 210

ORT- .________ 1~6

PER__.__. . 115

'>:·,i-:'~'.'i··.-'· .>. I,"!"",~, ,.-:

. 'ftI~--...-..••-..--.-,~-".... 207 . ' .N'm. ~____ 171 .

N'rY~_. ~.~~~.!••~_••L.L_... 157;.

NET•.• ..__._. .._._ 118 '-', . \

'. I',

140

101 :

100'. '

i' '

DAS . ..__• 140

BEN._________________________ 196

VEN . . ._..... .. 190

'l'E:E.._•. ._________________ 174

WEN__________________________ 153

!tEE.... •.. 146

EN .___________ 131

SEV .__ ... ._. .___ 131

NET._. • ._ 118

PER . ._____ 115

TER_._._..••._••..••..._.•_. 115

RED. ._....•_.._. . 113

TED ._. •••••••-. •• 112

tOR.-------------------.---.. 21.8 FOU • •••••••• 152-

FIV.-..-.--------------..-.-- 135

DAB ....._ DER. •. •._.••_~:_

~RE---.-----------------.__~-

COM. .__ 136

ENT_. . • •• 569.,

EEN~.L_: __:__.__ ~~~~~~_'______ 196'

~E..--,.---------.---....-.".... J.7.1 . . T~__ "_'_~_~~~~ .__..~L~••~~· '1:tA, ., ERE.•••• • 138

EIG_. _.•__. 136

ERS••._._ . .__ 126

EQU~ c_~~_c_~~__~._.~.... 11'4

ERI. ._. . :~l.... 1'09

TA.m.E 10-':J3. "1'Ite"68 ~apM appearing 100 or m~time8 in 'the '.oo,OOO'UtitrB -oj Govemment

plain-text teleqram« airanged first alphabeticaU,!/according.tv their initial letter« and then

according to their ab80lute jrelJ.'U6ncies

AND "--"- 228 GHT • ..• 196

ATL__. ._.__ 160

ASH._________________________ 143

ATE •__._ 135

j

;, I

11
182

TABLB ll-A,.-TM 64- telragraphl ap1MfJ1'ing 60 or more timee in tM 60,000 kffers oj Go,emmlnl

plain-tezt teugramll arranged acoording to tw abBOl'lllefr~

I

TABLE ll-B.-The 54- tetragraphs appearing 50 or more times in tM 60,000 utters of GoVI'mment plain-text telegrams, arra'Tl4ea first alphabetically according to t/I,N initial letters, and th#m ,accord'tng to their aliaQl'llle frequencies

TION .___ 218

STOP________________________ 154

RIOD .___ 63

FROM._______________________ 59

COMM.__ ..... ••__ 98

OMMA.• • 71

TWEN ._ 152

EVEN. 168

IVED________________________ 62

ASHT --------------- 64

QUES___ 87

HUND________________________ 64

OURT•__.__ ..__ .• 56

AUGH._______________________ 52

STOP._______________________ 154

RTEE ~____ 59

STAT 54

EQUE .__ 86

HREE._______________________ 134

ERIO ._______________ 66

DRED.__._ 63

FROM._______________________ 59

IRTY ._ 59

.. WENT_•. ..••_.__•••_.. 153

NINE__•__•__•.__._•..__• 153

MENT •. • ••_. 111

EENT________________________ 102

VENT________________________ 70

HUND ._.____ 64

CENT 52

EIGH._______________________ 132

AUGH._._____________________ 52

IGHT 140

ASHT___ 64

UGHT________________________ 56

OLLA________________________ 70

DOLL________________________ 68

THIR._______________________ 104

THIS________________________ 68

ERIO________________________ 66

FFIC________________________ 62

ENTY ._________________ 161

ENTH________________________ 114

ENtr'S .. 62

UNDR._______________________ 59

FOUR________________________ 144

COMM._______________________ 93

DOLL________________________ 68

OMMA________________________ 71

LLAR. __._______________ 71

OLLA________________________ 70

TION ._ 218

NlNE .____ 153

FIVE ._______ 135

EIGH._______________________ 132

HIRT ._______ 97

RIOD________________________ 63-

FICE._______________________ 50

THIS________________________ 68

EVEN .._ 168

TEEN. .__________________ 163

TWEN .__________________ 152

HREE________________________ 134

QUES ._. ._ 87

DRED________________________ 63

IVED ._._ 62

RTEE. ._ 59

UNDR________________________ 59

FICE. ._ 50

LLAR. ._ 71

STAT________________________ 54

FFIC________________________ 62

THRE._______________________ 149

THIR._______________________ 104

TABLE ll-D.-The 54- tetragraphs appearing 50 or more times in the 50,000 letters of Government

plain-texttelegrams arrangedfirstalphabetically according totheirthird letters and thenaccording

to their absolute frequencies

11111111111111111111111111111111111111111111111111111111111111111111111111111111111111I1111111111111111111111111111111111111111111111111111111111~11I111I11111II

!

IGHT________________________ 140

UGltt 56

133

TEEN__._____________________ 163

WENT 153

SEVE. .___________________ 121

MENT________________________ 111

EENT 102

REQU________________________ 98

UEST 87

VENT. .__ 70

PERL______________________ 67

CENT________________________ 52

NDRE. .__ 77

TABLE Ll-C.- The 54-tetragrapks appearing 50 or more times in the 50,000.letters of Governmenf

plain-text telegrams arranged first alphabetically according to their second letters and then

according totheirabsolutefrequencies

DASH..• .__ 132

LARS________________________ 68

NAUG . 56

Ifr,lt

.f!

WENT ._________ 153

VENT________________________ 70

UEST.__...• ._._ 87

UNDR._______________________ 59

UGHT ._________ 56

REQU________________________ 98

RIOD________________________ 63

RTEE.. ._____ 59

STOP_.__.__.•_. .________ 154

SEVE ._____________ _ 121

STAT ._. ._ 54

TION .__________________ 218

TElEN .____________ 163

1'WEN_.• . .______ 152

THRE.. .______________ 149

THIR. .__ 104

THIS .___________ 68

ASHT_. .____ 6:4

HUND. • 64

DRED ._________________ 63

RIOD________________________ 63

lVED_______________________ 62

MS_... .__ 62

FFIC . 62

FROM._______________________ .59

IRTY . .__.. .59

RTEE________________________ 59

UNDR.• ._.. 59

NAUG_.__.. .______ 56

OURT.__._._.__... __•__•• • 56

UGHT._.__._•• ••_......... 56

STAT__ •••__._. ••••_. 54

AUGH.. .___ 52

CENT._______________________ 52

FleE • ••. .. . 50

PERL______________________ 67

QUES .__________ 87

OMMA. .. .,1

OLL!. .. .___ 70

OURT•. .__ 56

LLAR.._______________________ 71

LARS..__.______ 68

MENT. .______________ 111

NlNE. ._________________ 153

NDRE.. . • 77

NAUG .. .. 56

HREE. .______ 134

HIRT

. 97

HUND ._________ 64

IGltT. .______ 140

lVEo. ._ 62

IRTY .____________________ 59

THIR..______________________ 104

EENT 102

REQU ._. .__..._.__ 98

HIRT 97

OOMM.._______________________ 93

QUES . .. 87

UEST 87

EQUE._______________________ 86

NDRE .. 77

OMMA.._______________________ 71

LLAR._______________________ 71

OLLA._~ . •__._. 70

VENT._•••_._.__•••_••_.__••• 70

OOLL..•••••.•• ••_•••_.... 68

LARS________________________ 68

THIS • 68

PERI• 6"

ERIO .__..__ 66

DASH..._••••••_•.•••__.•_•.__ 1.32

DOLk ._______________ 68

DRED________________________ 68

FOUR • ..__ 144

FlVE ._.________ 135

FFIC . 62

FROM. .________________ 59

FICE. __.__. ._____________ 50

COMM..__••.•._•._•..__••_•.__ 93

CENT ._. ._.___ 52

EVEN .___ 168

ENTY•__• 161

EIGH. .._ 132

ENTH._______________________ 114

EENT---__. .. 102

eQUE...______________________ 86

ERIO________________________ 66

EN'l'S. •• .__ 62

ASHT_..• .__.•_.__• 64

AUGlt..•..•_._._•• •.••••• 52

TION. • 218

EVEN________________________ 168

TEEN________________________ 163

ENTY 161

STOP________________________ 154

WENT 153

NINE • •__•• 153

TIEN. •• ._ 152

THRE________________________ 149

FOUR_______________________ 144

IGHT________________________ 140

FlVE. .___ 135

HR&E.•••••-••--•••--........ 134

EIGH..•••••__• ••••••__•. ·13

DASH.. ._._._ 132

SEVE________________________ 121

ll:N'l'H.._______________________ 11~

MENT • ..• 111

;. ;1

i

~~_~~ li ~~~
184 185

TABLE ll-D, Concluded.-The 54 tetragraphs appearing60 or more times in the 60,000 letters oj

Government plain-text telegrams arranged first alphabeticaUy according to theirthird letters and

then according to their absolute frequencies

TABLE ll-E.-The 64 tetragraphs appearing 60 or more times in the 60,000 letters of Government

plain-texttelegrams arrangedfirstalphabetically according to theirfinal letters and thenaccording

to their absolute frequencies

REQU________________________ 98

THRE________________________ 149

HIRT_______________________ 97

NDRE________________________ 77

LARS________________________ 68

PERI________________________ 67

OMMA.._______________________ 7r

OLLA._______________________ 70

FFIC________________________ 62

HUND------------------------ 64

DRED________________________ 63

RIOD________________________ 63

lVED________________________ 62

N~-"--------------------- 153 THRE________________________ 149

FIVE._______________________ 135

HREE._______________________ 134

SEVE-_---___________________ 121

EQUE._______________________ 86

NDRE._______________________ 77

RTEE._______________________ 59

FICE._______________________ 5°

NAUG________________________ 56

OURT________________________ 56

DASH .____________ 132

UEST________________________ 87

ENTy________________________ 161

ENTH. ~__ 114

ENTS________________________ 62

DASH._______________________ 132

EIGH. .__ 132

ENTH._______________________ 114

AUGH.__ .____________________ 52

PERI________________________ 67

DOLL._______________________ 68

COMM.._______________________ 93

FROM._______________________ 59

TION________________________ 218

EVEN________________________ 168

TEEN________________________ 163

TWEN________________________ 152

ERI 0_______ 66

STOP________________________ 154

FOUR_______________________ 144

THIR_______________________ 104

LLAR_______________________ 71

UNDR_______________________ 59

IRTy________________________ 59

FOUR_______________________ 144

EQUE .. 86

NAUG________________________ 56

FlVE________________________ 135

SEVE________________________ 121

QUES________________________ 87

THIS________________________ 68

LARS________________________ 68

ENTS________________________ 62

WENT .__________ 153

IGHT 140

MENT________________________ 111

EENT 102

HIRT________________________ 97

UEST .__ 87

VENT 7°

ASHT________________________ 64

UGHT .______________ 56

OURT .____________________ 56

STAT 54

CENT .__________ 52

REQU________________________ 98

ENTY 161

IRTy________________________ 59

TABLE 12.-Average and mean lengths oj words

Number of Number of Number of letters in times word letters word appears

1 378 378

2 973 1,946

3 1,307 3,921

4 1,635 6,540

5 1,410 7,050

6 1, 143 6,858

7 1,009 7,063

8 717 5,736

9 476 4,284

10 274 2,740

1l 161 1,771

12 86 1,032

13 23 299

14 23 322

15 4 60

120 9,619 50,000

oJ,;... J.;:. (1) Mean length of _ellll888Lm_mmu m m __mmnm m __mu__m u __n __n_ 5.2 Letters.

(2) Average length of messageB----------------------------------------------- 217 Letters.

(3) Mean length of meBBag6B. • • 191 Let~ers.

(4) Mode (most frequent) length________________________________________________________________________________ 105-114 Letters.

(5) It is extremely unusual to find 5 consecutive letters without at least one vowel.

(6) The average number of letters between vowels is 2.

1

___________________________JJ
1iI,

INDEX

(131)

ij

I'1

I'~
INDEX

Paragraphs Paps Aocented letters.. o-"___________________________________________________________ 5b 8.

Alphabets: Bipartite 300 59.

Deciphering 31c 52.

Direct atandard., 12a, 16, 19 18,26,31-33.

Enoiphering__________________________________________________________________________ 29b, 31c_____________________ 49, 52. Keyword-mixed. 31d 53.

Mixed._________________________________________________________________________________ 12a, 15a, 19, 21d, 22b, 18, 25, 31-33,

24c, 31b. 39, 39, 41,

52.

Reversed standard. 12a, 16, 19b, 2Gb 18, 26, 33, 36.

Standard. .--- 12a, 15a, 16, 19, 20b, 23, 18,25,26,31-

3&. 33, 36, 40,

65.

Systematically mixed.____________________________________________________________ 31c, e 52, 53..

Analytic key for oryptanalysls..________________________________________ 6d, 50 9, 103-104-

Arbitrary symbols.______________________________________________________________________ 13h, 48_____________________ 22, 100-101.

Assumptions 46h 98.

Average length of messages, 11b___________________________ 16.

Baeonlan cipher 35e_______________ __ ___ _ 60.

Beginnings of messages_________________________________________________________________ 32e 54-

Biliteral substitution .________ 41._______________________ __ 70-71.

Bipartite alphabet . 35b, c -- 59.

Blanks, number of_____________________________________________________________________ 146 . 24-

Book sy&tems 4ge ~__ 102

Censorship, methods for evading. 47c___________________________ 99.

Characteristic frequency of the letters of a language 9d, 14b, 25 12, 23, 41.

Characteristic frequency, suppression of 37, 4lJ '63, 71.

Checkerboard I'ystems__________________________________________________________________ 44, 45_______________________ 73-83, 83.

Checkerboards, 4-square________________________________________________________________ 44~.__________________________ 73-83.

Chinese Official Telegraph COda_____________________________________________________ 4Be_ 101.

Cipher: Baconian 356. 60.

Component ~_____________________________________________________________ 3'"___________________________ 57-58.

Distinguished from code__________________________________________________________ 6c, 3&______________________ 9, 64-

Text, length of, as compared with plain text, 4Oc 69.

Uni .___________________________________________ 41c ---______________ 70.

Classification of ciphers 12a, 13,47, 50e,J-----c

-- 18,18--22, 99,

104, 104- Code systems 4a, 4111, 47b, 48d, e 7, 71, 99, 100,

101. Distinguished from cipher ._______________________ 6c, 3& • 9, 64-

Completing the plain component_____________________________________________________ 20a, 34a 34, 57.

Concealed messages______________________________________________________________________ 47c . 99.

Condensed table of repetitions.______________________________________________________ 27i 46.

Consonants:

Distinguished from vowels.______________________________________________________ 28, 321: 46-47, 53.

Relative frequency of lOa, 13, 19 18,18--22,81-

33..

In succession________________________________________________________________________ 3k_________________________ 53.

Conversion of cipher text •• 214, e, 34c "_81,38, 58.

Coordinates on work sheet____________________________________________________________ 26d 42.

(139)
140

Paragraphs Pages Coordination of servieea.,__ ___ _ __ _ __ ___ ___ ___ ___ ___ ___ ___ __ ____ __ 2e . .. .__ 4.

Crests and troughs-.--------.------------------------------------------- .. lOa, 14b, 411, 44c • 13,23,71,74.

Absence of . --- . -----._-- -----------------------__ ---- -___ 14c "_.__•__._.__________ __ 24.

Deciphering alphabets ---- .. _ 31c___________________________ 52.

Dictionary words used as code words__. . . __ 47b • •••• 99.

Digraphlc substitution ._. . ._ 41c, 42, 43_._. . 70, 72, 72-'18.

Digraphs:

Characteristic frequency---------.---------------------.-------------. 25_.. 41.

Weighted according to relative frequency 29_. . .________ 48-49.

Distribution:

Dlf.f~~:~~:~~~-:_~~::~_::~:~~::~~~::_::::~:~:~~:~:~:-::~~:~-~ffi:~~:::_:::-~~~:~~-:~~H: ~~. Elementary sounds, characteristic frequency of . .______________ 14b_._. • ._ 23.

::~~~:~~g:~~:~::~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~;~~~:~::~:~~~~~~~~~~~~~~~~~~~ ~:: Equivalent values_. . ._____ ___ __ 39b_. ._____ ________ 66.

Figure ciphers., . . ._. ._________________________________ 13h, 48___________ 22, 100-101.

Fitting distribution to normal .________ 17b, c, 19, 38e 27, 28, 31-33,

F' .. -, 65.

F

oreignl 'languege cryptograms------.-------- -__ -__ . --- . --__ 5b, c_.__._-_- .____ 8. ormu as. . . .________________ 33d_. 56.

Frequency distribution . . . . 9, 17, 19, 26e, 440 •. 11-13, 27-28,

31-83, 42,

74.

~::~i:o::~-~-i-~~d~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~: ~ ~ ~ ~ ~ : ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ;~:~~~~~~~::~~~~~~~~~:~~~~~~~~ :: 28.

Fourpart : . "_. 38d • 65.

~~~2~~~_~~_~~~~~~-~~~~~-~~~~~~~::~~~~:~-~~~:~-~~~~:-~~~~~-~~~:::.~~~~~~~~~~~~~~~-~~::~~~::~-~ ~:~_!~~:~~~~:~~~:::-~~~::~~~~~ !E!:: ~;~;~: Frequency method of solution 18, 24d, 29. 29-31,41, 4S--

49.

General solutions in cryptanalysis . . . .____ __ 46i .__ 98.

General system, determination oL . . . 4a, 6; 13, 50 . 7, 8-9, 18-22,

103-104.

Generatrlx., . . .____ ____ _ 20a •••__ ••._ __ 34.

Goodness of fit . . . .... 17b__• • . 27.

Grilles • . . . .. __ ___ _ __ ____ ___ __ 47c • ••__ _ 99.

:~:~f~e~=~~~~~~~~t;~~~-----~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:~~~~~~~~~~~~~~~~~~~~~~~: ~i~~-~~~__~~~~~~~~~~~~~~~~~~~~~ ~~: Historical examples of muItiliteral systems .. 36 61.

~:E~:~~-~:~ii~i~~~~~~~~~~~~~~~~~~~:~~~~~~:~:~~~::~~~~~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ : ~ : : : ~ ~ ~ ~ ~ ~~~~~~~_~~~::~~-~.~.~-~~::~~~~~~~~~ !~i. Intelligible text obtained by chance 21b • 38.

~:~~~:~~: :;::::~.:::~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~:~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~57. Japanese Morse alphabet__.. 5b, 48e 8, 101.

~:~:;~~~:~~~~~~~;;:~~~~~~~~~~~~~~~~~~~~~:~~~~~~~~:~~~~~~~~~~~~~~~~~~~~~~~~~~~~ i~~~~~:-~::~~:~:~::::~~:::~:: ::~O3-l 04.

Language employed in a cryptogram. . .___________ 4a, 5 . . . 7, 8.

Language frequency characteristics . . . __ . ._.._. 9d, 25._. . 12, 41.

Language peculiarities__. • . . .._._.•- . . __ .__________ 5b .________ 8.

141

Letters: Paragraphs Pages

Accented.------------------.---------------------------- .__________ 5b 8.

Low~frequency-------------------------------------.----- • . __. 31c 52.

Missing . ._.________________ 5b, l4e______________________ 8, 24.

Low-frequency consonants . l3d, 3lc 19, 52.

Medium-frequency consonants ._________________________ l3d__________________________ 19.

Messages: Beginnings and endings amenable to cryptanalysis________________________ 32e ._______________ 54.

General phraseology 49a__________________________ 101.

Hidden.._______________________________________________________________________________ 47c.__________________________ 99.

Military text ._._______ 10b___________________________ 15.

Missing letters.____________________________________________________________________________ 5b, 14e______________________ 8, 24.

Mixed alphabet 15a, 22b, 24c, 31L 25, 39, 41, 52.

Mixed sequence ----------------------------- 2Id 39.

Modified Playfair • • ---------------------- 46d ._______________ 86.

Monoalphabets . ----------------------------- 1b____________________________ 1. .

Monoalphabet distinguished from polyalphabeL 12, 14 18, 22-25.

Morse alphabet, Japanese, Russian --- 5b, 48c 8, 101.

Multiliteral substitution- --.-----.------------- 35, 37, 4Ic 59-60, 63, 70.

Multiliteral systems, historical examples oi.: . 36__. 61.

Normal distribution. ... • ._________________ 17b, c • 27, 28.

Normal frequency . ------------------ 9, 11, 25____________________ 11-13, 16-17,

41.

Deviations from . ------------------ l3b. . •• . 19.

NUUs- . ---_-------------------------------- 40, 47c • •------------- 68-69, 99.

New York Tribune, ciphers in ._. · ----- 36 61.

Patterns --------------------"----------------------- 33d • 56.

Phraseology of messages.__" ----------------- 49a .______ 101.

Plain component, completion of . -- 20a 34.

Plain-text unit__. --------------------------- 41c_. • 70.

Playfair cipher. • 44, 46_______________________ 73-83, 84-98.

Modified-- . . . -------------------------------- 46d__________________________ 86.

Polyalphsbetic cipher distinguished from monoelphabeb...c., . 12, 14 18, 22-25.

Polygraphic substitution ------------------------------------------------ 41_. 70-71.

Prefixes in triliteral distribution · ---------- 27e__. · ·_ 44.

Prerequisites for cryptographic work 2 . 2-5.

Probable-word method . -.--.------------- 33____________________________ 55-57.

Pseudo-polygraphic systems----------------------------------_------------------------ 41e___________________________ 71.

Punctuation in telegraphic text ._.. ---- lOc .__________ IS.

Quadraliteral cipher . ---------------- 35d .___________ 60.

Quinqueliteral cipher.. . ---------- .---------. 35e • 60.

Random text, number of blanks ---.-- 14/--------------------------- 24.

Relative frequencies. • . lOb, c, d, 11, 14b•. 15, 15,15,16-

17,23.

Repetitions--------------------_-_-------------------- l3g, 24b, c, 27 21,40,41,43-

46.

In a code message ---.--------------- 38c___________________________ 64.

Of consonants ._. 32c___________________________ 53.

Of digraphs and trigraphs --------- 27f · ·~______________ 46.

Condensed table of .• ------------- 27i__• 46.

Reversed standard alphabets ------------- 16, 20b • 26, 36.

Reversible digraphs indicated on worksheet .• 26/ • • 43.

Russian Morse alphabet • 5b, 48c_. 8, 101.

Security of monoalphabet using standard alphabets ._. ._______ 23____________________________ 40.

Sequences: Known . •• ._________________________ 23 40.

Mixed. . . 21d 39.

Unknown 23 40.

148274--88----10

I
i42

Paragraphs PlIglllI

Solutions of a subjeotive nature_______________________________________________________ 3 5.

Specific key ------- 4, 7, 19a, 311'______________ 7, 10, 31, 52.

Standard alphabets 15a, 16, 20b, 3Se 25, 26, 36, 65.

Subjeotive solutions --------________________ 3 5.

Substitution:

BillteraL_______________________________________________________________________________ 41____________________________ 70-71.

Digraphic 41c, 42a 70, 72.

Distinguished from transposition 12, 13 18, 18-22.

Polygraphic -------------_______________ 41c___________________________ 70.

M ultiliteral, __ 41c___________________________ 70.

Trigraphic ____ 41c________________________ 70.

Trillteral -________________ 41__________________________ 70-71.

Suffixesin trigraphic distribution___________________________________________________ 27e___________________________ 44.

Suppression of frequency 37, 40b, 41/-------- 63, 69, 71.

Symbols as cipher elements__________________________________________________________ 13h, 48_____________________ 22, 100-101.

Telegrams, average length of__________________________________________________________ 11b___________________________ 16.

Terminology -------___________________ 1_____________________________ 1.

Text, different types 01. lOb, c 15, 15.

Transposition distinguished from substitution 12, 13 18, 18-22.

Trigraphic cipher system. 41c.__________________________ 70.

Trigraphic frequency table_____________________________________________________________ 27 (footnote 2) . 44.

Triliteral frequency distribution 27 43-46.

Triliteral substitution 41__________________________ 70-71.

Type numbers for cryptographic systems 50/ 104.

Uniliteral frequency distribution 9, 17_________________________ 11-13,27-28-

Unknown sequences 23 40.

Variants 37d, 40b, 49c, d, 1________ 63, 69, 101.

102,102.

Vowels: Average distance apart 32c, footnote .53.

Combinations with consonants 28, 29______________________ 46-47,48-49.

Combinations with vowels_______________________________________________________ 29a__________________________ 48.

Distinguished from consonants 28, 32c 46-47, 53.

In succession_________________________________________________________________________ 32c__________________________ 53.

Relative frequency of lOa, 13, 19 13,18-22,31-

33. Word formulas ~____________________________________________________ 33d__________________________ 56.

Word lengths in a cryptogram 26c, 32e, 33d,I, g________ 42, 54, 56, 56,

57. Word patterns 33d 56.

Word skeletons___________________________________________________________________________ 30b, 32e_____________________ 49, 54. Work sheet, preparation 01. 26 42-43.
- - --,

r--..L--.

I 305-Comblned I

I

substitution-trans- I

position (to be taken

up iater) L (17d 22b) -l

b. S. GOVERNMENT PRINTING OFFICE: lUI

lOO-Code (to be

taken up later)

304-Substltutlon

(12-16)

CRYPTOGRAMS

(H, 38b,e, 48)

202--Monographlc I

.-------F-- 3oa-Transposltlon

(to be taken up

later)

ANALYTICAL KEY FOR CRYPTANALYSIS I

(Numbers in parentheses refer to paragraph numbers in this text)

I I ,

- - - 403-Monoalpha- 404 -POlt:IPhalyalphabetlo betio betic (to taken

taken up (35) up later)

ter)

I I

Ig I 503-UnUitersi 504-Multllltersl

(41) (35-36)

I

Ie II ~Etc'l 607-Clphers com- IlO8-Ciphers com- 609-Slngle equlva- 610- Mul tl~e-

(4Ig) posed exclusively of posed of fi~res, lent substitution equlvalent In tlletters symbols, or ter- (35-36) tutlon

(15-24) mixtures of letters, (37-40)

ligures,and symbols.

(48a-b)

I

703-Standard 704-Mlxed cipher 70S-Num ber 01-1 700-Letter ciphers 707-Number 70s-Letter

cipher alphabet alphabet phers (35a-e, 3oa) ciphers ciphers

(16-22) (26-34) (3Ob, c) (38) (39-40)

I

I

B04-D1rect I'-

80S-Reversed II806-systematlca1lY IIS07-RBndOmmiXed I 808-4-Alphabet 809-Rectangles 810-Book method (lila, 2Oa) (19b, 2Ob) mixed (4Ic-e) schemes with num- bers from oo-gg (39-40) (4ge) (38a-e)

901 - Key w 0 r d 902-0ther types mixed (3Ie) (3Ic-d)

148274-38 (Face p, 142)

605--TrI!!I8ph

(41g)

402-Po

(to be

Ia

1i02-Systematlca

derived eqnlvalen

(41-46)

803-0ne-square designs

(Playfslr)

(46)

702- Checkerboard

designs

(44-46)

802-Two-square designs

(45)

701-SlIdlng alphabets

(41e-n

801-Four-square designs

(44)

WI-Random tabular equivalents

(4Ig)

I For exp1aDatJon._ Par. &().

I 601-DigraphiC I 602-Trlgraphic

I

I

i