Howard N. Smith 

Howard W. Lewis 

REF ID:A58016 .. , 

CONFIBENTIAL 

I ' t 

A METHOD OF CIPHERING 

Palo Alto, California 

Novemter 14, 1954 

Declassified and approved for release by NSA on 08-12-2013 pursuantto E .0. 1352a 

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CONFIDENTIAL ...,_ ,. 
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Those authorized to read this paper are 

requested to reveal its contents to no 

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Please sign your name and note the date 

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REF ID:A58016 

A l\!ETHOD OF C IPEERIUG 

The purpose of this paper is to describe an original method 

of ciphering in order that it may be properly evaluated by an 

expert cryptographer. 

Brief1y, this is a relatively simple method of ciphering in 

which there is no fixed pattern of any kind and, therefore, no 

repetitions of a meaningful nature. The cipher is continuously 

changing in a completely random manner, and never repeats itself 

in a predictable way, but only as the result of pure chance. The 

number o~ possible keys to the cipher is extremely large, the key 

can be changed as often as desired, and knowledge of both the 

ciphering principles and procedures and of previously-used keys 

ta is of no value whatsoever in breaking an enciphered message. 

" Unless the key that was used is known, a message can only be 

broken by methods based almost entirely on trial-and-error, and 

the probability of such methods being successful within a reasonable period of time is infinitesimally small. Furthermore, the 

solution may not be recognized when found, and can never be known ~ 

with absolute certainty. It is suggested that for all practical 

purposes the cipher is completely indecipherable. 

In order to describe t~e cipher, it will first be necessary 4 

to des~ribe a simple device whichycan be used to illustrate the 

procedures for enciphering and deciphering messages. This device 

consists of two gears which have twenty-s;x teeth each or one 

"' tooth for each letter of the alphabet. The teeth on each gear are 

marked from 111\" to "Z" in a clocl(wise direction. One of these 
REF ID:A58016 

gears is called the "message wheel" and the other is called the 

ncipher wheel." The wheels are free to rotate when engaged, and 

the cipher wheel can be disengaged from the message wheel, rotated 

or nindexed" from one to twenty-six teeth in a clockwise direction, 

and then re-engaged with the message wheel. Thus there are twentys1x possible engagements or the wheels. There are two fixed 

reference points, one for each whe~l, which ind~cate the messagecipher relationship between the letters on the two wheels. This 

• relationship is fixed for each engagement, and is different for J I 

each of the twenty-six possible engagements. 

' 

The manner in which the key to the cipher is selected and 

used Will make clear that f~r the device Which has JUSt been 

described, the cipher has twenty-six times as many keys as there 

are d1fferent ways of arranging the twenty-six letters of the 

alphabet. Each key consists of one of the twenty-six posslble 

engagements of the wheels plus one of the factorial twenty-six 

possible arrangements of the alphabet. Thus there are 1028 or 

ten billion billion billion possible keys to the cipher. 

One ot these keys has been selected for purposes of illustrating the ciphering procedures. The first part of the key, one 

of the twenty-six possible engagements of the wheels, was selected 

by placing twenty-six letters in a hat, drawing one of them out at 

random, and noting it to be "F." Thus the engagement of the wheels 

which constitutes the first part of the key is such that when the 

letter "A'' is indicated on the message wheel by the .fixed re.ference 

point for that wheel, the letter "F" is indicated on the cipher 

•heel by the fixed reference point for that wheel. 

The second part of the key, one of the factorial twenty-six 

possible arrangements of the alphabet, was selected by placing 

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REF ID~A58016 

twen~y-s~x letters in a hat, drawing them out one-by-one at random, ~ ~ ~ 

~ ' and numbering them in the order in which . they were drawn. Thus the , ~ 

arrangement of the alphabet which constitutes the second part of 

the key is as :t'pllows: 

"' 

M - 1 A - 10 N - 19 

0 - 2 y - 11 J - 20 

L - 3 F - 12 w - 21 

'1' - 4 K ~- .13 I - 22 

s - 5 z - 14 E - 23 

c - 15 x - 15 H - 24 

D - '7 G - 16 R - 25 

Q - 8 p - 17 B ... 26 

v - 9 u - 18 

Having described the ciphering device and selected a key, it 

is now possible to illustrate the procedures for enciphering and 

deciphering messages. The manner in which the key is used will be 

made clear by means of the procedures themselves. 

The essence of the ciphering procedures is that the engagement or the wheels, and thus the relationship between the message 

and the enciphered text, is changed between every letter of the 

message in a manner which is completely random. For each engagement of the wheels, two letters are enciphered: the first letter is 

the next letter of the message, and the second letter is a letter 

~rom the key which indicates the amount that the engagement of the 

wheels is to be changed before proceeding. Thus a message containing 

x letters will produce an enciphered text containing 2x-l letters. 

Assume that the message to be enciphered is Poe's classic 

statement, "human ingenuity cannot concoct a cipher which human 

ingenuity cannot resolve. 11 The initial engagement of the wheels for 

both enciphering and deciphering is the engagement specified in the 

first part of the key, so the first step is to engage the wheels in 

this manner. Then the first letter of the message, "H," is indicated 

on the message wheel which results in "Y" being indicated on the 

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REF ID:A58016 

cipher wheel. "Y'' is thus the first letter of the enciphered text. 

It is now necessary to change the engagement of the wheels in 

a completely randoM manner. This is done by randomly drawing one of 

twent7-six letters rrmtt a hat, noting that it is "K,, 11 and then 

returning it to the hat. Rei'erring to the second part of the key, 

,tt is noted that "K" is the thirteenth letter listed. Thus "K" calls 

for indexing the cipher wheel thirteen teeth. First,, however, "K" 

must be enciphered. When "K" is indicated on the message wheel, "V" 

is indicated on the cipher wheel, and "V" is thus the second letter 

of the enciphered text. 

The cipher wheel is then indexed thirteen teeth and the next 

letter of the message enciphered. "u" indicated on the message wheel 

results in "Y" again being indicated en the cipher wheel, and "Y'' is 

thus the third letter of the enciphered text. Another letter is then 

drawn at random from the hat, noted to ~e "c," and returned to the 

hat. "C" indicated on the message wheel results in "Q" being in- . . dicated on the cipher wheel, and "Q,11 is thus the fcurth letter of 

' the enciphered text. The cipher wheel i~ then indexed six teeth as 

,, called for by "C," and the next letter of the message enciphered. 

This procedure is continued until the message has been completely ,, ~ 

enciphered: the cipher wheel is indexed between every letter of the . ., 

message a numbe~ of teeth determined by randomly drawing a letter 

' 

rrom the hat and noting its corresponding number in the key, the 

letter drawn being enciphered immediately prior to the actual 

indexing. 

The procedure ror deciphering the message is essentially a 

re-enactment or the enciphering procedure except that the cipher 

wheel now has the initiative and the message wheel is the follower. 

First, the wheels are engaged in the initial position as specified 

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REF ID:A58016 

in the first part of the key. Then the first letter of the enciphered 

text. "Y•" is indicated on the cipher wheel which results in "H" 

'being indicated on the message wheel. Thus "H" is the first letter 

of' the nie~sage. The second letter of the enciphered text., "V., 11 is 

then indicated on the cipher wheel which results in 11K11 being . indicated on the message wheel. Referring to the second part of 

the key, it is _'l.oted that "K"' calls for indexing the cipher wheel 

thirteen teeth., and this is done. The third letter of the enciphered 

text, ny.,n is t~en indicated on the cipher wheel which results in 

nun being indicated on th13 message wheel. Thus "U" is the second 

letter of the message. This procedure ls continued until the . ... ~ 

enciphered text has been completely deciphered. 

~ 

It is now appropriate to consider the problem which this method , of ciphering presents to the intercepter of an enciphered message. 

It is assumed t.l"1at the intercepter has full knowledge of the cipher-

' 

ing principles and procedures and has a ciphering device such as 

the one described above, but does not know which one of the ten 

billion billion ~illlon possible k~ys was used to encipher the 

message. 

First of all., it must be realized that depending upon the 

length of the message., thousands., millions., or even billions of the 

possible keys will produce messages that make sense, and the cipher 

1tse:J_f will in no way indicate which of these messages ls the 

message that was enciphered. This can only be determined from the 

~ense of the messages themselves. Thus the only way in which an 

enciphered ~eesage can be broken is to determine keys which produce 

messages that make sense until a message is produced which, from 

the particular sense that it makes, is concluded to be the message 

that was enciphered. Obviously, the message may not be recognized 

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REF ID:A58016 

when found, and can never be known with absolute certainty. For 

purposes of the problen at hand, however, it is further assumed 

that the lntercepter will be able to recognize the message when 

it ls found. 

Since the cipher has a finite number of keys, it is theoreti- , ~ 

cally possible to break an enciphered 11!.essage by testing possible 

keys on a trial-and-error basis until the key that was used to ~ ~ 

encipher the messa£e is tested and ~presurnably, the message recognized. It can be quickly demonstrated, however, that trial-and-error 

alone is totally ~practical. Assuming that the message could be 

tested at the rate of one billion keys per second, it would take 

320 billion years to teqt all of the possible keys, and the key 

used to encipher the message would be tested, on the averaee, at 

the end of fifty percent of the possible trials or 160 billion 

years. Through extreme good fortune, the key used to encipher the 

message might be tested at the end of one millionth of one percent 

of the possible trials, but even this would require 3,200 years. 

Thus the probability of breaking an enciphered message within a 

reasonable period of time by means of trial-and-error alone is so 

extremely small that for all practical purposes it is zero. In 

order to significantly increase this probability, the probable 

number of trials required to find the key must be very greatly 

reduced by means of supplementary analysis. 

There are three basic methods of analysis by which the 

probable number of trials required to find the key can be reduced. 

Because of the nature of the problem, however, all three of these 

methods are nece~sarily limited to ~ncreasing tho rate at which 

messages that make sense will be produced, and thereby increasing 

the probability of producing the messaee that was enciphered within 

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REF ID:A58016 

a reasonable period of time. It bears repeatine that a very large 

number of t~e possible keys will produce messages that make sense, 

and there is no way in which the key that was used to encipher the 

message can be identified other than oy the particular sense of 

the message that it produces. 

The ~irst method of analysis is based on the fact that at any 

point in an enciphered message, ce~tain ensagements of the wheels 

are more likely than certain other engagements because certain 

l~tters of the alphabet appear in the languaee more frequently 

than certain other letters. For exampLe, assume teat a letter of I • 

the message is "B" in the _enciphered text. 1.11en "B" is indlcated on 

the cipt_er wheel, the enL,at,ement of the wheels which indicates "R" ~ ~ 

on the message wheel is ~ore li~ely than the engagement which 

indicates "K'' on the message ·wheel because "R'' appears more 

rrequently than "K" arid is more likely to be tne letter of the 

message. Thus at any point in the message, the twenty-six possible .. engagements of the wheels can be arranged in order of liklihood . as determined by the relative frequen~ies with whicn the twenty-six 

letters of the alphabet appear in the language. This means that if 

a family of keys is defined as one of the factorial twenty-six 

possible arrangements of the alphabet plus all of the twenty-six 

possible engagements of the wheels, at any point in the message, 

and particularly at the beginning, the twenty-six ~eys in each 

family can be arranged in order of priority for testing. By testing 

possible keys in order of overall priority, the rate at whJ~h 

messages that ~ake sense will be produced can be increased. 

The second method of analysis is similar to and supplementary 

to the first method: whereas the first method is concerned with the 

engagement of the v.heels at a particular point 1 the second rne thod 

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REF ID:A58016 

assumes an engagement at that point and ls conqerned with the change ,. in engageMent that immediately follows. It i~ based on the fact that 

if at any point in an enciphered message one of the twonty-sLx 

possible engage~ents of tho wheels is assumed to b~ the engagement 

at that point, certain changes in that engaeement are more likely 

than certain other changes because certain letters of the alphabet 

appear more frequently in the language than certain other letters. 

For example,, assume that a letter of the message is 11 rl 11 in the 

enciphered text,, the following letter from the key is "G" in the 

enciphered text, and the following letter of the nessage is "S'' in 

the enciphered text. If the engagement of the wheels which indicates 

"R" opposite 11 i311 is assu..med to be the engagement at that point, the 

letter from the key is "M" since "M" is indicated opposite "G" by 

that engagement. "l\111 is more likely to call for indexing twenty-tNo 

teeth than ten teeth because Nhen twenty-two teeth are indexed,, 11E11 

is indicated opposite "S, 11 when ten teeth are indexed, "~" is 

indicated opposite "S,," ana "E" appears more frequently than "~" 

and is more likely to be the next letter of the message. Thus if 

at any point in the message one of the twenty-six possible eneagements of the wheels is assumed to be the engagement at that point,, 

the twenty-six possible changes in that engagement can be arranged ' ~ - in order of liklib,ood as determined by the rela~lve frequencies 

with which the twenty-six letters of the alphabet appear in the 

language. This means that if a'fa~ily of keys is defined as one of 

the twenty-six possible engagements 0£ the wheels plus all of the 

ractorlal twenty:six possible arrangements of the alphabet,, for each 

letter of the alphabet,, each family will consist of twenty-six ~ .... 

groups of factorial twenty-five keys each such that the letter will 

call for indexing from one to twenty-six teeth over the twenty-six 

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REF ID:A58016 

groups, and at any point in the message, and particularly at the 

beginning, the twenty-six groups of keys in each family can be 

t9 arranged in order of priority for testing. This method of analysis 

can be used to supplement the first method described above and 

thereby further increase the rate at which messages that make sense 

will be produced. 

It should be noted that actually the first two methods of 

arl.alysls would be modified in specific situations to the extent 

that special frequency distributions of letters or probable patterns 

or letters would be more significant in that situa~ion than the 

general frequency distribution of letters in the language. For 

example, "E" appears in the language more .frequently than any other 

letter, but as the initial letter of a word, the frequency of "E" 

is to the frequency of "T" as 340 is to 1,194. Thus the first letter 

o:r a word is three and one-half' times more likely to be "'r" than 

"E•" Sinilarly, "Q." is always rollowed by "u," and if "Q" is 

assumed to be the letter at a particular point in a message, the 

next letter of the message will be "u" regardless o.f the rrequency 

with which "U'' appears in the language. 

The third method of analysis ls employed after a number of 

possible keys have been tested, and is undoubtedly the most 

signi.ficant o.f the three methods. It is based on the fact that in 

addition to the large number of possible keys which will produce 

messages that make sense, many times this nUIJ!ber will produce 

messages that contain one or more sequences that make sense, and 

by comparing the points where such sequences begin and end and the 

portions of keys operative over such sequences, sequences from 

different messages can be matched together to produce messages that 

make sense. For example, assume that one of the possible keys 
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REF ID:A58016 ~ 

produces a message that contains a sequence from the twenty-fourth 

letter to the fifty-first letter that makes sense. If another of 

the possible keys produces a message that contains a sequence that 

makes sense which begins at the fifty-second letter or ends at the 

twenty-third letter, and if the sense of this sequence would supplemeht and extend the sense of the first sequence, the two sequences 

can be joined together to produce a longer sequence that makes sense 

p~ovided that the portions of keys operative over the two sequences 

do not conflict with each other or with the change in engagement 

required to join the two sequences together. Note also that sequences 

can be extended a number of letters in either direction to JOin with 

other sequences by means of the first and second ~ethods of analysis 

described above, or, more importantly, by means of trial-and-error 

guessing based on the sense of the two sequences being Joined. In 

this rr.anner, the rate at which messages that make sense will be 

produced can be increased, and it is important to note that depending 

upon the liklihood that the sense that was enciphered will be recognized, the messages produced will be those whic~, because of the 

particular sense that they make, have a greater liklihood of being 

the enciphered message. 

It was stated above that in order to significantly increase 

the probability of breaking an enciphered message within a reasonable 

period of time, the probable number of trials required to find t~e 

key must be substantially reduced by means of supplementary analysis. 

The three basic methods of analysis which can be e~ployed were then 

described, but no attempt was made to determine whether or not these ~ 

methods wo~ld substantially reduce the probable number of trials 

required and thereby significantly increase the probability of 

successfully breaking an enciphered message. This aspect of the 

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REF ID:A58016 

problem has not been fully analyzed, and will not be dealt with in 

this paper. It see~s likely that these methods of analysis would not 

be of pr•actical significance relative to the total problem presented 

by the cipher, and that for all practical purposes the cipher, in 

its present form, is indecipherable. It is possible, however, that 

this may not be true, and because this point has not been resolved, 

it is necessary to assume that it is not true, and that the indeoipherabillty of the clpher must be increased. 

One method by which this can be accomplished is by increasing 

the number of teeth on each wheel which, in effect, increases the ... 

number of possible keys to the cipher. For example, if ten teeth 

are added to each wheel to provide for the nU111bera zero through . ' 

nine, the cipher will have thirty-six times as many keys as there 

are different ways of arranging twenty-six letters and ten numbers 

or 1.3 x 1043 possible• keys. Thia la 1.3 q~adrillion times as many 

keys as there were when each wheel had twenty-six teeth, and the 

time required to~t~st one trillionth of one percent of the possible 

keys at the rate of one trillion trials per second would be 4.2 

billion years. Similarly, if thirty-six more teeth are added to 

each wheel to provide for twenty-six capital letters and ten 

punctuation marks, the cipher will have 4.4 x 10105 possible keys 

or fifteen quadrillion quadrillion times as many keys as there are 

atoms in the known universe. This method will not affect the basic 

simplicity of the ciphering procedures, and will greatly increase 

the indecipherability of the cipher in terms of the practical 

problem which the cipher presents. Note, however, that while the 

cipher will be changed in degree, it will not be changed in kind, 

and the three methods of analysis described above can still be 

employed. Since it was assumed that these methods would be of 

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REF ID:A58016 

significant practical value when there were twenty-six teeth on each 

wheel, it must be further assumed that they would be of significant 

practical value recardless of the number of teeth on each wheel. 

This assumption becomes increasingly unlikely as the number of teeth 

on each wheel increases, but because the actual significance of the 

methods has not been determined, the assumption must be made. There-

.fore it is necessary to invalidate one or more of the three methods 

of analysis and thereby increase the tceoretlcal indecipherability 

of the cipher. 

Because the first and second methods of analysis are based 

entirely on the fact that the various letters of the alphabet appear 

in the language in known patterns and with known different frequencies, 

these methods would be of no value whatsoever when dealing with a 

language in which the letters of the alphabet appear randomly and 

with equal frequency. Such a language can be easily constructed, in 

eff~ct, by constructing a simple code which, in addition to completely 

invalidating the first two methods of analysis, will make the problem 

of recognizing the Message when it is found considerably more difficult by tremendously increasing the number of possible keys which 

. will produce messages that make sense. 

It is important t~ note, however, that the nature of this code 

is such that whether or ~ot tbe code is secret is of little consequence, and it can be assumed than an intercepter has full knowledge • 

of the code in addition to knowleftge of both the ciphering principles 

and procedures and of previously-used keys. Therefore, once the code 

has been constructed, it will never have to be changed. Actually, 

~ . use of the code should be thoug4t of as just an additional step in 

the cipLering procedures because its purpose is not to make the cipher 

secret or complex in any way, but rather to invalidate methods of 

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REF ID:A58016 

analysis which would ot~erwise be theoretically possible and, 

presumably, of significant practical value. Thus the code inc~eases 

~ the theoretical indecipheraoility of the cipher but does not affect 

its fundamental nature: unless the key that was used is known, the 

cipher defies solution solely on the basis that the probability of 

finding the key within a reasonable period of time is infinitesimally 

small. and there is no way in which the key can be positively 

identified when it is found. 

For purposes of illustrating the construction of the code, 

assume that there are thirty-six teeth on each wheel to provide for 

twenty-six letters and ten numbers, and, conseq~ently, that the cipher 

has t~irteen sextillion sextillion possible keys. The number of 

permutations of thirty-six things taken three at a time when each 

thing may be repeated up to three times is thirty-six raised to the 

third power or 46,656 which means that it is possible to make a . total of 46,656 different three-letter arrangements or code wo1•ds 

from the thirty-six symbols included in the cipher. Therefore, for 

purposes of illustration- assume that the code to be constructed is 

to include 46 1 656 different words. Because o~ the nature of the code, 

this number of words is not as laree as it at first appears since a 

different code word must be assigned to each grammatical form of each 

word that is to be included in the code. Thus the code will represent 

' an effective vocabulary in the order of fifteen thousand words which 

would probably be of adequate size for most purposes. ~ote, however, 

that there is no limit to the number of words that can be included ~ 

~ 

in the code: for example, it is possible to make 456,976 different 

four-letter code words fro~ twenty-six letters alone. A falr•ly 

conservative vocabulary was selected because in order to increase the 

number of possible keys which will produce messages that make sense 

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REF ID:A58016 

to the maximum. extent possible, it is necessar1 to assign words to 

all or the possible code words, and desirable t~at the words ass1gned 

~ be of fairly common usage. 

The first step in the construction of the code is to select 

from the laoguage the 46,656 words that are to appear ln the code 

and arrange them in alphabetical order. Then 46,656 slips of paper 

are placed in a hat, each marked with a different one of the possible 

three-letter code words that can be made from twenty-six letters and 

ten numbers. The slips of paper are then drawn fro~ the hat one-by-one 

at random, and the code word on each slip noted opposite the next 

word in the alphabetical list in the order in which the slips are 

drawn. In this manner, a language-code dictionary can be constructed. 

~or deciphering messages, a code-language dictionary will be needed, 

' 

and can be easily constructed br arranging the 46,656 code words in 

"alphabetical n order ("A'' through "9 11 ) and noting opposite each its 

language counterpart. 

~ 

The manner fn which the code is constructed is such that the 

twenty-six letters and ten numbers will be distributed randomly and ! 

with equal frequency throughout the code. Although certain code words 

will be used more frequently than certain other code words because of 

:.. 

the relative frequencies with which their language counterparts appear 

in the language, if the 46,~56 code words are arranged in order of 

frequency and classified into percentile groups, it is almost a ~ -

certainty that each of the thirty-six symbols will appear an equal 

or almost equal number of times in each group, and an equal or almost 

equal number of times as first, second, and third letters within each 

group. Thus a symbol-frequency table developed by means of wordrrequency analysis will indicate that all of the symbols have the same 

probability of being first, second, and third letters of a code word. 

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REF ID:A58016 

it this point, aGain consider the problem whtch confronts the 

1ntercepter o~ an enciphered message, this time a message which was 

translated into code before being enciphered. As stated above, it 

can be aesumed that the intercepter has full knowledge of the code 

1n addition to other knowledge previously conceded. 

Because the twenty-six letters and ten numbers appear in the 

code randoml~'and ~ith equal frequency, it is no longer possible to 

arrange possible keys in order of priority for testing by means of 

the first and second methods of analysis. Thus the only procedure 

available is to test possible keys solely on the basis of trial-andarror and attempt to increase the rate at WPich messages that make 

sense will be produced by means of the third method of analysis • ., 

Note, however, that because every one of the 46,656 possible code \ T 

words appears in the code book opposite a real word, every three-

• ' 

letter sequence produced by every possible key will be a word that 

ma~es sense. This means that the number of possible keys which will 

produce messages that make sense will be tremendously increased, 

and the problem of recognizine the message when-it is found {and of 

,• 

recognizing that the message has not been found) will be considerably \ 

more difficult if not impossibl~. The third method of analysis can 

still be employed, but its ultimate effectiveness will be greatly 

reduced by the fact that sense will be produced at almost every 

turn, and the intercepter will essentially be in the position of 

having to guess the message with a seemingly infinite number of 

messages to choose from. This effect is maximized by assigning a 

word from the lancuage to every possible code word, and limiting 

the words assigned to those of fairly coMmon usage. Use of the code 

in this manner increases the theoretical indecipherabilLty of the 

c1pher by invalidating the first and second ~ethods of analysis, 

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REF ID:A58016 

and increases the practical indecipherability or the cipher by 

~ increasing the number of possible keys which will produce messages 

~ that make ~~nse. 

It should be pointed out that it is possible and perhaps 

~es1ra.ble to use the code in a different manner than that described 

above, and thereby increase the practical indecipherability of the 

cipher in a different way. For example, assU!l'J.e that the number of 

teeth on each wheel is increased to five thousand to provide for 

five thousand different symbols and, consequently, that there are 

five thousand times facto~1al five thousand possible keys to the 

cipher, a number which is almost beyond coMprehens!on. It is possible 

to make a total of t~enty-five million different two-letter code 

words from f~ve thousand different symbols, but this number is many . tinxes larger th8._!l the total number of words in the language even 

when each grammatical form of each word is counted separately. 

Assume, therefore, that the code consists of 350,000 words and 

represents an effective vocabulary in the order of 100,000 words. 

It is almost ~ certainty that the five thousand symbols will appear 

randomly and with equal or almost equal frequency in the sample of 

350 1 000 words just as in the total population of twenty-five million 

• 

words, and thus the first and second methods of analysis will be 

invalidated as before. Fowever, since most of th~ possible code words 

will not be included in the code, most of ~the two-letter sequences 

- produced by possible keys will not be meaningful words, and the 

previous effect of producing sense at almost every turn will not be 

realized even thoueh an extremely large number of possible keys will 

produce messages that make sense. On the other hand, the practical 

' ' indecipherability of the cipher will be greatly increased by the fact 

that the number of possible keys to the cipher wilJ be immeasurably 

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REF ID:A58016 

larger. Inc~easing the nur1ber of symbols increases the number or . possible keys and the number of possible code words, and while it 

is desirable to have as many keys as possible, it is also desirable 

to assign words to all of the possible code words, and there is a 

~imit to the number of words that can be assigned, particularly 

words of fairly conman usage. Therefore it is possible that the 

indecipherability of the ciphe~ will be maximized oy increasing the 

number of possible keys to a practical or theoretical optimum point 

beyond the point where words of fairly common usage can be assigned j 

•to all of the possible code words. It see~s more likely, however, 

that the nilm.ber of possible keys quickly becomes sufficiently large 

tor its purpose, and that it is more advantageous to include all of 

the possible code words in the code than to increase the number of 

possible keys beyond the point where this is possible. Note that ~ 

two-letter code words are more advantageous than three- or four-letter 

code words because a lareer number of symbols will be required to 

provide for a given number of code words, and thus the cipher will 

' 

have a larger number of pos~ible keys. One-letter code words would 

maximize the number of SYJ!lbols for a &~ven pumber of code words, but 

the purpose of the cod~ w9uld be d~teated since it would then be 

possible to employ the first and second methods of analysis based on 

the relative frequencies of words rather than letters. In summary, 

it seems likely that the theoretical indecip~erability of the cipher I 

would be maxiMized at something in the order of two hundred symbols, 

377 1.6 x 10 possible keys, and forty thousand two-letter code words 

fully assigned to an effective vocabulary in the order of twelve 

thousand words. 

The above paragraphs should serve ta illustrate the principles 

and procedures of the method of ciphering which has been developed, 

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REF ID:A58016 

and thereby make possible a proper evaluation of this method of 

~iphering. At every point in its development, the cipher is based on ~ 

concepts of randomness and probability, and while no attempt has been 

made to define the resulting indecipherability in mathematical terms, 

this car. be done by the techniques of operations research. It does 

not seem unreasonable to anticipate the result of such an analysis 

and suggest that the problem presented by the cipher is so extremely 

formidable that for all practical purposes the cipter is completely 

indecipherable. 

Before concluding, one important advantage should be mentioned; 

namely, that the cipher is both simple and practical. Certainly it 

would not be difficult to develop electronic equip~ent for use in 

major co:mmun1cations centers which would rapidly and automatically 

encipher and decipher messages including the encoding and decoding 

steps ln the ciphering procedures. At the otner extreme, a simple 

pocket device, es~e~tially a ~ircular slide rule, and a small code 

' 

book (if necessary·) would be perfectly adequate for applications of 'I' 0 I 

, a tactical nature. Indeed, th~ cipher is particularly suited for use 

at the tactic~l level because it is obviously more difficult to ,. 

maintain security at this level, and except for the ~ey currently 

being used, security is not required. This fact, plus the basic 

simplicity o~ the ciphering procedures, may make possible an increased 

number and variety of applications~· and may offer potential cost 

" 

savings of considerable magnitude. 

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