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EO 3.3(h)(2) 

PL 86-36/50 USC 3605 

21 July 1948 

REF ID~'A516913 ' 

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E03.3(h)(2) 

PL 86-36/50 USC 3605 

P..R 0 GE N I T 0 R 0 F 

Or 

CAN CRYPTOLOGIC HISTORY REPEAT ITSELF? 

* * * * * 

Being s personal account of a cryptanalytic 

cballer:::Jh involved a system very similar to and which vas successfully met 

before e vn of the machine age. 

By 

William F. Friedman 

Declassified and approved for release by NSA on 03-27-2014 pursuantto E.O. 1352a 

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E:03,3(h)(2) \,. . ..-' 

PL 86-36/50 USC 3605 

FOREWORD 

.In one respect, the classification of this FORRWORD and of the 

accompanying papers is a rathQr remarkable ano•ly and one that •Y 

be of int. erest.. I shall begin th~ rtory bv ~otin2 tbat vhen correctly used, the currently employed_ _ ]ts, cr7ptographio- a11y, almost an exact replica o~ a system developed over 30 years 

ago by the.Aaeric&n 'l'elephone and Telegraph Company, tor the U. S. 

Army in World War I. A rather detailed description of the system and its apparatus vas disclosed by the American Telephone and 

Telegraph Company in a technical paper vbich vas written by the 

principal inventor, an A. T. & T. Co. engineer naaed Vernam, and 

vbich be presented before the midwinter convention or the -American 

Institute of Electrical Engineers at Nev York City in February 1926. The1

Vernam\paper vas later printed in the proceedings or the 

Institute. It se.,fs almost a certainty that the. cryptographic principles on which~ l1s based stem directly from tbat paper. 

Our records shov that the A. T. & T. Co. development vaa' · initiated in 1916, but vas perfected too late to ba.ve been employed 

extensively for U. 5. Army traffic in World War I. A set ot tolir 

intercommunicating stations vas established in the autumn ot 1918, 

primarily fQr test purposes in the United 5tates,2 and a limited 

amo1mt of actual traffic vas handled in this system as a prel1ain&r7 

to possible wider usage by the U. S. Army, both 1n the United States 

and in Europe in 1918. In the spring or 1919, upon the close ot 

World War I and £or a nlllllber of reasons, one ot vhicb v111 soon be 

made clear, the system vas abandoned. Some 22 years later, in the 

race of a real need for secure teletypewriter communications and 

while awaiting the completion of nev equipment specially des11f1~d 

tor the purpose, I suggested that the old "double-tape system be 

resuscitated by the Signal Corpe as an emergency means or teletypevri ter crypto-communication. The A. T. & T. Co. vas very helpful 

1n this and the emergency system vas successfully used from the 

middle of 1942 until early in 1943, vhen it vas replaced by better ~·-- ones using more modern equipnent. 

* * * * * 

It vas the contention of all concerned in the original A. T. & T. 

Co. development in World War I~the engineers of the company and 

·. '.:\~~ 

.l 

thoae of the Signal Corps, as vell as the cryptanalysts in the r 

M1l:J.tary Intelligence Division, General Staff, in Washington-that the system and apparatus as developed and proposed for use was 

"absolutely indecipherable without the keys." Indeed, the Director 

of the Military Intelligence Division vent on record officially to 

that effect and a copy of the letter, vbich was actually prepared 

by Yardley (author of "The American Black Chamber"), is still ·available in our files. 

1vernam, G. S., Cipher Printing Telegraph Systems for Secret W1r.e 

and Radio Tele~phic Communications, Trans. A.I.E.B., Vol. 45, 

pp. 109-15, 1926. (Vernam is the man vhose name gave rise to the · rule which we nov call "Vernam addition.") 

2A document dated 23 Sept. 1918 entitled ~egulations for tbe 'l'est 

of the Printing Telegraph Cipher" is still extant. 

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-·--------~--~,--~------~RES'l:"'!Fr°"'I~DT"i'"=°:~xs~1,6~~rrr3~---------------------- ,." £ \I' <. 

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3.3(h)(2) 

86-36/50 USC 3605 

or possible interest to the reader are the circuastancee under 

which tbe apparatus and the system were explained to me in Nev 

York, in 'the early part of May 1918, as I was about to embark for 

var service in the Code and Cipher Solution Section of G-2', GHQ-ABP, 

in France. From the summer- o~ 1915 until May 1918, I bad been a 

member ot the staff of an institution known as the Riverbank Laboratories at Geneva. Illinois, a private research organization operated · by a so!evbat eccentric but wealthy Chicagoan named Colonel George Fabyan. One of the fields in vhich research vaa conducted at the 

.Riverbank LaboJ•atories by a small staff vas tb&t of cryptography, a 

·subject in Vhieh I took an interest as an avocation. But soon it 

became my vocation, when in the latter part of 1916 Colonel Fabyan made me Director of the Department of Ciphers in addition to certain 

other duties. Fl•om then until about the middle of 1918, in a quasi-, official relationship vitb, and at no expense whatever to, the 

Government (Colonel Fabyan, as a patriotic citigen, tooted all the 

bills), the Department of Ciphers conducted cryptanalytic-work tor 

the State, War, Navy, and Justice Departments. None of theae 

larga organizations bad any cryptans:lytic units whatever until the 

Army 2 established a unit (under Yardley) in the latter part ot 1917. 

It vas on the basis of this earlier quasi-official relationship , that a disclosure of the details of the A. T. & T. cipher machine. 

and its operation was made to Colonel Fabyan an~ to me in .May 1918, 

as noted. (Security considerations were just in their infancy!) 

As explained to us by the officials of the A. T. & T. Co., 

the cryptographic system theY. proposed vas based upon the uae ot 

tvo Baudot random-ke ta es 

y , e o er, exac c 

length; both vere to be changed daily. Single tapes vere never to 

be used--always both tapes vere to be employed simultaneously, in 

combination, to generate by their 1nteract1~n a single vel'J".long key of 999,000 characters. · 

I beard nothing more about this machine until April 1919, 

when I was demobilized and rejoined the staff at the Riverbank 

Laboratories, to resume my position.as head of the Department of Ciphers~vith no other duties. The A. T. & T. cipher vas then 

being carefully scrutinized by my staff. 

Having had a good opportunity to study the system, the contention of invulnerability to decipherment without the key (the word 

cryptanalysis had not as yet been coined) vas deemed to· be unwarranted by the cryptanalytic staff at Riverbank. After noting the· 

results of their theoretical studies and elaborating the reault·a 

further, I became the principal contestant of the alleged invulnerability of the system. For this and for other reasons, I was 

directed by Colonel Fabyan to put the results of our studies on 

paper and thereupon wrote a brief brochure entitled uMethods tor 

the Solution of the A. T. & T. Cipher Machine.n The pa.per was 

prepared in March 1919 but no copy vas sent to Washington at tb.&t 

1courtesy title (sn honorary colonel on the staff ot the Governo~ of Illinois). He died in 1935. 

2The Department or Justice bad one roving agent, on the Southern 

border, vbo from time to time solved some simple Mexican d1phers,. 

mostly monoalphabetic in nature .. 

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• 

tine. Instead, Colonel Fabyan began writing letters to certain 

people and made vhat appeared to them to be some rather broad 

claims. 

In August 1919, after a considerable amount of correspondence which was becoming rather acrimonious (largely because Colonel · Fabyan, purposely or inadvertently, wrapped a veil of obscurity around vhat he thought ve were able to do), the then Director ot 

Military Intelligence, Brigadier General Marlborough Churchill, 

sent Major Yardley to Riverbank to, look into the claims vhich 

Fabyan vas making as to the vulnerability ot the system. The prin- ciples ve bad elaborated to solve this cipher were explained to 

Yardley, who returned a fev days later, accoapan1ed by Lieut. Colonel , Mauborgne, the Signal Corps cryptographic e~.pert vho bad been 

directly in charge of the development and vho, 20 years later, was 

to become Chief Signal. Officer~ The proposed solution vas explained 

to both officers, but Colonel Mauborgne contended tbat Riverbank 

really did not k.uov the Signal Corps• •ethod ot use. Although it 

was true that permanently fixed lengths of key tapes (1000 and 999) bad been contemplated 1n the original method as proposed by the 

A. T. & T. Co., Colonel Mauborgne stated that the Signal Corps bad 

different ideas: the tvo key tapes, he said, could be variable in 

their lengths, prime nWllbers being preferable; and there vere other 

neY procedures in their usage vbioh would invalidate the solution 

proposed by the Riverbank investigators. The record contain• the 

tolloving: "Colonel Mauborgne left v1th us a rough pencil sketch 

ot tbe manner in vb1cb the machine is !!2!. used; reiterating bis 

opinion that as now used, the cipher is invulnerable •••. Colonel 

Mauborgne said further that it ve could break the cipher when used 

in accordance with these rules be vould then ac.knovledge that ve 

had broken the cipher as uaed b7 the Signal Corps." 

' A day or two after the departure of these officers, tvo copies 

of my paper of March 1919 vere sent to Washington, one tor the 

Signal Corps, the other tor G-2. 'l'b.e conference also resulted in 

an agreement that Riverbank would accept the gauntlet thrown dovn 

by the Government and vould try to prove its contention ot vul- , nerabiliti of the cryptographic system by solving a set or •challenge _ messages. 

The Riverbank cipher start studied the nev situation.presented· 

by the change in procedures adopted by the Signal Corps and found 

it unnecessary to change its original position regarding tpe vulnerability of the system. Again I vaa asked to put the results 

of our studies down on paper, and wrote an addendum to the original· 

paper (Addendum No. 1),, which is dated 19 A~st 1919. '!'he 

Riverbank staff then avaited vith cont'1dence (not umnixed, however, 

vi th some trep:J.dation) the receipt of a promised ,set ot 150 cipher 

tapes representing the neballenge messages.n These were to consist 

of messages sent in one day's traffic among four simulated stationa 

forming a simulated net. 

Unfortunately, when the cipher tapes arrived, on 27 September 1919, there vere found among the "challenge" cipher tapes tour · plain-text tapes, the latter having been inadvertently included. 

Rather than accept this "bust• and becloud the issue further, we 

iwaediately notified the authorities in Washington ot tie error and "'. · on 8 October 1919 received a nev batch of cipher tapes. '!'his time.· , ·· 

IJ: must admit, however, that we nevertheless derived considerable · benefit from the "bust," for it told us much about the construction of the messages--the natUPe of the addresses, signatures, 

etc. It v111 be ·seen later hov useful this knowledge became in ··· ,, solution. I do not think ve could have met the challenge auc,ce•.-;. ::·' · fully bad it not been for this error! 

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no plain-text tapes vere among the challenge messages and the Riverbank staff began its work .. The labor vas somewhat arduous and after 

some six weeks• steady work, often 12 hours a day, my collaborators 

had all deserted me, when all our efforts seemed fruitless and the 

problem a hopeless one. However, with what appears to me today as 

rather dogged determination (hov I yearn for those days of youth!), 

I stuck to the task all alone. Finally, on 8 December, exactly tvo 

months after receipt of the "good" challenge messages, I, too, came 

to vb.at seemed the end of the trail--mentally "dovn but not out." 

Reviewing the situation quietly, with my feet on top of ·my desk 

and pulling at my pipe (yes, I smoked one in those daysl), I came to 

tvo conclusions: first, the principles of solution vere correct and 

had to yield the results we vere seeking; second, somebody bad made 

an error somewhere in the vork and the error had to be found before 

further progress could be made. What we bad received from Washington · were perforated tapes and these had to be transcribed into characters 

on sheets of paper. Could it be that one of my assistants or I bad 

made an error in this first step? There were three crucial messages 1nvolved--they had been the raw material for endless experiment--and I decided to check the transcription from the tapes myself. No 

sooner thought of than I proceeded to the task. 

My ruminations were quickly rewarded when I discovered tb&t ~I!!. character bad indeed been omitted accidentally in transcribing 

one of the three tapes--but that character was at a very crucial 

point. Making the necessary correction, I called my staff together, explained the situation, and asked for volunteers to tackle the 

problem once more. There vas 100~ response (all six of theml), 

although I could easily detect that my staff remained cynical but 

had decided to humor me in my fatal delusion. However, it was no 

delusion, and I, myself, was the lucky one to dis~l it. For within 

ten minutes and vith mounting internal excitement (some of my readers 

will recognize the symptoms) I bad obtained, as a resultant of the 

trial' of two hypothetical addresses, the letters EQU. Not much, to 

be sure--ve had often before obtained excellent trigraphs, tetragraphs, and even pentagraphs that turned out to be discouraging accidents. But I continued, thinking to myself: "If the next 

let't;er turns. out to be a vowel, preferably an I or an A, maybe I 

really have something here!" The letter that turned up vas the 1 letter I--EQUI! Hardly able to represa my excltement, I vent on: 

"In tha name of all the· patron saints of the Kingdom of Cipher, let 

the next letter be the letter P," I prayed. And a Pit was! I've 

got it!" I shouted, "I really have, this time." It was a. bit difficult to convince my collaborators and echoes of disbelief reverberated. But soon, gathered about in a tight huddle, a convincing 

demonstration, consisting of adding a few "good" letters 1mmed1atel7 

before and after EQUIP, left nothing more to be desired---except the 

reconstruction of the key tapes. The challenge bad been success- 1 fully met, but it had taken much longer than had been anticipated. 

The two unknown key tapes vere reconstructed coincidentally with the solution of a fev of the challenge messages and then, to 

prove beyond shadow .of doubt that the system had been ~olved, ve 

enciphered three messages of our own, addressed to certain officials 

in Washington, using the reconstructed keys. Our messages were 

enciphered "by band," for we did not have any of the machines. The 

Telephone Company in Chicago kindly gave me access to a keyboard perforator, by meana of vhich, very laboriously (by the "hunt and 

pec1l'method), I punched out the cipher tapes. The latter were then 

sent by mail to Colonel Maubprgne in Washington, vhere, promptly on 

1Because of the transcribing error mentioned above. But not all the . time lost on that account was sheer waste, for it vas during the 

period of fruitless struggle that all -the sbol"t cuts were developed which greatly hastened solution once the error had been found • 

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receipt, they vere deciphered b7 machine with his ovn key tapes. Colonel Mauborgne 1mm.ed1ately thereupon and without resel'V&t1ona 

acknowledged, as promised, that the validity or the Rivel'bank contention had thus been fully proved.1 Soon Colonel Mauborgne and 

Major Yardley visited us once more, to learn the details. The auceessful outcome of this experiment naturally called for another 

addendum to the original paper, and this became Addendtlll No. 2. 

By this time the cryptanalytic starr or the Military Intelligence Division, finding itself in a rather embarrassing position and insisting tb&t the initial point of departure in the Riverbank 

solution vas a knowledge of the starting points of tb..'9 tvo key tapea for each message (hov true!), proposed that these initial points be 

disguised by means ot a specially prepared small code and then 

enciphering the code groups by thre~ independent mixed alpbabeta. The proposed method (but not the code or the special alpbabeta) vaa 

aublllitted to the Riverbank staff tor cOJ1111ent, and I wrote a third 

addendum to my original paper (Addendum No. 3), proving the inadequacy of the proposed •etbod of disguising the indicators. Tvo 

copies ot Addenda Nos. 1, 2, and 3 vere now sent to Washington. BJ 

this tiae the var vas receding into the di• past, the Army autbor1 ties vere tired or somewhat groggy over the vbole buaineas, and 

thought it best to call a halt to it. Aa a consequence, 1'urtbe~ 

vork on the A. T. & T. Co. Cipher Machine vas stopped and the -1 

machines put in storage. Soon thereafter I lett Riverbank to accept ~ 

the position which vaa established tor ae in the Ottice ot the Oh1et 

Signal Officer in Washington, as the chief (and only) cryptaiial7at. · I did a little research, vben tille permitted, on iaproveaents· in ttae 

printing telegraph cipher and proPQsed one which vas soon made . public b7 the issue ot a patent. (Bow ~ive ve vere in thoae daJ'•.! · · 

;;;UJ;~~~~Q;~!d~~!l 1mnrovp}nt disclosed in this patent be adopt•d .• 

i::C:5°3 .3(h)(2) 

PL 86-36/50 USC 3605 * * * * * 

t.... ~~ ~!~~d t~~ :e::: :~u:~;:~:ic~:ra~!~~t=CJ ;r.- A. T. & T. Cipher Machine, even though they were vritten 118.D.J ~ear• 

ago, might still be of aoae value or vould, at leaat, be ot hiator- i 

1cal interest. A search through the old files at Arlington Ball .. yielded '· a copy of the basic paper, AddendUDl 1, and Addendum 3, but. 

alasl a very thorough search of all tiles 1n Washington tailed to 

turn up a copy ot AddendWll 2. A letter to the Riverbank Laborator1 .. ·brought nothing. Colonel Fabyan bad long ago departed to the ne:zt 

vorld, as had bis secretary. The Deaprtment of Ciphers bad ceased 

functioning soon after .,- departure and all its files bad been. 

destroyed. So there vas no Addendum 2 to be bad, which vaa w:itortaJ:a..-

ate, because it was perhaps the most interesting one of tb•• &11: · it vaa the one vh1ch dealt in detail with the solution ot the challenge mesaages. The only material I could find.among ay old and 

very dust7 personal papers vaa a badly marked up t1rat draft ot 

Addendum No. 2, vith many diagrams missing but v1th considerable 

number of mlscellaneous. sheets of notes, queer "doodlings," eto. I. 

1Folloving 1s quoted from a letter dated 29 Dec. 1919 tr~m Colonel··. 

Ma.uborgne to Colonel Fabyan: "You have done a great vork anct1our 

contention of last March is sustained - that the :method of u~1.ng .. the printing telegraph cipher as ·used last year by the SigllALl Corps was decipherable. This is, perhaps, the toughest individual cipher you have ever bad to tackle. 'l'o the victor belong ' 

the spo1lsl" 

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PL 86-36/50USC36"((s 

do not know,.'\fhetber it vas vorth th~ ~ffort, but I have done my 

best to recons.truct Addendum 2, vi thin the ~~mi ted time at my disposal. It isnqt adequate, and I am sure th&ttb~,final Addendum 

2, vhen it left Riverbank, was a very much better paper~ HJ;:;Jv 

it is my hope that<s.ome of our workers and. collaborators on 

may find in these.papers some tiny fragments or interest. or me; 

they are an echo of interesting even,ts of a distant age; but the 

thrill of a success.ful meeting of a serious challenge is still 

vivid in memory.l 

I have made no changes whatever in the texts o.f the basic 

paper, or in Addendum No. 1 and Addendum No. 3. Because of the 

unfortunate failure to find AddendumNo. 2, I have had to use, as 

noted above, the first •draft. This, too, I have faitb.f'ully repro- duced v1ihout changes of a materi,al nature• The papers should 

there.fore be read, not in the light of the present state of crypt- analytic science, ·but in the light of the a.rt as it was in 1919-

a long time ago, when considered in terms oft.be progress that has 

been made since then. 

In the light of these resuscitated papers of long ago, one 

fact takes on a s,pecial significance: the present usa.ge .of a system . over 30 years old points to a lack of sophistication or imagination in cryptographic invention. This lack receives.confirmation vhen 

we take into consideration other things that ve know, and,l feel 

that::::Jld not be too pessimistic about the futur· ..e. C~ren.tl· .. y, the roblem is, in certain respects, much more dif'fi;:.cu=lt.:.· ~--, 

than e one which conf'ronted the Riverbank staff in 1919. 

than were ose nvo ve 

the Riverbank solution; nt by far is this difference.~ 

e are 

the 

latter nei~t~h~e~r:......:.k~e~-=~e::.......:w~a~s::......::e~v~e~r~u~s~e=-~i........:~s~e::..:.:=:....&...~~~==-~~m=bui~na==--___, 

tion and 

it is the case that e 

Finally, there is one more aspect well worth noting and or 

current interest. 

The Riverbank staff solved vb.at was for those days, I think, 

a very complex problem, and it accomplished the task under circumstances which, considered in the light o.f what can be done 

cryptanalytically today, were rather difficult. 

In the first place, the starr was very small in numbers and, 

with one exception, its members bad relatively little training in 

theory and very little practical experience in "operations" a& 

lAs of possible interest to my readers who may care to look into 

it, there is on file a paper entitled: '.'Extracts from correspondence relating to ~olution of A. T. & T. Printing Telegraph 

Cipher," together with certain letters which explain vhy the 

Extracts were prepared. They give further dets,ils of the story 

and its background. 

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EO 32_(h)(2) 

PL 86-36/50 USC 3605 

conducted in these days. In the second place, its procedures and 

tools vere relatively veakand undeveloped, for modern methods.and 

techniques vere just in their infancy. In· the third plaee, it bad 

only one set of messages on which its contention of vulnerab111t7 

bad to stand or fall. And if it had failed on that single set, it 

would have co•pletely fallen dovn on the job it bad undertakenfor no other set of\messages, I feel sure, would have been •de 

ava.ilable to permit another trial tc;. be made. In the fourth place, and possibly Qr greatest import, the Riverbank staff solved the 

problem without the a:td ot maebinery or any kind whatever. 

Of course, ve vere always on the lookout for "short cuts" and 

"band" aids to speed up\ the cryptanalytic testing. I do not tbink 

ve suffered from lack ot imagination, but the •chine age in crJPtanalysis had net yet dawned. Tabulating machiner7 vas just in 1ta 

infancy; its use as an aid in cryptanalysis was not even conceived •. 

But the Riverbank staff, small as it was, without adequate training and e~perience, lacking special machinery, using vbat •Y 

today seem rudimentary methods, and having onl7 a single, relatively small sample to begin with, nevertheless successt'ully met the 

challep.ge of:te1"ed by the Sig®-1 ·Corps and G-2. Today, v!th the aid 

of high-speed electriea l and electronic devices,, vi th much advanced 

cryptanalytic theory, methods,\ and techniques, vith an adequate stsf'f of' enthusiastic, competent researchers, and a plurality of' 

sources from vbfch eoca.myles to be vorked upon can be .selected, 1t 

seems to me tha_ _should not be a hopeless problea. While 

the odds against our present workers •Y be greater than the} vere 

against the Riverbank workers, th$ tools and methods of the former 

aro very much better than those of\ the latter; and over and be;yo.nd these considerations' there 1s this\one: the urgene71 importance, and possible fruits of a succea•f'ul\11eeting of tbe 1948 challenge 

are so much greater than those of the 1919 challenge that no cOllparison vb.atever can be made· in thes• respects. Just as the 

Riverbank workers met the challenge presented to them in 1919, with 

far less at stake, so I ·feel sure oUl'I \workers vill success- '. 

fully meet the far more difficult but aueb aol'e important challenge 

ottered them in 1948. 

21 Jul;y 1948 ;,.·, 

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~------~------~~--\_,------~R:E-F-T:JT:-:'k5~r6~9~1~~~------------------------.., 

j 

C 0 NT g ITS. 

Adnnt.8{11•, 11pect and••• ot op.-atS.. umnq md 

po..S.bilit.iee in the -r ti cU.ttimlt7 ot dlial,li&Mn&. 

-..1aw • .-. tt.apr ot OY•laPJU8 partJ.me or ........ , 

nt••ld.tJ' tar cwt.ala ohuMtere 1lldab operate U. mahb md are neo-

·~ a s-rt ot th• aisfMr •• .. , rec1.P"OC1V !n oi]:t.- SIQ&re 

2. Solut.ic.o ot •incls le)' meseaee a which overlapJ detecting 

owrlappjng placu. 

3. Solution ot double l"UllllJng k87 mesaaaae which overlap; reccnat.l"\lot.iCCl o! lte19 froa 801.Ted or capbJred lll888AtJN• 

4. DeciJ:ttarmert. b7 aiperillpoeition ot cfC].ea with not.hing given 

except. that. 1h1ch 1a im.-mt in the machine iteelt. Decipherment at aubindicators. 

6. Cipher square or chart. 

{a) Haw it 1a constructed, pr.tmar7 form. 

(b) Cllanced from prl.mey into seoondarr square tar ccr1-

venienceo 

(c) Reciirocal ralati<n5 however U8ed. Jlakes reconstruction 

or square easy. 

j 

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v 

PRIHCIPL~ mm> IN TRI SOLUTICll re TU A. T. • '· 

KACHm; CIPHIR. 

ln .1me. 1918, thwe wu ~t.tecl fer Gar __,natS.m bJ t.Jl• 

A. T. ' T. Q:apw(,f. and the ott1ce of the Cid.et S!gnal OftiOll" ot tile 

ad.toed ::ta.tee /trf/ff1 det..O.. and .-pl.e• o~ the 10l'k ot a oi)iMr MDhina 

to be teed 1n tNnaitU• 11ent ot.Udal cClllmdaatima. Attw cnd.dereble Dt\lltJ' - haft fo:t•d t.hl Ofdnb t.ba\ t.h• .,.w. ,... ... aerta1n 

•allne •ea which pmit ot • attack 1IPOll the cisf\_. and red• it mate 

tor mat tere or 1.mportmoe. 

We ehall tr.v to 8how tirat. that t.be •l!&bteat oarelamea on tbl 

pll"t ot 8JJ7 indiv.ldual entrusted "1th the actual •l'k of 11101p11_.1q 1llll 

lay all tb.s mesaagee enaiph.-ed by.._ ot the ... k87a Opl1 to •117 S>lut!on.. Since carelnmeu an ta'le part ot the pc-•C11'JD91 to be entruatec:l wit.b 

tm oper&t1.cm ot the machine and ~ce on thG.1- part ot tll• 19sons tor 

evt1r7 precaution naoesea.17 ill cilfl_. work are to be 4U1>ected, the ez:latenoe 

ot this opening for m att.aok aut. be admitted. SeconcSJ.7. we shall, at temp, 

to chow~ granting not onl1' an abeold.e]Jr intall.1ble operatic:n ot tihe maohSne 

b7 the peitBOnnel. 1 but aleo the theomioal absolute !mdlaisf\erabilit7 of a-, 

massa;;e .:inciphered 'bJ" means ot a ramom-med, e1D61.e. nan-repeating. runnSq 

k8)', that the mechanics or the machine, and certain tea. turea of the qatem, 

are euch that an attack ill not onl.1- practicable, mt ea.q Wlder l'lDl'al canditione. 

It will be wmeces881'7 to II' ~ detalle of the oparaticn of the 

nachine- inamlllch ae this report ia addressed onl.7 to those who mbm1tted it 

tor examination. 

~Ve shall di scusa the solution of tllO c 88EIB: 

(1) i.lbere L1eeffS,gt;s h.<lve been encifhe1-ed inCorrectly, 

two or more bejng in the sane keya. 

(2) lihere messages ha• been enciphered correct.)¥' 

none being in th• aan.e 197s. 
"E ID : xsr6"913 

., 

1. SOUJTION OF A CASE l'JHERE mo MFSSKZS HAVE BSBR 

ENCIPHmED BY 1'HE SAMS REJS. 

Let ,. BUppoae that- in the two •asaaaa g1Te!l belar the ts.rat 

bas baen enciphered b7 the -ye indicated am that. through an 0"1'8ight 

or careleaaness, the secmd message was thm enci!Dtre4 b7 the - Imp, 

beginning at a:xact.l.7 the aame point 1n each ke7. '?ha rnult ot aucb an 

erro:r 1a that both meuages haw bee ma1Jilered by 1;119 ama sillgle kl'T, 

and we may disreprd tor the preaent the tact t.hat. a double -.V was •ed. 

We give the dstiaila ot the aoluticn ot such a case. not. because thl!lzre is 

auqth!ng origtnal or seemhlgq :Impossible contained th.-ein~ but bec8Wl8 . 

cert.ain phases of the prmciples eluo1dated will be used lit.er int.he di.a--. 

oasa~ of a more co.uplloated case. 

!! l l ! A Si l !· 

l. E Y 'l PP QPJUY Q.4 RU V YXJIJIO X6RDP 

YN3RF V7GCG 3RRXQ YGGTE IF ORT 

• 

TYGIH JBPSS DFJSB IWMAX ClGX3V 

ELHYU PYJNX LKKWV OYSCR XIBetc. 

etc.et.a. CEL2W C3SKC 

2.EYTPP QPJMY Q.)p RR B _,; SJE7H FJ.14F.3 

JINOAU FVGC!l JIECI X3I7P 1t3GJI 

T D W I 1'1 SE7E2 KZ2P6 SH I 2 S FLWY.3 

UQHAU YVLDMT GESGC D V Y J 'l' X L Q etc. 

etc, et.a. 4HZUF CR3LX JP63Q u Q 

We nay disregard the first seven letters in both measages1 

since they deal ldth the key indicaton• Tm next. f'our letters, J ,H,Y,Q, 

being conmon to tx>th messages> probabJ.y rei:resent ~' (tunctiona of 

machine: carriage return, line teed, letters). We may begin worldng, 

therefore, trom that point on, as shown below, pitting the messages direct3¥ bemath each other. 

-2-

1 
''-

Yess .. l &.• 4 n ~·: v H x H H 0 x 6 N D p y N 3 n F v 7 G c G 3 N R x 0 y G. G 

lless ~2 "'" t' R R B S i f. 7 H F II 4 F .3 'fl N O A U F V G C ?.I J X E C I X 3 I 

Mas a .,l - ? 1~ I F ~ R rr T Y G ! H J B P S 5 D F J S B K IT J.f A X C G X 3 U 

Jloss.,2 - '! f' K 3 G J I T D ~1 I 11 S 8 7 E 2 I Z 2 P 6 S H I 2 S F 1. l1' I '3 

lleee ol •• F. L R Y U r Y J N X L K K W. U O Y S C R X I E et.c. etc. C B L 2 

Keas~ 2 - U '1 H A H ': L D 1! T G E S G C D V 14 J ! X L 'l etc• eta• 4 R Z U 

Mess ~l - "! C 3 S K C 

Kess ,,2 - ? C R 3 L T. ~T P 6 3 Q U Q 

Bow in all mHsar,es \19 mq expect. to find bat.ha a~s of 3's 

(spaces) a.rid 442 (ce.rriaga rot um and line teed) 1 repeated irwgularq at 

intervals t.hroughout the mesaa~-ea. Ir \'18 can locate 1n om ot the meaeagea 

a series or 3 •s or the combination 442, 01' &r\Y othw plain taxt, t.hm • lllll;I 

find whe.t. the plain tat ot the correepond1ng portion of the oth• mesaage ie. 

The ooapleto &J1U.&Bi.r,y ot tho cipher square, giving rill• to reciJa"Ocal relations between tho three elemnta, ke7. plain text and cipher, in a JD8llDlr to 

bo e~la1J1ed bel.Olll, .lll&kae 1t poa•bl• to racover the single Jmy• given the 

cipi_. ani the plain text. Thie is the tint weaknlae in the al.pi_. a;yateao 

In this ex..-U.•. we ma7 start. ott Iv a88llldng ~hat tba plain text 

ot ore of the masaaees ccneiets ot noth~ bit a s .. 1 .. ot 3's• and then 

find oa.t et the plain text ot tha other mesaege muld be m thia a88Wllpt1ml. by referring to the dphEr square; that is, b7 timing the single ke:y 

1etters concemed tor the tentatively deci)ilered portions and appqing the 

to the corresponding portions in the ot.har message o For oample, the first 

cipher letters in the two nessagea as arranged tor deciphercent are 4 and Po 

It we asswm that the plain text. equivalent or 4 1s 3, then the kay letter 

would be N, 1n which case the plain text equivalent ot P would be G. If', 

on the other hand, we assume that the plain text equivalent ot P ia 3, thln 

the 1cey letter •·culd be L, in which case the plain text. equivalent. of 4 would 

be G W..so, wt the ":result of <JSSuming the key letter to oe 3, a.ppl.y:i.ng it to 

4 1 which gives N .t and then applying N to P, 1s also GJ and tha result ot assming the key letter to be 3,, ap~ing it to Pp which gives L, and thci applyine l 'tO 4» is also G" Tt:ies• relaticns,, :J.5 stat".'Jd above, ~ld true because ot the complete rec!procitq ot the cipher aquareo It ie cle_. therefore. that we can omit. for the pre•ct, tho intermediate step or deterndning 

-3-

, 

I 
REE' ID:AS1"6'"9J:~3~~~~~~---------------~ 

the key letters, and find a~ the pl.Ain tut of the other meaaage 

directly trom the sq.is.re, by considering only the three element.as assumed 

plain tm., e1~ or ... ,,. 1 1 and al.lit .. ot -up 2• 'ftiU om be ._. 

in one operation by proceeding down t.he ool\11118 headed, tor .-p:i. b7 4 and 

P 1 1n the oiphar aquare, unt.U we coa to .3 in cine ot the colunae, wJe:reupon it will be f'ound tho.t G 11 in tba other cal.um on. the aam Una u 3,, 

or we can proceed down the ml1111U1 headed b7 4 and 3 to P Jn cne ot the colWlllS, whereupon G will be found to be opposite P in tha oth_. columl en t.h• 

8fUne line. An:Jr t.hree letters ma7 be chosen to find the tourt.11 1n like .manrur, since the tour elements, 4, P, 3 and G,, exhib1t oOJIPlete recipiooit)r. It 

Ylill be noted that t.he letters 41 P,, 3 and G appear at the to~ cormre ot a 

rectangle 1n the c1 mer sq.i.are. and that there are six times 32, or 192 nob. 

rectangles in thia square, at the corners ot which the let ten 4, P 1 3 and Q 

will arpear. See Fig, 1. 

Pm. l. CIPHER SQUARE 

ABCDEPGHIJKLKHOPQ.RSTUVWXYZ234567 

A70FR2CBQS4RZSl6?HDIW3XTVPLEUJKOA 

BG7QTOHAFSLPJSISICWUDVUR3R46XZI2B 

CPQ7UKAH04SEUL2POB3JVDTXW6SRRIZrc 

DRTU743WXI216YSZSVAHBCQGHKOJFBPLD 

E20147R6YURCWXFBQPJ3ZI5LHHTASDVOB 

FCHA3R7QBJI2SZEY6GU4XRWVTOMIDSLPP 

GBAH~6Q7CMZY4IP2NFT5RX3DUIJOVLSE~ 

HQFGXYBC7LS6I40R2AVZ3WRUDESPTMJKR 

ISS41UJUL7FDHGRVTZNAPEOY6WQ32C·BXI 

J4tS2RIZ,F73BQUWXUEC6HYOPVGDlAHTJ 

!NPEIC2Y6D37XWAQBOSR54ZULGVFJUTHK 

LZJK6WS4IHBX7CVR3SOQ2.YNEIUATPGPDL 

KSSLYXZI4GQWC7T3RJPBN621EDFVOHAUN 

WIY2SFEPORUAVT7H06IDMJLSZBXC43WQR 

0 6 E P 7. B Y 2 N V ~1 Q R 3 H 1 C K L X 4 5 I J S F D G JI T U A 0 · 

PYK05Q6N2TXB3RGC7EHWIZ4SJAUHLVDFP 

QRCBVPGFAZROSJ6KE7XLUTD3R21YW54NQ 

RDry3AJUTVNESOPILHX?KGFHBQ564C2YZR 

SIMJN34SZACRQBDXWLE7Y26PbTHUEPGVS 

TWDVBZXR3P652NU.IUGY7QCAFSELHOKJT 

U)VDCIRXWEN4Y6J5~TF2Q7BHGLPSAKOUU 

VXUTQ5W3ROYZN2LI4DH6CB7PAJKMGPESV 

WTRXGLVDUYOllEK5JS3APAHF7CI2ZQ6.H4W 

XV3WHMTUD6PLKEZSJRQOFGAC74R5BY2IX 

YPN6MHOKEWVGUDDFA2STSLJI473QZXRCY 

ZL450TUJSQGVAFXDUI6HEPl2W37WYBCRZ 

2B6NJAXOP3DFTVCGHY4ULSHZSQU7IRXB2 

)UXRFSDVT2KJP04ULWCEHAGQDZYl?N653 

4JZIEDSLMCAUGHJTV52FOKP6YXBRH7QW4 

SJlIZPVLSJBHTFk'WU.D4YGKOEN2RCX6Q735 

602YLGPEKITHDUQAFNZVJUS41CRBSW376 

7AB,CDEFGHIJKLMNOPQRSTUVWXYZ234567 

.-4-

' 
--~~~~~~~--~~--~RE-~B~~~~l~6~9~1~3t--~-----------------,,: 

~ 

l ) \..,_..," ..._, 

Applying this procese ot ase\.111ng one or the messages to consist 

exclusive]¥ of 3va~ the illain text of the oths- message is sham in Fig. 2. 

on the line labeled ''Equivalert.s of 3.n 

Keasage l... 4 R M V M X H !f O X 6 N D P Y N 3 R F V 7 G C G .3 R R. X 

llcBsa P,8 2~ P R R B S J E 1 H F V. 4 F 3 JI N 0 A U F V Q C II J I E C 

EquivaJ.ente of 3- G 7 L A X L R ·o 4 ff A 7 7 P F J 0 F C Q G 3 3 2 J t B Q 

l.Cesaaee 1- Q Y G G T E I F O R T T Y G I H J B P S ' D F J 5 B K W 

~~~e~ IX3I7PK3GJITDWIWSE7E2XZ2P6SH 

&!uivalel'lts of .3- Y N G O H ;; F F I S L 3 0 F 3 A R JI L 7 B 2 0 F F I C A 

Meeaar,e 1- l! A X C G X 3 U E L H Y U P Y J N X L K It W U 0 Y S C R 

Message 2- 1 2 5 F l.. Vf Y 3 U i H A II W L D M T G E 5 G C D V JI J T 

Fquivalents of 3- V S I 3 N R Y 3 2 3 I. S E A I H D N R H F l•' Y K f E V 

Message l~ X I E etc. etco 

Message 2- X L Q etc .. etc .. 

Equivaleni»s of )- 3 T L 

Not.a the underlined port.ions ot what is appannt.J¥ excells nt plain 

texto Th0 first one spalle out 3Q? ~ mi~ suggests 3CF3. 'l'wenty-t1&0 letters 

beyond that 111 find 30l'3AIW, which suggests 3'.)P'3ARM!So Five letters be;yond 

that, we find CFFIC, which suggests 3(FF'ICE3• or 3(FFICER(S)3, or 30FFICIAL3. 

These plain text portions may or IIJa7 not. belong to the same mesaage. since 

we cmmt tell~ to Vihich message E.J\1 t.entativel7 deciphered pc:rtion belongs .. 

Let us now tr.v a series of 442 1s in plaoe ot a series of 3'•• In 

other v1ords, we ~ assume that one message consists exc1U81veq of a aeries 

or 4421a, and see rlhat the plain text would be f'or t.he oths- messa~e. We my 

start by assuming 442 to occur at the begi.ming of one message, arid see what 

it gives· for the corresponding place in message 2, thus: 

llesaage 1 - 4 R N 

J!essage 2 - P R R 

Asswned plain t$xt - 4 4 2 

F,quivalents of~ - P 4 H 

Since P4H does not oonatitute aey part of a plain text v.ord, we 

try the seqtcme 442 one space to the righto Thus: 

Uesss.3e l - 4 R n V 

llessago 2 - P R R B 

Asaumed plain text. - 4 4 2 

Equivalents or 41.2 - 4 vs 

! 
This cold:d.natim, 4vs, is likewise no part ot a plain text; 

word,, so we tt7 the aequenae 442, c:ne, t110, three • • • • • spaces to 

the right:; taking not.a of atl the epod combinations llhich Nault in 

the other meseageo Row,, a short cut to this process is to fill out 

on one line the equi"flllents or 4; on a line belc:M1 the equivalmta ot 2J 

then the f'irst two menbers or 8117 aet or the three equivalents ot 442 llill · 

be found b7 taking tl'C seq\Jent letters on the :f'irst of the two Unes of 

equivalents, and the thiJd member of the set or three ecpivalents w:Ul be 

found direct3" to the right ot these t11> letters on the lower line. 

'l'hwr: . 

Jlessar.e l .. 4 R U V M X 

lies saey 2 - P R R B S J 

Equivalents ot 4- P 4 V K Z V 

Equivalents ot 2- H S 6 H 

(P4H 

Equivalents or 442 ( 4 v s 

in successions ( V JC 6 

(I Z B 

( etc. 

App.qing th 1s process tlroughout both messages,, we have what is 

ahonn in Fig. 31 which incl.11ies the equivalanta of 3,, since 118 mA1 as wall 

coni>inl the reau.lte or both uperillllnts into one figure to see it w can · 

plece tog et.her such port.icws of the tentative decipharment. • _., be 81.ven. 

rm. 3o 

•sa~l-4RMVUXMMOX6NDPYl3RFV7GCG3RRX 

•sa~2-PRRBSJE7HFK4FlUNOAUFVGCHJXEC 

Equivalents ot 3 - G 7 L A X L B 0 4 H A 7 7 P F l 0 F C Q G 3 3 2 J Y I Q 

Equivalents or 4 - P 4 V lt Z V Y H 3 0 K N B G E 4 H E 2 6 P 4 4 C U B A 6 

Equivalents ot 2 - H S 6 H 5 V C L S I I T l 2 V J 4 Z II 2 2 3 F ~ D Z 

•s~~l-QYGGTEIFORTTYGIHJBPSSDFJ5BKW 

llessaee 2 - I X 3 I 7 P .K J G J I T D W I 1T S E 7 E 2 K Z 2 P 6 S B 

Equivalents of 3 - Y N G 0 H W F F I S L 3 0 F l A R ll L 7 B 2 0 F F I C A 

Equiv al.ents of 4 - B 7 P H O S E E R D V 4 H E 4 K I T V N Y C ft E E R 2 It 

F.quivalents or 2 - i1 R U V L Y J 'J7 ! H 2 V J 2 S N G H rJ l V J J 7 4 S 

Message l - M A X C G X 3 U E L H Y U P Y J N X L K K i1 U 0 Y S C R 

Kessage 2 - l 2 5 F L W Y :3 U Q H A M r/ L D U T G E 5 G C D V M J T 

:Equivalents or 3 - v s I 3 N R I .3 2 E 3 L 5 E A I H D N R H F F I K I E v 

Equivalsits or 4 - L D R J 7 I n J c F 4 v i1 F K R 0 s 7 I 0 E E B A z F L 

Equivalents or 2 - 0 A 7 2 RN ~·7 2 3 U 2 HD US 7 L KR H L J J W D 6 U 0 

Jlessage l - X I E ••••• et.c. 

!!,BS&B! 2 - X L Q ••••• etc. 

Etluivalents or 3 - 3 T L 

Equival.ed:.s or 4 - 4 l! V 

F.qu1valents at 2 - 2 P H 
ImmDc:liately prccoding SCli'JARM (the result of a series ot sewn 

3•a) wo have L anl before that ERA (the result o! 442). Noting that the L 

can be joined to tho ERA and then to the 3<F:3ARU, we have the toll.O\dng: 

Plain t~ of one mes sage - O R P S · 4 4 2 3 3 3 3 3 3 3 3 A N 

Plain ta~ ot other message - 3 G E rt E R A L 3 0 li' 3 A R )f Y 4 

Iz:uoodiately followi1'!.:; the place wl'ere ARll occurs, we have the 

follo\'ling: 

Plain tst of one rres sage - N Y 3 0 F F I C 

Plain text of other message - 4 4 2 J 3 .3 3 3 

We can join the ae t'ID portions, and asauning that CIUS js a part. 

or the name 3SIGNALJCORPS # we have: 

Plain text or one message - .3 S I G N A L 3 G O R P S 4 4 2 3 .3 .3 

Plain tt;:J(t of other message ... .3 A D J U T A N T 3 G E N E R A L .3 0 

Plain te>.-t of one Jll').Ssage - 3 3 .3 3 3 A N Y 3 0 F F I C 

Plain teJtt of other measage - F 3 A R M Y 4 4 2 3 .3 .3 3 3 

' With this amount of. intel.llgible text to build upon,, it is not a 

difficult matter for the or,yptogra.pher to compl.ete the decipherment or these 

two rneesages., applying the principlea 0lucidated above, tdth this modification: that continuation or text in one mes~e reeulte in continuation ot 

text in the other, without a recourse to the assumption of a series or 31s 

or 442's. 

To recover the key we have but to take the plain text or either 

zrsssase~ and one or the ciiner messases and refer to the ci}iler square. Were 

the tvi10 nessases exactly the sane in length, it 1V0uld. be jmpossible to tell 

whether the cipher rnessa.ee labeled l above applies to the plain text. message 

beginning ro ALL OFFIC.ffiS, or to the other message., In this case, havever1 

the r!1essages are not the Slllle length. The endings are as tollows: 

1. • • • • • C E L 2 W C 3 S K C 

2. • • • • D 4 H z u F c R 3 L x J p 6 3 Q u Q 

Tm deci?ierment up to the p:>rtion where the two messa~s no 

longer overlap is as follows; 

-?-
E" ID : A5I'"6 9'I"3 

l ••••• CEL2WCJSKC 

2 ••••• 4HZUFQRiLXJP639U9 

OFFICER 115 

VOCATE3GEN 

It is cvida'lt that the second message ends • •••• VOCATB3 

GmERAI.3£1 and we can now attach each cipher to ths JrOpar plain teact. 

Cipher message l begins '?O ALL. <FFicm.5; cipher message 2,. COL J B 

EJ.!mSON. 

The c:or.pleted work appe8l'S as shfllm in Fig. 4. Tie solution 

of such a case present no great difficulties to the deci,lilerer~ although 

the irocess mey be ratmr slow. 

FIG. 4. 

Singl.e kef _..,;.. ________ A H 9 4 0 L 0 X C It 0 l I Z X 2 4 II 'r 

Plain text of Cl'le mc:issage- 4 4 2 5 T 0 3 A L L 3 0 F F I C E R S 

Plain tsct or other mceaaae- It 4 2 5 c o L l J 3 B 3 E M E .a s o I 

Ci}hlr - - - . - E Y T P P Q P J ll Y Q 4 R ll V 11 X M U O X 6 N D P r ~pmr----EYTPPQPJUIQPRRBSJE7HFM4F3K 

Singleb7-~MUDCH6R52PIVSZB2GQAST4HHZV2 

Plain text - 3 0 F 3 T H E 3 s I G I A L 3 ·c 0 R p s 4 ,. 2 .3 3 3 3 3 

Plain text - 3 3 3 C A R .E l A D J U T A N T 3 G E N E R A L 3 0 F 3 C~~---N3RFV?GCG3NRXQYGGTEIFORTTYGI 

Cipher - - - N 0 A U F V G C Y J X E C I X 3 I 7 P K 3 G J I 'l' D W I 

Single kB7 - T K X Y D R F Y I L S E L P I B t P B H W 7 P Z W X G P 

P.l.ain tut - 3 3 3 A N Y 3 0 F F I C E R S 3 N 3 T H E 3 S I G N A 

aaintat-ARUY44233lJ3ITJIS3REQUESTEDJ 

Cipher - - - H J B P S 5 D F J .5 B K VT M A X C G X 3 U E L H Y U P I ~~~---WSE7E2KZ2P6SHI2.5FLWY3UQHAMWL 

Single key - B Tl R S B P A Z H 6 R 6 • • etc. 

Plain text - .3 C 0 R P S 3 D E S I R I M G • • etc. 

Plain text - T H A T 3 I N F 0 R M A T I 0 N • • etc. 

Cipher - - - J N XL K K l"l U 0 Y S C R X ·1 E •• etc. 

Cipher - - - D M T G E .5 G C D V U J T X L Q • • etc. 

Single ke7 - l X K C V W Z R 1l 0 P N 6 4 

Plain text .... I C E R 6 JI .5 

Plain t.eict - A T E 3 G E N E R A L 6 JI 2 

Ci}i'ler - - - 2 W C 3 S K C 

C~mr---UFCR3LXJP6)QUQ 

• • 

• • 

• • 

• • 

• • 

• 0 p II 5 

• • OFF 

• 0 voe 

• • CEL 

• • 4HZ 
BE 

2. SOWTICN CE A CA!3E Gl'ml FIVE U1!1SIGES OORRECTLY 

ENCIPHERED, NONE BEINl IN THE SAHE IEJS. 

It. is clear thnt ir om key 18 1,,000 letters in lengt.h md the 

other 999,, tm :resultant single ke7 could n«. begin to repeat 1tselt until 

999,,000 letters Jave been enciphered. Thia f'act obviouaq precl\llfee the 

possibillt.y or an attack uμ:>n the sane principles as eJ;>lainecl in t~he preceding section, sinee orerlapp~ messages would Vflf7 rareJ.y, it ever, occur 

acept as the result or errors. l'llile it is true that the resultmt single 

ley 1a a n:>n-repeating,, random-mixed 1m7,, 19t the fact that th1B •Snile 1m;J' -

results trorn two ke79 which remain constant,, though shitting w1 th regulari\7 • 

permits an attack to be made upon the s7stem. 

It 1s clear that U a J!8saal)t beg:ldlwith the keys OCB.-<>01,, after 

1,,000 letters have been ancifhered, the longer ley ...Ul have .made one ao.mplete rnolut.ion, and the short.er ke7 11111 have made one coq>l.ete rewlution 

plus one letter, reeulting in 1-oinging back the longer kfl' to 001 ml the 

shorter key to 002. 1'bese tm revolut.ions constitute what we sha.ll tA!ra a 

SYcle• and m thia instance, the tlret cycle will haw been co.apleted. A.ft.er 

21 000 lot.ters,, the longer key wlll haw made e:mctJ.y two coDplete revolut:lans, 

thl shorter one· win haw made t1'0 letters mre than two coq>lete revolut.ions~ 

resulti~ in bringing the longer key back to 001. and the shorter kq to 003. 

This 1110uld be the end of the second cycle. These r-elations exl.sting bet.•en 

the two keys end the cycles are illustrated graphical.11' in Fig • .5 • in which 

sequent cycles are super:llnposedo 

FIG • .5. 

Cfcle l. longer key - B Q Z V .3 P N V 6 0 R K etc. • o V X II 

Shorter ley - N V A C X Q 5 R T S B Q etc. • • R K R 

Cycle 2. longer lcs;y - B Q Z V ) P N V 6 0 R K et.c ••• V X lf 

Shorter key - V A C X Q 5 RT S B Q etc •• R KN V 

Cycle 3. longer key - B Q z V 3 P N V 6 0 R Jt etc. • • V X JI 

Short.er key - A C X Q .5 R T S B Q etc • • R K V N A 

Cycle 4. Langer key - B Q Z V 3 P N V 6 0 R I etc. • • V X 11 

Shorter key - C X Q ' R T S B Q etc. • • R JC V N A C 

etc. etc. etco etc. 
ve shall talal aa tho measure ot a complete cyal.e the longer kBy. 

Note that we may regard the longer key as. statiClM.17, and merely shift the 

short Er ley ono letter to the lett aftara eaeh cycle has bean completed. 

The msis or the attack on this case consists in (1) determlning 

and euperimposing sequent eycl.ee; (2) assuming the presence of such characters 

as 442 end 33333, which cannot be eliminated am st.ill have the machine 1\mct:ion proper~; and (3) recovering the keys step by st.ep simultaneous:W with 

decipherment. 

In order to simplifY the explanation ot this case we shall show 

first how the double keys are recOYered and tested as to correct.nesa, using 

a certain amunt of cipher text. with its correspording plain text, diaregardill! tor the present the Ql&stion of how the latter is obtained. Ve shall aaet.111e that the portions ot t«Kt given below belong to the saae section or three 

sequent eycltH, and that we have the plain text tar the first t11> eycleso 

Fm. 6. 

Cjphsr - CJ N U Q R X ; etc. 

Plain - 4 4 2 5 A 6 II et.c. Q.ycle 1. 

Cipher - 2 S 4 W P W N etc. 

Plain - 6 II 5 UH L E etc. Cycle 2. 

Cipher - S E 4 Y K I 4 etc. 

Plain - etc. Czola 3o 

Row the successive stops in the recove~ ot the d:>ubl.e kBl' are 

illustrated graphicall,y in Fig. 7. and the subsequent. discussion will ret81" 

to the VSZ"ious secticns ot this figure. 1'8 do not know mat the canbinatim 

of' letters in the longer and the shorl#er key 1s whkh produces ciiiJ.er letter 

G from plain text 4 as the f1rst cipher letter in cycle 1,, and cipher 2 trom 

plain text 6 as t.he first cipher letter in cycle 2o .Ebt we my &SSUD8 in 

cycle 1 that the first letter in tie longer kev is A, in lthich case the coiresporriing letter on the shorter key must be z, as ah<Mn in (1) ot Fig. 7; 

in cycle 2,, remembering that the longer Jey remains stationary,, and that 

the shorter one shifts one space to the lett after each cycle,, it tho first 

letter in the longer key is A1 then the corresponling letter in the shc:rter 

key, to produce cipher 2 trom plain text 6, must be G1 as shOM'! 1n (2) ot 

-10-

1 

l 

REF ID:A516913 (' ,., ' 

Now since the sh>rter koy has ahi£t".ed one letter to the left in 

cycle 2, the letter G can be ptaced neAt to Z on the shorter key in cycle 

lo See (3) or Fig. 7. If the letter in the second position on the shorter 

kf.G' 1n cycle 1 is G, in order to produce cipher N f'ran plain tsxt 41 t.bo 

carrespording letter in the sane cycle on the longer key rm.ist be Vo See (4) 

ot Fig. 7., 1'& may now place V next to A on the longer key in cycle 2. See 

(S) ot Fig. 7. 

In order to produce cipher letter S from plain tooct M in conjunctim 

with V as the letter in the longer key• the second letter on the shorter key in 

cycle 2 must be Uo See (6) of Fig. 7. We may now pl.ace U ne~ to G on the 

shorter key in cycle 1, as sham in (7) of Fig .. 7, and find the corresponding 

letter on the longer key. It ie 2. See (8) of Fig. 7., 

The proocess set forth 1s continued, resul.ti~ finally in the reconstruction or a double by \'hich will produce from the ciphEr letters given 

in both cycles tm correct corresponding plain text. Thus: 

Cycl..e lo 

Cycle 2. 

Longer key - A V 2 X 7 JI V 

Shorter key - Z G U I D G X 

Cipher - - - G N U Q R ·X 5 

Plain text - 4 4 2 5 A 6 14 

longer key - A V 2 X·7 J.f V 

Shorter key - G U Y G G X lV 

Cipher -- - 2 S 4 1'1 P ~·'l N 

Plain text - 6 !.I 5 U N L E 

'\Ye mq teet the correctness or these keys by applying them to 

cycle 3. Thus: 

Cycle 3 

Longer key - A V 2 X 7 M V 

Shorter key - U Y D G X :·r 

Cipher - - - 8 E 4 Y K I 

Plain tt11et - E R A L. L Y 

\\8 see here the ending of a word like GENERALLY am we may feel 

sure of our keys. 

Now in the reconstruction of our keys above,, we began Br"bit.ra.r~ 

wjth A as the first letter 1n the longer key. l\6 might have begun with acy 

other one o£ the 32 possible lettf:tl's of v1hich the cipher square is conposed, 

and thus b.d.ld up anothqr pair o! keys which, though in ext.em.al appearance 

althogeth .. different !':rom the pair recovered above, wruld serve just as vtell 

as the latter. In short., it is }X>ssiblc to derive 32 different pairs of keys; 

-ll-
REF ID: A516913"°"' . r., J 

8JJ7 pair or lhich might be thl original pair. but since all pairs give 

equivalent results, it will be unnecessary to f'ind out which pair was 

realll' the criginal. 

In t.he preoed1ng aanple, the decipherment of superimposed 

portions ot 07cles 1 and 2 was given, it havirg been stated that '"' should 

dimiegard tor the r:x>ment the ouest.ion ot hon this deciphel"l!lent was irocured. 

We shall mw proceed to the next step, which is to deciJ:iter ard reconstruct 

the ke19 e:imultaneouazy, given no decipherr.ient whatever t.o start with. For 

thia caae we ehall show the steps in the actual solution ot a Jroblem where 

onl.J five messages have been intercepted. Sime the prmciples to be eluci.-

dated require but a small ,Im"t ot a larga- bo<\r of text, it will not be necessary to give the mole ot each or these five messages. llb shall show t.irst 

•rel¥ the key indicators and the length or each message. 

IEY INDICAT015 AND LENJTH OF ~.'l!SSAGES. 

l. 08>-050. Length, 61D lett81"So 

2. 670-68J. Length, 555 leliters .. 

3. 225-216. Lengt.h, 482 letters. 

4. 7"1-698. Length, 884 letters. 

s. 591-583. Length, 572 letters. 

Asaurdng keys or 1,000 and 999 lettm-s, we may indicate graphical~ the relatiw positions in which these messages will tall by a diagram 

such as that shown in Fig. a. lh this diagam we show emctly mere each 

mssage begins and ends, what the key indicators are~ etc. We can take tor 

ezperiment any vertical section or these supari.nposed cycles. Let. us take 

the section consjsting <:£ 25 letters in each of messaees 1, 2, 4 am 5 as 

indicated by the serrated lines in Fig. s. This diagram shows that letters 

· 1 to 25 ot message 1,, 391 to 416 of nessaee 2, 354 to 379 of message 4 and 

470 to 495 ot message S tall Vlithin this section. 1\9 thererore take those . 

letters from our measa~s. They are as follows: 

lies sage 1. Letters l-25. 

5Y2'1C 3RHK6 R7ZlA J4UX6 CJOAJ 

-12-
REF ID:A516913 

r- r"'""'\ . 

Kea sage 2. Letters 391-416. 

5JOOB G)L77 D?SVZ BTVm 50mG 

llessago 4. Letters 354-3790 

XCHL'l JQJUH 11A5C3 \'NIMBF ST?UI 

llessage 5. letters 470-495• 

CXURW KY,2!' F7002 GVRNP 26N'lR 

Let us place these rour portions directly beneath one another a 

CJ7cle l - 5 Y 2 7 C 

Cycle 2 - S J B 0 B 

C,cl.e 3 - X C H L T 

Cycle 4 - C X U R W 

3 RN K 6 

G.3L77 

JQJUH 

K)Z2Y 

FIG. 9. 

R72QA 

D7SVZ 

WA 5 C 3 

F70N7 

J4UX6 

BTVIR 

WVWMBF 

GVRNP 

CJOAJ 

50BRG 

ST7UI 

26NTR 

low it we can find the plain text for the series o:t letters 

which tall directly beneath Q'lO another in cycles 1 and 2 we can begin 

to reco11Bt.ruct the keys. It become a question thel'6fore or assuming 

ti. plain text for the .first tew letters of cyles 1 and 2, recovering 

ttB keys upon the basis or such tsitative decipherment and thEll testing 

them upon cycles 3 and 4. If the tentative decir:herment is correct. the 

application of the cbuble kay to cycles 3 and 4 must result in the pro= 

duct.ion ot 1ntelllgiblG text. It aich a result is mt attained then it 

mans that the tentative deci}ilermant upon which the recovered double key 

1s based is not correct. and we proceed to 'b-y a different tentative decipherment for cycles l and 2.. The incorrect ansunption can involve eithereor both or the series or tentatively deciphered letters. Clwiously. 

it we can be certBin or the decipherment of one or the series we will be 

on surer ground md will have to modify our asswnption only for the other 

or the series wren our trials 0£ recovered keys prove the tentative decipherment to be incorrect. Now the beginning of nearly every messaee 

can be assumed to be JJ+25 • in order to insure a proper adjustment of the 

receiving machineo Ult us begin tmrerore by assuming that our message 

l starts with 4425, and since tho portion or this message Wiich falls 

w:l.thm tho secticxi t.o be analyzed contains letters 1 to 25 • we may insert 

ttntatiV\117 the decipherment of the first four letters ot message l as 

4425. Then let us assume tor the rnanent that the portion direotly beneath 

-13-
i . 

REF ID:A516913 

/") . 

. in message 2 consists or a series of J's, :reconstruct the keys for these 

t.110 portions (as illustrated in Fig. 7) and test them on cycles 3 and 4o 

Thi result ot these steps ia sho1Wl in Fig. 10. 

nG.10 

Ioiger kq - A S R 4 

Short_. 1mJ' - H 0 R 9 

C7cl• l. Cipmr - S Y 2 7 c 3 R N etc. 

Aseumed plain text - 4 4 2 S 

longer lmJ' - A S R 4 

Shorter kll7 - 0 R Q B 

Crole 2. Cipher - S J B 0 B G 3 L etc. 

Aseumad plain text - 3 3 .3 3 

Lenger ley - A S R 4 

Shorter Jey - R Q H 

Cycle 3 Cipher - X C H L T J Q J etc. 

Resultant plain terl-H V R 

Io~er ka,r - A S R 4 

Shorter ke7 - Q H _ 

Cycle 4. Cipher - C X U R ':I K 3 Z etco 

Rel!ultant plain teKt-G N 

These results prove that the assumption or a series or )'s for 

the beginning of cycle 2 is :incorrect. since the letters given tor cycles 

3 and 4 fonn m!ntelligible text. We theretore try out another probab1e 

comination tor meesaae 2, such as HE3., retaining as our decipherment ~ 

the correapo:nding portion of message l the combination 4/.t25 • snd see what 

reealt thia gl.ves. A list ot the po.qgraphs which would recur most trequent.]¥., and Wdch would be tested 1n conjunction with 4425 for message 

l, is given in the following table: 

33333 

3THE3 

3AND.3 

Df G3 

EREJ 

3'1'HA 

Itn.'3 

HE(3)R(3) 

'J)F'Jr 

ATI 

HAT.3 

EBT3 

HE(J)S 

TI003 

E31"B 

HlS3 

3<Jl3 

INJ,r 

WA-8,R 

vm 

IT-3,H. 

T.3TH 

3ARE3 

N3TH 

3ALL3 

)WIT 

D.3TH 

Sll.N 

S3'l'ff 

Tm (3) 

RE()jA 

61lS3 

6N53 

The mccessive trials take verrr little time, since the correct.-

·' 

nese or mv trial 1s speedil.7 proved or disproved by appcying the reall.tant 

ke1B to cycles 3 md 4. In this case, the trial of the polygraph .3<>13 re-

-14-
REF ID:A516913 r- r"'\ . 

sults 1n cxcellert. combinations ·in cycles 3 and 4.. ThUB: 

Fm. n .. 

longer ley - A S P U 

Shorter ley - H O P A 

Cycle lo Cipher - S Y 2 7 C 3 R N etc" 

An aimed plain tarl - 4 4 2 5 

Longer ley - A S P M 

S hart.er krJy - Q...E.. A '7 

Cycle 2,. Cipher - 5 J B 0 B G .3 L et.co 

Assumed plain text. - 3 O N 3 

!.onger key - A S P M 

Soorter key - P A 7 - Cycle 3a Cipher· - X CH L T J Q J etc,, 

Resultant plain text - 4 4 2 

Longer kDy - A S P M 

Shorter key - A 7 ·-- C)'Cle 4o Cipher - C X U R W K 3 Z etc o 

Resultant plai.n text. - C 0 

It 1a evident that in cycle 3 Wfl have struck a. ttcarriage return 

and llm teed; n in cycle 4. we probe.bl.7 have a woro. begi.."llling with CO, and 

w can try to build upon this digraph such words as suggest. themselves. as 

the fbllowirg: 

CODE 

COLUJll 

OOLLEC'l' 

COllE 

OOIW«J 

Crl~HAI'I> 

COJl>AN! 

CONDITICW 

CONNECT 

CONSIDEF. 

CONTRACT 

CONVOY 

COPY 

CORRECT 

CCST etc .. etco 

It mq tab considerable ti.ma w test out all of the \'Ords 

mich suggest themselves, but it if: only the start. which is looorious. 

tar after this the messages alr.nst solve themselveso Let us see what . ( p 

happens when we tey CO!~!AND. Giveni ? in cycle 4. the b!.3nk let,ter is . u 

II 

1. This enables us to place F bE11eath )( in the la-1er key in cycle 3, and 

(M . 

gives A as the plain teY.t letter. Given (? in cycle 4, the blank letter is R. 

(R 

(M 

With these additional lower key letters 5n place th~ooghcut 

our deci hcrment we have t!;.:i tolloldng: 

-15-
Cycls l. 

Cycle 2o 

C,-cle 3 

Cycle 4 

REF ID:A516913 

~ "'. 

FIGo l2 

Longer key - A S P 1l 

Shorter kBy - H O P A 7 F R 

Cipher - .5 Y 2 7 C 3 R N etco 

Assumed plain text - 4 4 2 5 

longer kay - A S P JI 

Shorter !my - 0 P A 7 F R 

Cipher - 5 J B O B G 3 L etco 

Assumed plain tEJKt 3 O N 3 

longer key - A S P JI 

Shorter key - P A 7 F R 

Cipher - X C H L T J Q J etc. 

Resultant plain text - 4 4 2 A 

loD{;er key - A S P M 

Short~ key - A 1 F R 

Cipher - C X U R W K 3 Z etco 

Resultant plain text - C O M M A N D 

We are no\'J ready to determine the next letter in the 1C11ger key,, In 

(? 

the column headed by the letter to be sought,, :in cycle 1 we have (7 ; in 

(? (? (C 

cycle 21 (F ; in cycle 3,, (R • (? 

(B (T . (? (? 

It is evident that we want such a letter in the upper key as will p:roduce the 

best pl.ain text letters from the given cipher letters to add to the already 

deciphered taxt.. We could tey out all the letters of the al.tilabet 3n turn, 

beginn~ with A, thus: 

It A 1s the ) (A (A (A 

up,Pal" lmy let- ) 1n cycle l_.(7 : F; in cycle 2, (F = Q; in cyc1e .3,(R : B 

tar then ) {C (B (T 

If B is the ) (B (B (B 

upper key let- ) in cycle 1,(7 =Q; in cycle 2, (F = F; in cycle 3,(R =A 

tar then ) (C (B (T 

If C is the ) (C (C (C 

upi:er key let- ) in cycle 1,,(7 •7; m cycle 2, rp G• m cycle .3 (R ., H ... -, ter then ) (C (C (T 

etc. et co etc. 

A short cut to ... the finding of these successive equivalents is 

accoq>lished ~ the use or the slphabets or the cipher aquare cut apart and 

n¥>unt.ed upon strips" It will be noticed that the successive equivalents for 

the coni>ination ~ in ~cle 1 are F, Q, ?, o " o ... ; for the combina.tiun: 

R 1n qcle 21 Q1 F, G, o o o o ; tor the cod> inatim T in cycle 3, B, A, H, • o o o o 

Now note the alphabets in the cipher square headed b,y the intersec= 

7 F R tion letters of the conbinations c 'B an<JT, vizo 1 C, H, and G, respectively., 

In the C alphabet the sequerce begins F, Q, 7, .. • .. ., It is evident that this 

alphabet. \'li.11 give the co.nplete sequence of letters resulting from the application 
{'> REF ID: A516913~. 

7 ot the nccea.S.w lettere ot the &1.phab9t. to the coni>ination c • The R 

alpbllbet 1'11 likma• giY• the coJllJ]ate aequeme ot letters reeulting trom the 

F applica~ion ot thl aur::cusl.Ye letters ot the alph4bet. to the coabination BJ R~ 

and tile 0 alphabet will glve those appqizg to T• 'l'beretore, it we taJm the 

alplabeta or the cipher aquare, cut them apart,, mount t.hem en a trips, select 

tll>ee head8cl by the lette1"8 c, H, and o, 81d set th• eo that the letters ot 

all thr• ooincida throudx>ut their length, we hare the coq>lete aeries ot 

let.t.ere reeulting tJ'Om the appl,ication ot the ncceasive lett..en ot the alphabet 

to these combinations. '?._, successive letters or equivalents ot this operation 

will all be found on the 8111119 Jmo:lscmt.al lines. B.v setting the 7 alphabet oppoeite our et.ripe, the letter in the long_. ka:y necessar7 to produce t.he equivalmta which tall m the aane lln• will be indicated on the 7 alphabet at the 

UM tS., ae ahCllll 1n rSg. 13. 

rm. 13. 

Ii!I 

B Q FA 

C?GR 

D U X lf 

EIJ'6 

PABQ 

GHC7 

107C 

I 4 L II 

JS5Z 

116Y 

LMI4 

ML4I 

120P 

OPR2 

p 0 2 If 

QB./& p 

R3VT 

SJZV 

TV.JR 

U D l1 X 

VTRi 

\f x u 

lWDU 

· Y 6 Bl 

Z5SJ 

2RPO 

3RTV 

4.IJIL 

SZJS 

6YKE 

It the hS&h trequenq letters appear 1n reel on t.t.ae st.ripe., 

• om begin b7 ael•ting t.hat horizontal line which contains all 

red letters. In thJa caae,, "it h V as the letter in the longer key 

tOl/t' t.he aolwm md_. cliacweion,, the three high tr9:1.uency letters, 

T 1 R,, and ) are givc. These, added to our partial deai]iurment, 

giT• the fbllollings 

C~el 

Cycle 2. 

CJ'cl• 4 •. 

rm. l4 

longer key - A S P Jl V 

Short.er ke,y - H O P A 7 F R 

Cipher - 5 Y 2 7 C 3 R B etco 

P.J.ain tact - 4 4 2 S T 

longer kB7 - A S P M V 

Shcrtal" }my - O P A 7 F R 

Cipher - S J B 0 B G 3 L etc• 

Plain text - 3 0 N 3 R 

IongeJ" key- - A S P M V 

Shorter key - P A 7 F R 

Cipher - X C H L T J Q J et.c. 

Plain text - 4 4 2 A 3 

Longs- laay- - A S P M V 

Shart#81" ka7 - A 7 F R C 

Cipher - C X U R l1 IC 3 Z etc. 

Plain text - C 0 M J! A N D 

-17-
REF ID: A51691~' 

(V 

' 

In cycle 4 we have ~~ which gives C as the corresponding let-

(A 

~ in the shorter kBy, as shown already in Fi.8. l4. We mq t17 out m 

qycl.e 2 the letter E after R. This muld give Z as the letter 1n the longer 

k., tor that column. Applying Z to all the conbinat. ions in this colUD11, "" 

ban tht followings 

C)"Cle l. 

C)rcle 2. 

CJ'cl.e 4. 

rm. is 

longer Ja9y - A S P U V Z 

Shorter key - H 0 P A 7_ F R C 

C~mr - 5 Y 2 7 C 3 R N7 etco 

Plain text. - 4 4 2 S T 0 

LCllger key - A S P M V Z 

Shorter ley - 0 P A 7 F R C 

Cipher - 5 J a 0 B G 3 L etco 

Plain text - 3 0 N 3 R E 

longer ke;y - A S P M V Z 

Shorter key - P A 7 F R C 

Cipher - x c H L T J Q J etc. 

Pltdn text - 4 4 2 A 3 H 

~-- kq - A S P M V Z 

Sharter !my - A 7 F R C L 

Cipher C X U R l'i K 3 Z etc. 

Plain text C 0 M ll A N D 

h .f!rst message begins with TO, am we rray place a 3 s.:n... it. 

Thle gl.vee the letter in the longer kay which applies to that colU1111, viz., 3; 

ard thie• in tum, gives the plain text letter C following E in cycle 21 making 

1t probable that the ward ia RECEW? or RECElVING or RECORD etc o Thls: 

Cycle l. 

Cycle 2. 

rm. 160 

longer key - A S P H V Z 3 

Shorter key - ff .0 P A 7 F R_..Q 

Ciphar - 5 Y 2 7 C 3 R N etc. 

Plain t eitt - 4 4 2 5 T 0 3 

Longer key - A S P ll V Z 3 

Shorter key - 0 P A 7 F R C 

Cipher - 5 J B 0 B G 3 L etco 

Plain text -- 3 0 N 3 R E C 

Lorger le7 - A S P !f V Z 3 

Shorter key - P A 7 F R C 

Cipher X C H L T J Q J etco 

Plain text 4 4 2 A 3 H 

long.- key - A S P !4 V Z 3 

S barter key - A 7 F R C 

Ciphar - C X U R W K 3 Z etc o 

Plain t ett - C 0 M U A N D 

-18-
REF ID:A516913 

(Z 

From the colli>ination (? 1n cycle 4, L is givci as the letter in too 

(K 

(N (3 

shorter ke1. which• in turn,, in cycle 3, in (L , eives t~ plain text. letter E, 

(Q 

{? 

suggesting t.'ie word HF..AVYo re can test out the words which suggest thanselves in cycles 2 and 3, and see Vlhat we get in cycles l and 4; or wa can 

teat out the \'\Ords which suggest themselves in one cycle by applying the 

resultant key letters to any other cycle at the proper point. 

Enough ot the irocedure has beEn shown to prove that the method 

is perfectly practicable. 1.£ 4425 tried out at the beginning ot the message 

does not yield good results, there are many other places to try out. the same 

cod>inat.ion further along; tor this co.mbinatim, 442, must appear at intervals of api:ro.ximately 55 to 70 letters,, Or,, this failing, the 8lds or mesmf!l'S can be tested tor 615. i. e •• "period .. " Should the decipherer be fortunate 

ea;,ugh to find two m~saagea 11h1ch begin Y1ithin me or two letters or one 

another in sequent .cycles, then it will be mmecessaey to a:rsume aJ\Y plain 

text other than 442S. a-, it he shC11ld find that the beginning ot Cl'le message 

falls within the sane section as the end of mother, the plain text will be 

4425 and 611.5.. l1hfl'l a place is reached where the proper continuation ot the 

measages is ditticult by reason or the tailUl"e or the preceding text. to suggest the succeeding text, recourse is had again to the alphe.bet strips o 

It is to be noted further that these alphabet strips may b3 uaoo 

to find the letters in the short.er key as well as those in the longer key., 

The arra."lgement of the messaees into soquent cycl.ee is such that the letters 

ot' the shorter key are slll.Uar on diagonal lineso Given the letters of the 

· longer ker and the c.t}iler on a diagonal line, aie proceeds to set the atr1Jl5~ 

applying the sane principles as before, remembering only to add the high 

frequency oombinations found diagonally on the at.rips in the messages as 

. arranged tor decipherment.. The letter opp:>site the high frequency combination on the 7 alphabet, will be the diagonally <X."nst.=-.rt letter of the 

ahort.81" ley O· 

'1'he complete decipherment together with the double key for these 

part.ial massages is shown in Fig. 17 .. 

-19-
longer ir.,-

Short.er lte7 

Cipher 

Plain t«t 

Lenger K91 

Shorter !Cey 

Cii)her 

Plain tst 

long8l" Key 

Short.er Key 

Cipher 

PW.n text 

REF ID:A516913 

Fmo 17. 

-ASPMVi)EK70JNALIRBGU3HWFD 

-HOPA7FRCLDPEKZTUMPAlULF7A 

- 5 Y 2 7 C 3 R H I 6 R 7 2 Q A J 4 C X .,C J 0 A J 

-4425T03ALL3RESERVE30FFICE 

-ASPMVZ)EK?OJNALIRBGU)HTIFD 

-OPA7FRCLDPEKZTUMPA~ULF7AV 

-SJBOBG3L77D7SVZBTV RSOBRG - .3 OM 3 RE C EI PT 3 0 F .3·A N .3 0 RD ER .3 F 

-ASP~V~3EK70JNALIRBGU3HnFD 

~PA7FRCLDPEiZTUllPA.3ULF7AVC 

- X C H L T J-Q J U H W' A 5 C 3 W ~1 11 B F S T 1 U I 

-442A)HEAVY.3BARRAGE.30N)THE 

longs- Key - A S P H V Z 3 E K 1 0 J N A L I R B G U 3 H ':'/ F D 

Shorter Key , - A 7 F R C L D P E K Z T U U P A 3 U L F 7 A V C 2 

Cii;her - C X U R W It .3 Z 2 Y F 7 0 N 2 G V R N P 2.6 N T R 

Plain tsct - C 0 lf JI A N D I N G .3 6 W lf l 5 T H 3 M I N E lV E 

\Ve have seen that the knowledge ~ the lengt.h ot the key was 

necessary 1n Ol"der to arrange the messages in the preceding case tor dac5pherment. Granting that the lengths of the tapes bearing the keys would 

be changed from dll' to dq, am that "breaks" bet.ween messages muld be made, 

it would nevert.heless be an eaq matt.or for the meJJ\}" to superil!lpose cycles 

correctlJ, witlaolit a knowledge ot these lengths or these "breaks", since 

the .ke7 ind1cators which must accompany each message attord ample data 

tor the ra.aoemant ot messages. For inotance in the preceding case we can 

determine the cyc1es to which each message belongs relative to the first 

message, 11Brel.y ~ fin:ling the ditterence between the key indicators for 

the several messa1~a, though we may not know how much of a l!Bssage is to be 

found in one eycle am how J!llch in the next cycle. 'lhus, the 1ndicators 

tor maeage 1 are Ot':O and 050, the ctttrerenc-.e being 10. Those far meaoa89 2 

are 670 and 600, the dit'ference also being 10. Therefore, the beginning 

ot the second nesaage is in the sane cycle as the whole of nessage lo The 

indicators for mes s&!f' 3 are 225 and 216, the difference being 9o This shows 

that nesaage 3, with respect to .nessage 1,, is in cycle 2; since in the first 

message the two key tapes are 10 letters apart as regards their points of 

or1gm, am 1n the third measage onq nine letters aparto Now the difference 
REF ID:A516913 

. bet.ween 225 and 000 is l6S. So that we may place the first le·tter or 

message 3, m ich belongs to cycle 2. \Dier the 165th letter of message lo 

We cm now fit in the rortion or message 2 which belongs in the second cycle~ 

since vie note that the placensnt ot message 3 allows roan tor 22S letters ot 

message 2 1n Cl'cle 21 leaving 330 letters, 'Which will be exactly enough to 

till up 1,,000 letters 1n the t.lrst cycle. However. we do not need to d:> ewn 

th18 mah, tor we can w:>rk with beginnings ot messages. Thua, given the 

tollawing eerie& ot key indicators tor as Jll8ll1' messages., they can be arranged 

u shown 1n Fig. 18. 

.VESS AO ES 

....... Indicatcrs Ditf- Cycle Mess- Indicators Dif't- Cycle 

... erence age ere nee 

l 4al-385 35 l 14 21.2-189 23 l3 

2 4»-399 3l s 15 517-483 34 2 

' JZ>-291 29 7 16 476-4')6 a> 16 

4 755-7';!} 26 10 17 706-6f!l 19 17 

5 830-802 28 8 lS 468-450 18 18 

6 10.3-079 24 12 19 316-299 17 19 

7 465-433 32 4 a:> Ol.1-994 16 3) 

8 001-978 21 15 21 050-035 15 21 

9 6'10-643 27 9 22 200..186 14 22 

10 210-177 33 3 23 286-2"13 13 23 

11 035-010 2S ll 24 09S-GS3 12 24 

12 212-190 22 14 25 001-989 ll 25 

13 SJ.6-486 30 6 

'ftlere are several p:>ints wh..J.·e an attack mq be mane, when the 

messages are arranged as shOIVll in Fig. lB. Both key's may be recovered completeJ.7 or nearly ao. No matter how the kBy indicators rmy be used, given 

a sutf1cient amount or intercepted traf'tic, mough text can be obtained to 

make it possible to arrange the cycles with reference to one another so 

t.hat a eo~ution mq be achieved... The cryptographer is guided by the key 

1nd1catore in his arrangement of massaw-s preparator,y to decifherlllVlt and 

noli b;y the order in 11hich th97 happened to have bean ~nt11 

-21-
I 

), 

I 

' 

REF ID:A516913 

ADDENDUM I .. \ 

OPINION HASED UPON THE SIGN/IL COOPS' IDVIFIED !ETHOD <JF USING 

THE A. T. & T. MACHINE CIPHER. 

'1he purpo-se ot this memorandun is t:o set forth our opinion. w.it.h the reasom,, . . 

that tha A. T. It T. nm.chine cipher as no" used by the Signal Corps is decipherable 

by the same principles as already established aai as already admitted to be effective by the representatives of the u. I. D. and the Signal Corps. 

The following is a transcriP-, of the rules for the opeJ-ation of the nachine 

tor cipher }m'poses. as set forth in a pencil memorandwn by Lt. Col. J .O .. Vau.borgne .. 

Cl-der of Punching Tape. 

10 line reeda 

6 lettera rep-esent 1ng DLl'Jlt~ ol. tape 01.ttiDp 

as PPPTUT ·(Ooo525) . 

During Capt .. 

Powler'e t1m 

aicipheriqi; began here .. 

letter - or letters designating cipher office• as "X" • "NP" etc .. l'Sgure Bhitt (6) 

Cipher bureau serial l'llmber of mssage 

Space (3) 

Figures (6) 

Check ar vord count in rlUllerals 

Letters. - line teed (S-2) 

Place tromDate 

Tl.Jiii filed 

Carriaga return - l.iJw feed,. 

Earl71919 

EncJpheri~ 

begins 

!fame - address - body ot roossaB<B - signature 

Friciphering ends. 

~line feed - 15 carriage returns .. 

Note - Tapea A and B var,y in length ct;,pending urx:tn nurr..ber of letters 

to be sent in one dllf. For e:xample, we mitflt use 700 oo the A tape 

and_ 699 on the B, or 650 on the A tape and J65 on the n, etc., 

* * * * * 

The differences between the original method and the modified method or 

using the machine can be summarized as tollCMs: 

<BIGIN!J.. J!J<1l'HOD 

l. Qie tspe is one letter 

longer than the other tape. 

2. The mzmber ot letters in 

TAPFS 

each tape is constant trom da;y to dq. 

-1-

llODIFIED Jl.l!,1.'HOD 

1.. cne tape may be my number 

ot letters loneer than the othEll" tape~ 

2. The tapes vary from day to dEUo 
REF ID:AS.16913 

r ~ 

SHIPTitG THE TAPES 

3. The tapes a.re eit htr 

not. shifted at all bet.ween 

messages or are shifted. together 

the same l'll.Dlber or letters. 

3. The tapes are shift.eel an 

unequal rmmber of letters after each 

message. For example, the A tape 

may be shittcd lO spaces, the B tape 

14. 

BPnlNMING OF mtCIPHmED MESSAGE 

4. Each message begins with 

the functions represented by 4425. 

4 •. The enci:rJt&l"ed portion or message 

begl.rm at once with tha name and aidress 

or the person to whcm the meesage is sent. 

mE CJi' FUNCTIO.tE AND PUNCTUATICW 

S. All functions and 

punctuation are used as in 

ordinary typewr:lt.tan matter. 

5. Some functions and pt11ctuation fDB1' 

or .IIBJ not be used, 1. e., there may be spaces 

( 3) be~ween V«>rds, oon:mas ( 6N5), paragraphs 

(44233333) etc., with the eucception of (442) 

which is absolutely necessary for th9 functiDning or the machine. 

We shall now show that tmse differences as set forth above d:> not change the 

nature or the ci}iler in a manner eo as to prevent an attack by exactly the 

.- prmaiples aa elucidated betora, first, because it is unDBcaesary to know 

either the lengtm or the tapes, or by how Jlllch they ditfer, secolJdly, because 

the ahltting ot the t110 tapes an mequal runber or letters ms no bearing up:>n 

the case at all, third, that even should the mciphermant begin with some un.knoVl'l 

text; md mt with the tuncticme JJ+2S that there is a sutficient nwd:>er or possibilities to tey a.it 1n other places; and fourth, that the presence or absence of 

certain tunctioos an:! ot JUl.Ctuatioo mey make tm problem a little more difficult 

but b;v no neans meolvahl.e. 

lo THE TAmS. 

In ord_. to eliminate all ambiguity we shall dafim the mrd "cycl.e" 

an:t the phrase "sequent cycles" as follows: 

(a) CYCLE. '!bat relation v1hich exists between the ta:> key tapes af'!:,er 

one tape has made cme conpl.ete revolution. Cycles may be measured by either the 

longer tape or the shorter tape, and in our l':ork we have used t:te longer tape as 

the .measure r:4 a cycle. 

(b) ~UENT CYam. TWD cycles are sequent 1'1ben the longer tape occupies 

tlm 8BID9 abaoll&e position in both cycles and the shorter tape is displaced one 

am on1¥ one J.etter in one cycle as compared with the othero In all the drawings 

and tlgaru this displacement is to the letto When the key indicators for one 

-2-
REF ID:A516913 

-•aa differ bJ an an:>unt, x, and those tor mother message dif fe:r by 

X + 1 or X - 1,, then we bENe a case or sequmt cycles. mten the lengths or 

the k97 tapes are unkno1111 this difference must be expressed in tf:l"ms ot 

eit.h_. a positive or a negative quantit7. E:mmple: Key indicators 075 .... 

125, ditterence =-so. Key 1nd1cators 125 .... 075, difference • + 500 

In th!t or:lginal mthod the kno'llledge th:lt the two tapes dii'f'ered by tut 

one letter in length enabled us to Bl.V that sequent cycles :rei:resented a displacement or the short.er tape of but one letter each ti.me. l}iis, in turn means 

tmt sequent revoltt.ions of the longer tape oo incide with sequent cycles. In 

other worde, a progressim t:rom sq the end or the secom revalutica to the end 

or the third revolution means a progression of one canplet.e cycle and represents 

a dl.aplacement of ooe letter or the short.er tape. 

It the tapes ditter in length by more than one letter,, tor example, it 

the t110 tapes dif'ter by 50 letters, then the displacement of the shcrter tape 

will be SO letters per reyol.tt.ion ot the longer tape,, in which case it is clear 

that a911nt pYOlutiona of th• longer tape wtll. not coincide with sequent srcleso 

Fig. lS and the diacussion applying to it shows clearly that these messages 

•re IRlplrinpoaed by reterence td the k97 indicators onlyo Tha crucial point is 

thia, that in the solution of a sip long message a lmowledge or the lengths o'r 

the ke7 tapes is absolutely eseantial; without th:is knowledge the length ot a 

eycle ani the displacement in sequent cycles never can be <btermined, which in 

turn means an inability to superimpose cycles so that the principles of solution 

can be ap!llledo But in the solution or a series or Jmssages a knowledge of the 

lengtm or the k97 tapes is entirely unnecessary,, sirx:e sequent cycles are 

determined not trom such a knowledge but mlely ~om the key indicators for 

the respective messages. The d:l.splacement in S!Q!lent. revolutioris nay be any number \ 

ot letter.a, & matter Of llO concem to US 1 but the displ&CE!!lent in ~equent 

ctcl.• (according to wr det1nition of the phrase) ia always one letter, and 

there can be no doubt that that neasages in sequent cycles can be tound, as will 

be illuetra.ted. below. To 8Wll up, therefore,, a lmowledge of the lengths or the 

two tapes 1a entirel.T 1111MC8Saary for the superimposition ot cycles, preparatory 

to dacipiermmit ot a aeries ot mes eageso 

-3-
REF ID:A516913 

2o DAJLY V ARIATI('fi lll lENlTHS OF TAP~" 

Tm tacl; that theres is a daily variat im in t l'1' lengths or the tapes in 

tbs mod1fied method as conpars1 vdth a constant length in t.he origl.nal method 

has no bearing up:>n the case becaus<t as stated in the μoeceding sectitn1 a 

knowl8dge of the lengths or the tapes is unnecessary tor the eolutiai of a 

series or mes sages, and secondly, because the fact or constancy in tba lengt.hs 

(u "~as the case 1.n the original net.hod) ie 2'r ae of m importance in such a 

aalutiono 

3. SHIFTING THE TAPES. 

Tba shitting of the tapes, toget.her or sing~,, equal Ol" t:nequal distames 

in all instances has no bearing uJ,On the case, bacause such shift.ing does not 

preclude the JX>ssibility of the occurreooe or sequent cyc.l.es. As a matter of 

tact• the 1.ll!CJUal shi.tt.ing ot the t.9.J?!S, after oach message, ie a highly ger- . OW! procedure because it makes possible tho accid8ltal encipherment or two mes9gs bi an identical resultant a1"a1.e kv, 1. eo 1 such proceeding introduces 

•8111 possibilities ot "overlaps. n Evel'l" case in which the ditt'ercmoe bat.ween 

the key indicators is the eamD represents a case of m "overlap". 

4. FUNcTioNS ELIMINATED AT BIDINNING. 

Tho tact that in the original met.hod messages began to be enciphered. with 

the functions 4425 only eliminated the necessity of assuning plain text £or the 

beginning of a message., 1. e • ., if we know tmt each message begins with 442.5 1 the 

trial or the most frequently recurring polygraphs in the corresix>rxling positicn 

in the next sequent cycle is all that is necessary to get a start. H oviever, in 

the modif'ied l!Bthad tmre remain many othtr points of attack, for the mcipher= 

meilt begins with a name and an address. This must contain, in milit~ messages, 

titles, initials, pmctua.tion end functions. such as fitJJre and letter shi.fts, 

. period, spaceao All of these afford easy openings for attack, especially in 

view of the fact. that the sending and the receiving stations can be determined 

w 1th a !air degree of pro babll ity o 

5o ELIMINATING PUNCTUATION etco 

The elimination of all punctuation, and such functions as space and paragraph 

would not ccmplicate the solution any more than their absence in ordina.cy cipher 

muaagee doea. H01'8ver. the !unctions 442. (carriage retum and line feed) are 

-4-
REF ID:A516913 

abaolute]J' neceaaa17 tor the proper ope:ration ot the machine and theirnf'ors their 

eHm5nat1Dn 18 impoasibl.e. '?tie length ot lines is not highly variable in nature, 

and 1t ia reasonab]3 certain that in the bod7 or the message the .f\anct.icms 442 

mat. recur at intervals approximating 60 Dtters. 

The in11catora arw:1 legtbs or the following series of 17 massages 11.lustt-ate tJie f'oregoing points. This series ot h7Pothetical messages was drawn up 

according to the rules as la~ down in the memoran.dun submitted by the Signal 

Cbrpe, md retresent. what happens in the traf'fic ot 01l4' one station ot poas:fb~ 

" tom-. '?his station has been assigned one f'ou:rt.h ot the length of' one tape, :1n 

actcordance with the plan set forth. The tapes tor the day are 700 and 670 letters 

in 1ength. Station 1 has been assign®<! the region hm OOl to 160 on the short.er 

tape. At m time mat th& dif teren<Jt between the key indicators exceed 1601 other• 

wiae Station l lf111 be encroaching upon the region assilJlad to anothtll" stat~n. 

or as •• shall es.y,, ht telll be "out ot bounds." Tm data fer this series ot 

hfpot.hetica1 -sage• are u tal.lo•z 
REF ID:A516913 

TAPF.S 

700 - 670 

Message l. 076 - 055 (a) : 21 (b) 

J6l - M cc) JJl - 4l (d) 

2. 442 - 417 ~a) =25 (b) 

206 - 3>6 c) 648 - 623 (d) 

). 418 - .362 (a) =56 (b) 

~ ... '.368 (c) 

18 - ?'JO ~ - (:J70 (e) 08 - o&i (d) 

4 .• 090 - 068 ~a) = 22 (b) 

w-~ c) . 75 - j (d) 

10. 658 - 532 (a) = 126 (b) . ¥!l - l€f (c) 

lJ.45 -1019 

700 - 67,0 (e). 

445 - 349 (d) 

U. 449 - 385 (a) : 64 (b) 

500 - 508 {c) 

957 - 893 

70Q - 670 (e) 

':67 - 22.3 (d) 

12. 260 - 236 (a) = 24 (b) 

~a - ~a (c) ifs - 54 (d) 

13. 4g) - 350 (a) = 130 (b) 

216 - 216 (o) 

5. 362 - 262 (a) : 100 (b) 696 - sfZ (d) S - 2§1 (c) 9 - 549 (d) 14. 698 -· 571 (a) = 127 (b) 

267 - ~7 (c) 

6. 655 - 5~ {a) = 105 (b) 

688 - 688 (c) 

965 - 838 

~ - 6~0 (e) 1343 -1238 25 - 1 8 (d) 

~ - 6~ (e) j - 5 (d) 

7• 649 - 5'fl (a) = 52 (b) m - 30; (c) 

954 - 902 ZOO - 6:ZO (e) 

254 - 232 (d) 

s. 259 - 232 (a) = 'Z/ (b) 

J?l - 323 (c) 

582 - 555 (d) 

9 195 - 076 (a) = 119 (b) 

~ - 447 (c) - 523 (d) 

15. 272 - 170 (a) : 102 {b) 

208 - ~8 (c.) 

480 - pa (d) 

16. 495 - 'J'IJ (a) : 96 (b) 

416 - 416 (e) 

9ll - 815 zoo - 6'N (e) 

211 - 145 (d) 

17. 225 - 202 (a) : 23 (a) 

~08 - ~00 (c) 33 -JD (d) 

KEY TO EXPLA.~ATORY MAP.KS: (a.) Indicators at beginning of I?essage., 

(b) 0,ycle as deter.mined from their difference. 

(c) Length of mcssageo 

(d) Fbsitions of tapes a.t end of message., 

(e) Subtraction for length of ta~s. · · 

-6-

REF ID:A516913 (' ,, 

ADDENDUM 2 

SUMMARY 

In this Addendum ve shall shov: 

a. hov the test messages submitted by the Signal Corps were 

deciphered. 

b. that the present system, vh1ch employs key tapes differing in length by more than one letter, is much more unsafe 

tban the former ~ethod in which key tapes differing in length by 

one and only one letter were used. 

c. how the trials for possible plain text are reduced to 

simple terms, enabling a great number of trials to be made within 

a short time. 

d. methods of solving cases not involving sequent cycles. 

1. PRINCIPLES USED IN THE SOLUTION OF THE TEST MESSAGES 

It may be said at the outset that the principles vh1ch were 

involved in the solution vere basically those set forth in the 

original manuscript and its Addendum 1. The steps vere as 

tollova: 

a. First, the plain text preamble for each message was 

read. This gave the key indicators, the serial number of the 

message, the number of vords, the plaee of origin and date. For 

example, the first message sent by the station at Hoboken gave the following preamble: 

EWWPPQA6Q.53656QR52HQ3P30F3E3HOBOKEN3NJ3SEPT36WW36TRP55P442 

"Translated," this would read as follows: 

322 * 001 (Series)A (No.)l 14(words) HQ P(ort) of E{mbarkation) 

Hoboken NJ Sept 22 5:40 P(M) 

Then the total number of characters in the message was 

determined by count, beginning vith the character immediately tolloving the 442 and extending to the beginning of the series 

of 2's or 4vs at the end of the message. 

By classifying the tapes in accordance with their points of origin, and then in accordance vi th their seria.l numbers, the 

following list resulted: 

List of Messages 

WASHINGTON SERIES 

Message Message 

Bo. Indicators Le!;!Sth No. Indicators Le~th;. 

l 126 • 001 278 8 687 * 228 491 

2 406 * 281 321 9 393 * 082 182 

3 729 * 604 380 10 577 * 266 438 

4 324 * 347 213 11 .~Jo::* o67 252 

g 539 * 562 230 12 484 * 321 304 

771 * 155 276 13 002 * 626 331 

7 261 * 432 423 14 335 * 320 484 
.. REF ID:A516913 

('-- ~ 

Message Message 

No. Indicators Le!!B!h No. Indicators Le!;3th 

15 034 * 167 314 46 474 * 123 421 

16 350 • 483 341 4~ 110 * 5l!.6 319 

t.~ 6i3 * 187 237 431 * 228 359 

1 5 * 426 264 49 005 * 589 400 

19 887 * ~3 333 50 407 * 3(2 326 

20 7-6 * 8 281 51 735 * 0 1 582 

21 2•2 .. 032 182 52 532 * 625 273 

22 Jt.26 * 216 326 53 020 * 261 309 

~' 754 • 544 270 54 331 * 5~2 150 

2a9 • 1i1 629 55 -483 .. 0 5 403 

~~ 0 ,. ... 1 9 1959 56 101 * 490 403 470 * 213 228 §~ 506 * 256 378 

~b 100 .. 443 304 099 * 636 783 219 * 110 43~ 59 097 * 1'+3 492 

29 6ri • 549 30 60 591 * ooti 221 

30 1 1 * 220 481 61 02h .. 221 381 

31 664 * 064 214 62 40 * 602 237 

32 093 * 280 410 63 647 * 202 327 

33 5~ * 053 254 64 189 * 531 295 

34 . 6 * 309 236 65 486 * 189 300 

35 212 * 547 244 66 001 ~ 491 195 

36 458 * 154 2~5 ~~ 198 * 049 424 

5A 735 * 431 3· 2 624 * 475 411 

312 * ~6 323 69 250 * 259 318 

39 637 * l 491 70 570 * 579 262 

40 3§0 • 335 142 71 047 * 204 161 

41 4 7 * 479 318 "{2 210 * 367 208 

42 020 * 160 27~ 73 420 ° 577 202 

43 297 * 437 37 74 624 * 142 149 

44 673 * 984 206 75 775 * 293 133 

45 094 * 382 378 

HOBOKEN SERIES 

Mee sage .Message 

No. Indicators Length No. Indies. tors Length 

1 322 * 527 191 19 772 * 605 294 

2 515 * 194 532 20 186 * 971 215 

3 971 * 089 195 21 403 * 479 456 

4 460 * 287 203 22 733 * 298 370 

g 665 * 492 253 23 446 * 031 314 

133 * 108 229 24 762 * 578 407 

~ 364 i:· 339 429 25 479 ~ 117 165 

008 * 131 388 26 552 * 285 354 

9 398 * 521 3370 ~~ 121 * 002 366 

10 770 ~ 254 213 489 ... 370 751 

11 198 * 469 177 29 455 * 484 1089 

12 377 * 009 245 30 759 * 297 396 

13 624 * 256 235 31 3~0 * 056 1200 

14 733 * 493 358 }2 7 5 * 619 562 

15 4,4 * 214 275 33 942 * 544 523 

16 711 * 491 345 34 300 * 430 512 

iA 271 * 199 178 35 027 * 305 495 

451 * 379 224 

I -2- I 

I 

I 

I 

I 

I 

I 
REF ID:A516913 I 

r ~ 

NEW YORK SERIES 

Me a sage 

lf o Indicators Legs th 

Message 

No Indicators Leegtb 

1 714 * 001 157 13 576 * 002 236 

2 086 * 160 307 14 714 * 24-0 272 

i ~95 * 469 235 15 201 * Sl.4 302 

91 • 067 761 16 505 * 179 2,5 

~ 618 * 191 205 iA 742 * 416 231 

038 * 398 365 188 * 010 2A6 

~ 405 ~ 126 329 ·19 418 * 288 2 4 

736 • 457 571 20 752 * 574 134 

9 528 * 397 316 21 io1 * on 128 

10 ~9 * 076 585 22 231 * 201 133 . 11 6 • 024 359 ~~ 366 * 3~6 143 

12 220 * 385 253 511 .. 4 1 91 

MORFOLK SERIES 

Message no. Indicators Le!!13th 

-l 518 * 001 514 

.2 247 * 517 320 

3 569 * 200 271 

4 055 * 473 274 

5 331 ... 110 

6 612 * 391 ~~ 

~ 215 * 142 . 163 

380 .. 'oA 139 

9 521 * 44 446 

10 182 * 257 677 

11 OA4 * 297 407 i 

I . 12 4 3 * 067 227 

13 712 * 296 273 14 200 * 571 279 

15 481 * 213 195 

16 678 * 410 990 

-3-
REF ID:A516913 

. b. Bext, the lengths of the tvo keys were determined from 

a .il,i).~hematical analysis of the foregoing lists. Consider, for 

example. the .first few meBsages emanating .from Washington, ps.yfng 

particular attention to the key indicators, and the length of each 

message. For example, Washington 1 begins at 126 * 001 and 

contains 278 lettersl. It is evident that at the end of the message the keys vould be at points, hereafter designated as "loei," 

278 lettePs beyond the original 1001. Thus: 

Washington l •••• 126 ~ 001 

Length •••• 2aa 2za 4 4 ii 279 

The ke7 indicators for Washington 2 are 406 ~ 281, tvo in advance, 

respectively, of the loci where Washington 1 left off. It is evi-

'dent that be~ore beginning on the next message Washington 2, which 

has 322 letters,. the encipherer "slipped" both key tapes two letters. 

Adding the number of letters here again to the key indicators, we 

have the tollow1ng: 

Washington 1 . . . . 126 it 001 

Length -· ... 2~8 2t8 41'. * 2~ Slip . . . . ~ 2 2} Washington 2 . . . . 06 * 28i 

Length . . . . 1_22 t22 

728 *03 

Washington 3 begins at 729 * 604, in other words, after s ."slip" 

ot 1 letter in each key. 

Nov Washington 3 has 380 letters. Let us add 380 to the 

key indieators. Thus: 

Washington 3 .... 729 * 604 

Length •••• 280 ~o 1169 i tl4 

The result should correspond< approximately vith the key indioatora for the next message, but Washington 4 gives as indica~ 

. tors 324 * 347. It is evident, therefor~, that both key tapes have completed one revolution and are 323 and 346 letters, respectively, beyond their initial loci, viz, 001. If now ve find 

the difterence between the theoretical pair of indicators, 

1109 * 984, and the actual pair, 324 * 347, ve shall begin to 

approximate the lengths of the keys. Thus: 

Washington (theoret1oal initial loci) 

4 (actual " " ) 

1109 * 984 

324 * g47. 785 * 37 

We begin to suspect that the longer key is about 785 

letters in length, the shorter, about 637. We must, therefore. 

determine not their approximate lengths, but their exact lengths. 

If there vere no slip between Washington 3 and Washington 4, then 

the numbers 785 and 637 would coincide with the exact lengths of 

the keys. We do not know whether there has been a slip betveen 

these tvo messages, or, if there has been, whether the slip was 

the same for both keys. But we do not h.a.ve to determine that 

lwe shall use the word "letters" to include all the characters 

and "functions" of the machine, as they appear on the cipher tapes. 

-4-
REF ID:A516913 

1111led1atel7. Let us turn our attention to a case in which only 

one or tbe key tapes completes a revolution vithin a messa~e. 

Por exaaple, consider Washington 5, vith key indicators 53 * 562, 

length 230 letters; and Washington 6, with key indicators 771 * 155, 

length 276 letters. Let us calculate as before • 

Washington 5 

Length 

•••• 539 * 562 .... 2g0 2§g 1 9 i 7 

It there has been a slip ot tvo letters on both key tapes, then Washington 6 should begin at 771 • 794. But in reality, the 

Jce7 1nd1cators tor this message are 771 • 155. Still assuming an 

equal elip ot tvo letters, then locus 792+ 2 ::: 194, which coincides 

v1th locua 155· Taking the difference, 794-155 = 6}9, which would be the exact length ot the short key. Above, we bad determined 

the &pprozimate length as 6-,7. 

Applying the saae process to determine the exact length 

ot the long key, taking Washington 6 and 7 for calculation, we 

rind the ~olloving: 

Washington 6 •••. 771 * 155 

Length •••• 246 2!6 10 1 * 4 1 

Washington 1 begins at 261 * 432. Since the indicators 

as regard.a the abort key differ only by 1, ve assume an equal slip O~ 1 ror both keys. Therefore locus 1047 -t- l = 1048 Vhich coincide& vitb locus 261. Then, likevise 1 1048-261 = 1~1, the exact 

length of the long key. Our approximate length was 785, as 

detel'll1ned above. 

It nov remains to test these determinations on all mesaagea, their correctness being based upon the consistency vith 

V..b1ch the theoretical key indicators for each message agree with 

the actual, taking into account the assumption that the tvo key 

tapes vere slipped an equal_ distance in every case. There may be 

a variation in the amount ot slip between successive messages, but 110 long as in each case both tapes are slipped tbl'ough the 

aaae distance, the result vould be exactly the sane as though each 

aeaeage were 1, 2, ., ••• letters longer than is actually the case, 

v1th no slip whatever involved. A careful study of the calculations vh1cb follow vill shov that there could not possibly be any doubt about the correctness of the tvo determinations, 787 and 639. 

There are several discrepancies, it is true, but they vere due to 

errors, or carelessness on the part of the encipherer, as vill 

be discussed later. 

Bator& g1v1ng tbe complete calculations for the series 

ot measagea, ve shall introduce into the discussion a feature 

vb1ch concerns vbat ve bave termed latent dacles. (For definition ot the ordinary cycle see page 2 of A endum 1.) 

Consider Washington -,, for example; it begins at 729 * 604, 

or in the 125tb cycle and ends at 322 * 345, or in the minus 23rd 

cycle. The message involves, therefore, at least tvo cycles. 

But there 1a in reality an additional cycle involved. For 1 after 

the message bas proceeded for 36 letters, the short key is at 

locus 640, Which coincides vith locus 001, since the key is 639 

letters in length. But vhile the short key is at locus 001, the 

-5-
REF ID:A516913 

long keJ is at locus 729 36, or 765. After the 36th letter, there~ore,, tbe mesaage proceeds in c7ele 765-001, or e~cle 764. 

fhia ve term the hidden or· latent c1cle, 1n contrad1st1nct1on with 

the open or patent eyolea (~blch are shown b7 the key indicators 

theJlaelvee), because the existence of the latent 07cle is d.!scloaed onl.7 b7 the calculations made as a result or the determination ot tbe exact lengths ot the two key tapes. These relations 

oan be demonstrated very slllpl7,, thua: 

Vaabington 3 • • • • 729 * 604 

(leJJgtb 38o letters) •••• ~ tS 

7 i 60 

or 

765 * 001 

C,-ele 125 

But this aesaage ia 380 letters 1n length and continues 

to be enciphered after the 36th letter. Proceeding tor 23 letters 

aore, the long ke7 reaches the locus 788, vhich ia in reality locus 001,, since the long key 1a 787 letters in length. 'l'he ~hort 

key, atter 23 letters, is at locus 024. The difference betv~n 

the tvo loci 001 and 024 is therefore -23, and the aesaage is nov 

proceeding in the lat~nt -23rd cycle. It continues to do so until 

the end ot the message. !hese ~elations are summarized mathematic-

&117 in a standard form as follows: • 

Xeaeage Bo. 

Waah1ncton 3 

Indicators 

~21 . r1 

Bnd ot Vaah. 3 •• 322 * 45 

Letsth Partia Total 

23. 

321 380 

Cycle 

125 

764 

-23 

~e calculations which apply to the entire series of messages 

are aa tollova: 

Message 

Bo. 

l 

2 

' 

WA5HINGTON SERIES 

Indicators 

126 * 001 21a i+a 

4o4 ' 1'9 

' 66 2 • 281 2) 

322 g22 r . 153 1 1) 

-6-

Leys th 

Partia Total 

278 278 

322 322 

36 

Qlcle 

125 
REF ID:A516913 

.f' ~ 

.Message Lets th Ro. Indicators Partis '.rotal C;y:cle 

3 cont•d. 765 * 640 

765 * 001 764 

1i * o~t 23 

001 * 024 -23 

,21 ~21 321 38o 22 *45 ~ 2 2) 24 * 347 

212 2gg 213 21} 

. 

rT 2 II 5 2) , 5 'B • 562 

gf.; 6 64® 78 

617 * 001 616 

lg2 1!22 152 230 

. I 9 a is, 

2 2l 

6 ffi * i55 M - i~ 7 • 17 17 

001 * 172 . 276 

-171 

~gg., If 2.5.9 __ 

' l . ll 1 61 * 4)~ 208 208 208 

11'.69. 646 

469 • 001 468 

2li 21~ 68 • 21 215 423 

8 £ ~ l2l B * 228 

101 101 101 

7'"88 • 329 

001 * 329 -328 

311 311 311 

}12 i 640 

312 * 001 311 

3l;f 1: o~ 79 491 

~ 2 . 2) 

9 ~3 * 082 . 1 2 182 182 182 

575 * 264 

' 2 2l 10 577 * 266 

211 211 211 

788 * 477 

001 * 477 -476 

16i 162 163 

16 * 640 

164 * 001 163 

64 64 64 438 

228 * 065 ~ 2 2} 11 30 i 0"67 

-1-
REF ID:A516913 

~ 

Message Bo. Indicator a 

Le IS th Partia Total Ozcle 

11 230 * o67 

21 ~2 252 252'1. 

4 19 

12 ' 84 2 I 321 22 

~-&@ 304 304 

001 * 625 -624 

A i ll 13 02 I 626 

14 14 14 

016 * 640 

016 * 001 15 

!~J ' Si~ 317 }}l 

~ 2 2l 

1- 35 •.}20 

g20 ~20 320 

55 •iir> 

655 * 001 654 

~ii l~ 133 

001 * 134 484 

-133 

0'~ I lg; 31 

~ 2 2l 15 34 i !67 

316 316 ,16 i16 50 *8' ~ 0 Ol 16 50 i 48' 1~7 1~1 157 

5 7 i 6 0 

507 * 001 506 

184 184 184 341 

691 I 185 

~ 2 2l 17 9' • 187 

~11 * 2~~ 95 

001 * 282 -281 14i 142 143 238 

14 I Ji'.25 

' 1 1} 18 145 i 426 

214 214 214 

359 i 640 

359 * 001 358 

4~~ * o~¥ 50 264 

! 2 2} 19 11 .. 653 

~:~) 333 333 

20 

-8-
REF ID:A516913 

(' ~ 

Xe a sage Lerth •2· Indicatoi-a Partla 'l'otal C;r;cle 

20 746 * 388 

42 42 42 

788 • 436 

001 • ,.,0 -429 

210 210 210 ~11 i 646 

211 * 001 210 

2~ 2~ 29 281 

~"' • o3 ~ 2 21 21 '~ • 632 

182 182 182 182 

-1'24 a: 214 

22 ~ 2 2l 2l> • 216 ~26 226 326 326 

~52 " 51f2 2 2) 2, 54 4 544 ~ 34 :;4 7 • 578 

001 * 578 -577 62 62 62 

063 I 67"~ 

063 * 001 62 

1,4 1z4 174 270 

2 1 • 175 

24 ~ 2 2l ,9 I lf7 46~ 46g. 463 

70 i 64 

~001 701 

~ . 86 . 

~-· 

001 .. 087 -86 

8o 80 80 629 

l>81 4 167 ~- 2 2) 25 83 * 169 

471 4il 554 I 0 .?) 

471 

554 * 001 55:; 

2; 2~4 234 

7 i 235 

001 * 2:;5 -234 

ftgg i i~~ 405 

406 * 001 405 

382 ,82 382 

788 * 83 

001 * 383 -382 

~~ * g(t 257 

258 ... 001 257 

211 211 211 1960 

469 4 212 

26 ' 10 1 l} * 213 

-9-
REF ID:A516913 . r"· ~ Meaeage Le rs th Bo. Ind.icato:ra Partia Total C;tcle 

26 470 • 21§ 228 22 228 228 

698 I 441 

~ 2 2l 21 00 • ,,, 

1= '*'I 88 

001 • 5,1 -530 

1¥8 ' tin 109 

110 • 001 109 

106 lo8 lo8 ,05 218 i 109 

28 ' l . ll 19 • tto 

1i ' ;i+ 437 437 

~·2 21 29 58 • 52'9 

ti~ I Ja 91 

1-9 • 001 748 

·~~ 39 

001 * 040 -39 l:fi . l~ 175 ,05 l I 2 

30 i~ I 22~) 420 420 420 

601 • 640 

601 * 001 

6~ * o~ 56 476 

,1 ~6I * aJ) 

1211- 124 124 

788 I 188 

001 * 188 -187 

~ BI 87 211 

er • 215 

,2 !~ i 2sS) 

i6o g6o 360 53 140 

453 * 001 452 

46 46 46 406 ~9 i 647 

~ 6 6l 33 05 * Os3 2~1 2~1 251 251 

~b .. ,, 

34 of • 36~) 

1~ • 3Sl 

27 

001 • 336 -335 

206 206 206 233 

207 .. 54~ 

~ ~ !2l 35 1 r 5l'7 

-10-
Message No. 

39 

40 

41 

42 

44 

REF ID:A516913 

(' 

Indicators 

3 • 431 

1~, "a~ 001 * 484 

l~ l~ 17 * 60 

157 * 001 

14g 149 }0 * 150 ~ 6 6) 12 If~ 

g23 ·712~ 35 * 1 ~ 2 2) 37 ii 481 

la§ l~l 7 ... 6 2 

001 i> 632 

8 8 o(}g • 640 

009 * 001 

~l * '~~ 34 l ' .. J}5 J) -

140 140 

1~ II 47~) 8' .. ii1§ 

161 161 

64"8 i li46 

648 * 001 

140 140 

788 • llri 

001 * 141 

o~i * i;i ~ 6 6) 

73 * 174 

' 

Le th 0 

Part1ai8 ~1 

93 

148 241 

272 272 

53 

156 

149 

323 

151 

8 

327 486 

140 140 

161 

140 

272 272 

20.3 

167 370 

-11-

Cycle 

-

304 

-483 

156 

-631 

8 

647 

-140 

499 
REF ID:A516913 . (' ...-.._, 

Jlesaage Le~th · Bo. Indicators Part!& Total C:rcle 

·- 673 * 174 

~ l~ 115 

I' 28 

001 • 289 -288 

oSB • ,~a 89 204 

.\5 !~I ,Jl 

s~. ii® 258 

,52 * 001 351 

116 116 116 374 468 I lif 

' 74 6 6l I 12~ m 314 i

1 

1 37 

001 * 437 

416 

-436 

102 . 102 102 163 i 539 f ~ 7) 47 l I 546 

2~. 643 94 

2M * 001 203 

221 221 221 315 

425 i 22~ 

48 ~ 6 6l 31 * 228 

~:~) 355 355 

49 

005 * 589 -584 

o~ • 6i~ 51 

o~ ... 001 55 

ioi I'~ 345 396 

; 6 6l 50 ;;:; 288 

69~ * 001 694 

~~· ~~ 34 322 

6 . 6) 

51 5 I 041 

1; i l5§1 53 

001 * 094 -93 

:!2i g2~ 523 576 l2 I l~ ' 8 l 

52 532 " 625. 

5}; • 6¢6 15 

547 ° 001 546 

241 241 241 

788 i 242 

-12-
REF ID:A516913 

(' ""'"\ 

Jleaaage Le!8th 

Bo. lndioatora Partia 'f otal C1cl!, 

52 788 • 242 

cont'd. 001 * 242 -241 

. oii • ~~ 13 269 

A 6 6l 53·; M I 261 

,~.~ 306 306 

~::if " 

54 68 

399. 001 398 

So 80 80 148 

4'f 9 I <581 

55 !s~ • os;l 

305 305 305 

788 i 3§0 

001 * 390 -389 

o~ • 4a! 94 . 399 

~ 6 . 6l 

56 ~t &"4§6 

l~O liO 150 

2 1. 6 6 2~1 * 001 250 

21 2~ 249 399 

57 ~6 :· : l 

282 2 2 282 

188 • 538 

001 * 538 

374 

-537 

o~ • 6~ 92 

~ .·6 6l. 

58 9~. 636 ·- 4 4 4 

163 i 640"· 

103 * 001 102 

~i~ i ~i6 6.39 

742 * 001 741 

46 46 46 

788 * l5li'>/ -46 001 * 047 

86 86 86 775 

087 * i~ 

~10 10) 

59 91 I 14} 487 487 484 48b 58 * 63 

60 . 59 ' t * 6' 'l 

-13-
REF ID:A516913 . ('°"' ~ 

Me a sage Lersth 

Bo. Indicators Part!a""T'ots 1 Cycle 

60 591 * 6.,1 

3 3 

5§2' I 6Jf0 

594 * 001 593 

~;r11 194 

001 * 195 218 

-194 

21 21 21 ~Ti 216 

61 . ~21 4 2~1> 

i15t i ~ 377 377 

! 4 4) 62 68 it 6b2 

11i~ i 6iS 38 

446 * 001 445 

m-~ i~ 197 235 

~ 4 4) 6, 47 i 202 

141 141 141 

788 * 3\, 

001 * 34, -}42 

182 182 182 323 

183 1 s25 ~ 6 6l 64· 89 * 5:51 i; 10~ 109 ~ i 64 . 

2~ * 001 297 

ksi i t~i 183 292 

65 &ti* l~} 

~:~) 297 297 

66 

001 * 491 -490 

14§ 14~ 149 

15 ¥ l>4 149 l~ it 001 4 44 44 193 

194 i oti~ 

~ 4 . l 

67 98 * 049 420 420 420 420 

618 * 469 

. £ i 5l 68 2 i 47~ . 164 16 164 

788 * 659 -638 001 * 639 

1 . 1 1 

00~ * 61'0 

-14-
REF ID:A516913 

' 

,-.....,, 

lteaaage lo. Indicators Le~b Parti& l'otal Czcle 

68 002 * 640 

coat•4. 002 * 001 1 

242 242 242 407 

244 i 243 

69 ~ 6 1:6l S't • 259 

~:~ 315 315 

70 61 l 61 

Si• 646 

631 6,o ... 001 

,; 'i; 157 

001 * l~ -157 

42 2 42 259 043 i 2015 ~.4 4} 71 47 • ~04 

~6g. !* 159 159 

~ 4 4l 72 io * }67 206 . 206 206 . 2o6 

>i16 1 sf! 

' 4 4l 7-, ~o • 5'-1 · 

JJ~ I 6~8 63 

483 * 001 482 

~ia I f ~ 1}7 200 

~ 4 4l 74 ~4 i 142 

14t 14~ 147 147 

. r·~ 4 4) 

75 75 " 293 

1~ i j~~ 13 

001 * 316 -315 

120 120 120 133 

121 w 436 

-15 
REF ID:A516913 . (' ~ 

HOBOKEN SBRIES 

Message · Lersth 

Bo. Indicators Part1a 1l'otal 01cl!, 

1 322 • 001 321 

H 191 191 

) 

Sis 1 194 

;~ ~ i~ 273 

001 * 467 -466 

l:ft i &16 173 

l~ * o~ 86 

17' 

532 ~6f> I 687 

~ 2 2l 

' ~ * 089 

A~*~; 197 197 

' 1 1) 4 6b * 287 

~ ~ 203 203 

60 $ ii 

~ 2 . 2l 

5 65 * 492 

li 122, 123 

7 I 615 -614 001 * 615 

()~~ • 6i~ 25 

026 * 001 25 lOt lOg 105 253 

1} * !b .. f 2 2l 6 33 * !68 22~ 22, 229 229 

~6 I 33 ~ 2. 2l 

7 64·* '3~ gOl gOl 301 

65 i~ 664 665 * 001 'i i i~i 123 

001· * 124 -123 

66~ i 1~ 5 429 

~ 2 21 

8 68 ¥ 131 

288 ~88 388 388 

396 *19 ~ 2 2l 

9 ~I 521 

112 11~ 119 

517 * 640 516 517 * 001 

251 251 251 370 

768 * 252 

~ 2 22 

10 76 I 254 

-16-
Kea sage 

J!o. 

10 

11 

12 

14 

15 

16 

17 

18 

19 

REF ID:A516913 

"' ,-, 

Indicators 

770 tt 254 

18 18 

188 i 272 

001 * 272 

~; it A~1 £ 2 2) 

24 * ~;6 164 164 18'8 i. 42() 

001 • 420 

71 ~l 072 4 4 i 

( 2 2} or 4 4r 

1 t 1'6 22 .. 64 

221 * 001 

211 211 

li32 * 212 

' 2 2} 

51 i 379 

224 224 

675 * 663 

£7~ 4 60~ 

Lens th 

Partial fotal 

18 

195 213 

177 177 

164 

71 

147 

211 

275 275 

77 

72 

196 

178 178 

224 224 

35 

76 

294 

-17-

Cycle 

-271 

f 

}68 

-419 

220 

72 

-76 
" . REF ID:A516913 

r'-· 1 

Message Le¥8th Ro. Indicators Partll 'l'ot&l Cycle 

19 184 * 26o aont 14. 

20 £ai i Ni~) 2li 21; 215 215 46 i 47 

21 ' ()3 2 21 I 4'9 

16i 161 161 ~ • 6>io ~ • 001 

224 

563 

224 224 188 i 2~5 

001 * 225 ... 224 

at~• 2~ 71 ~56 

~ 2 2l ' 22 -4ii ~ 2~ 342 (1l ' g,g 416 * 001 415 

28 28 28 370 444 I O®° 

2, ' 2 2l Ji'.6 * '031 

314 ,14 }14 314 r II -llS 

24 . ~ 2) 0 i 347 

26 26 26 L188 I 3'3J 

001 * ill -372 

E • 646 267 

268 • 001 267 

la4 114 114 4QI . 3 2 i 115 ~ 2 2l 25 

~~i II ill 165 165 

26 i; :::) 2~ ~~6 236 1 i 5 1 

001 it 521 

118 354 

-520 

118 118 

119 "I ~9 ..._ 

t 2 22 27 21 I 641 

121 * 002 119 

i~s r~ 366 366 

28 ' 89. 2 370 2l. 

2zo 2¢0 270 

759 I 6 ri 

759 * 001 758 

1~a, o~6 29 

-18-
.: 

Me a sage 

Bo. 

28 

cont'd. 

29 

33 

REF ID:A516913 

~ 

Indicators 

788 * 030 

001 • 030 

11-52 4~2 453 * 4 2 ! 2 . 2) 

70 i 656 

418 418 788 •. 474 

001 * 474 

166 166 

167 * 611'.o 

167 * 001 

604 604 I11 • 605 14 14) 

785 * 619 

001 

7~ * * 622 ~ 18 18 

619 * 64l'> 

019 * 001 

rd~ 8 Bl 

Le!Bth 

Partia Total 

751 

156 

177 

462 

294 ' 1089 

29 

314 

53 

418 

166 

604 1188 

18 

525 

130 

292 578 

-19-

Cycle 

-29 

610 

-177 

462 

-325 

314 

-473 

18 

657 
REF ID:A516913 

r- "' Meaaage Leys th 

Bo. Indicators Partia Total C1cle 

. ,4 ;,oo • 4,o 

210 210 210 516 • 640 

510 ... 001 509 

2~ 2~ 278 

7 • 2 

001 • 279 -278 

oS3 • 2~ 19 507 

,5 ~~f • 3o~> 

.~gi I B~ 335 

,62 • 001 361 

160 160 160 495 .,.. 

NEW YORI: 5BRIE5 

Jleaaage Lei8th Ko. . Indicators Partia Total Czcle 

l r-114 • 0011 713 

1M 1 ot~ 74 

001 * 0~5 -74 

o~ • 1~ a2 157 

~ 2 2l 2 86 * 166 20~ i01 307 307 

39 *67 ~ 2 . 2l 

95 * 469 

1~ lil 171 

5 * 6 0 

566 * 001· 565 

64 64 64 23~ 630 i 065 ~.2 2l 4 32 i 067 

ld6 1~ 156 

713 * 2 

001 * 223 -222 

:~~ i ~16 417 

418 * 001 417 

188 188 188 761 

606 • 185' 

-20-
,. REF ID:A516913 

(' ~ 

Message Bo. Indicators Leys th 

Partia Total Cycle 

• 606 * 189 

cont

1do ~12 12l 

5 18 I l§l 

1; l~O 170 

LZ'''P 01 .. 36 -360 

as2 .. ,~ 35 205 

~ 2 21 6 ;B * 398 

242 242 242 

280 i 646 

280 • 001 279 

12~ 12~ 123 ~65 

4o * 12 

' 2 . 2} 1 o5 * 126 

22. 1122._ 329 329 g-• -s5 

8 

2 2) 6 • 457 

1i * s6~ 52 

001 * 509 -508 

1,1 l~l· 131 1 2 ;: 6 0 

132 * 001 131 

i; i '§§ 394 277 

' 2 2} 9 28 * :397 243 gR * ~~- · 

671 * 001 670 

6M * oiA 17 

001 * 018 -17 

~ ~6 56 316 

057 .. 074 

{ 2 2) 

10 059 * 076 

~gj I ~~6 564 

623 * 001 622 

21 21 21 585 

644 I 0~2 

11 ~ 2 2} 46 * 024 

142 142 142 

788 4 166 

001 * 166 -165 

21~ 21~ 217 2!22 2l * 38 

' 2 2l 12 220 * 385 

-21-
REF ID:A516913 

(' I-) 

Kea sage Leysth 110. !Jldicators Partia Fatal Czcle 

12 220 • 385 

~-~~ 253 253 

13 ~7g i 64f 1 

•76 * 002 474 

2; 2~ 236 236 

1- fl: :21 

183 * ,{: 74 

001 • 'l.lf. -313 

i~.m 198 272 

~ 2 2} 15 01 * 514 

126 126 126 327 • 646 

32l • 001 326 

17 l~ 1I6 202· 

jo' • 1 

16 

2 2l 

505 * 179 

i~ • ~ti 235 235 

~ 2 2l 17 42 • 416 

46 46 46 

788 • 462 

001 * 462 -461 

1'8 m 178 

1 9. 

179 * 001 178 

1st • ooA 7 231 

18 f 2 2} 88 • 616 

2~ 2~ 4 ~ * 2 

276 276 

!o2 2) 19 6 * 288 284 284 284 284 Iso * s12 2 2) 

20 752 4 574 

7~ ' li1§ 36 

001 • 610 -609 

o,¥ • r>ig 30 

031 * 001 30 

68 68 68 1}4 

099 * 669 ~ 2 2) 21 oi * 671 

-22-
REF ID:A516913 

(' ~ 

Message Le rs th Bo. Indicators Partia Total Czcle 

21 101 * 071 

128 128 128 128 229 I 199 ~ 2 2l 22 ji i 201 

~· s~ l}' l}} 

llORFOLK SERIES 

Message LeIStb Wo. Indicators Partia Total Czcle 

l 518 * 001 517 2~ 270 7 i 271 

270 

001 * 271 -270 

244 244 244 514 

245 i 515 

' 2 . 2} 2 2f7 * siT 

12a l2g 123 3r • 64 

370 * 001 ~ii~!.,' 369 

l~Z 19~ l~ 220 

5 7 * 19 [ 2 2} 569 i 200 

2~ 21~ 219 

1 i 41 

001 * 419 -418 

22 :22 52 271 

053 * 471 ~ 2 2) 4 055 * 473 

16z 16I 167 222 i 640 

222 * 001 221 

io~ ios 101 274 

32 * 16 ! 2· 2} 

5 31 * 116 

2f~· 2~~ 279 279 

6 * 3 9 £ 2 2) 6 12 * 391 1~6 lt6 176 

7 8 * 5 7 

001 * 567 -566 

o~ • 64-6 73 

-23-
REF ID:A516913 

(°" ~ 

Message Lexa th 

lo. Indicators Partis Total Cycle 

6 074 • 640 

eont

1d. 074 * 001 73 

ii~ i li8 139 388 

~ 2 2l 

1 IS I 14~ 

16~ 16~ 163 163 

31 * }05 ~ 2 2~ 8 BO * :;01 

~f ~ dit 139 1,9 

2 2) 

9 2! I (48 

1~ 1~2 192 

7 4 6 0 

713 ... 001 712 

1~ • o~ 75 

001 * 076 -75 

ieg I ~~~ 179 446 

f 2 21 10 82 • 2a1 m. gltg 383 

565 * 001 564 2i 2~ 223 

1 ii 2 

001 * 224 

of~ * 2~~ 71 671. 

~ 2 2l 

11 74 * 297 i14~ g4a 343 

l7 *4 

417 * 001 416 

64 64 64 407 

481 ii 065 

' 2 21 12 83 * 067 226 22* 227 227 I1 * 29 2 2) 

13 712 i 296 

;m z6 Lt r~72_J 001 * 372 -371 li ltZ i~z 272_ 

1 * 5 9 

{2 2) 

14 200 .. 57i 

62 62 69 

269 * l>4o 268 269 * 001 

210 210 210 279 

479 ... 21t ! 2 2l 

15 Bi * 2l3 

-24-
"'I 

\ 

I 

REF ID:A516913 

r ~ 

Meitsage Leys th 

:no. Indicators fartia. fotal Czcle 

~- 15 481 * 213 i;t i i; 195 195 

£ 2 2l 16 78 i 410 

~~ 110 110 

i 520 

001 * 520 -519 

120 120 120 

l~i i 6116 

121 * 001 120 

6g~ 6i~ 639 1 ... l) 0 

760 * 001 759 28 28 28 

788 ii= 629 

001 * 029 -28 

~~ * i~~ 94 999 

Remarks on Calculations 

It 1a to be noted that these calculations exhibit a remarkable 

consiatenc7, and corroborate the calculated lengths or the two 

ke7s, 787 and 639, respectively. By the consistency of the calculations ve mean that it would be utterly impossible to have the 

calculated slip between messages equal for both keys in every case 

as a result of coincidence; tor, unless the assumed lengths of the 

two keys be correct, the slip would be unequal and inconsistent 

in m&nJ' places. The fact that they are .equal means tba t the 

encipherer vas consistent in slipping both tapes an equal distance 

every time. The idea behind an equal slip is not clear, for it 

entirely defeats its own purpose, which is to prevent the enemy 

rrom determining the lengths of the keys. Had the encipherer sli~ed 

them unequal distances in every ease, being careful, of course, 

to slip the short tape further than the long, no such consistency ·would have been possible to uncover. But, in this case, the pos- sibility of overlapping messages, would be greatly increased, as 

vill be shown subsequently. 

Aa mentioned above, there are several discrepancies, due to 

errors on the part of the encipherer. That they are errors, and 

not intentional operations intended to deceive the enemy is shown 

b7 their nature. For example, the slip between Washington 68 and· 

69 is 2 * 12. Evidently the encipherer meant to have Washington 69 begin at loci intervals sway from where Washington 68 ended, 

and probably misread the number 249 on the short ta.pe, making it 

259. This becomes the same as though he bad slipped the long 

tape 2 letters and the short one 12. In the New York messages another error of 10 is involved betveen messages 4 and s. !!!Q;, this error not occurred there would b.B.ve been af~orded about twice 

as many possible points of attack as were actuaii1 the case, as 

vl11 De shown_ later. 

-25-
REF ID:A516913 

Excellent corroboration for the determined lengths of keys 1• afforded by finding the total numbers of letters in all messages emanat1Dg from each station, adding the tota.1 amount of slip and then calculating as 1f only one message vere concerned. The 

final result should coincide vi·th the result obtained :from calculations for the individual messages. Thus: 

(1) Wash!_ngton Series 

Initial loci ••••••••••••••••••••••••• 126 * 001 

Total number of letters enciphered ••• 25834 25834 

Total slip • • . • • . • • • • • • • • • • • • • • . • • • . • • 132 !22 

S'UJll • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • .. • • '!!!'2"""00'!11"'9r.2--"ll!2~5.-98""'6,. 

Minus 33 revs. of long key) 6 and 40 " " short u ) ••••• • ••••• -.-.25.,.9G.17~1.____.-2-..5~5;.o;..;;..O 

Final loci •.•• ~ . . . • . • . . . . • • • • . . . . . • • . 121 * 426 

(2) Hoboken 5.eries 

Int t1al loci .................. • • . • • • . . . 322 * 001 

Total number or letters enciphered ••• 13503 1350' 

Total slip........................... 76 76 

sum. •••••••••••. Cl • • • • • • • .. • • .... • • • • • • • • • • p13-9-ol"!li-~1--3!P'!5~al"J!'o--

M1nus 17 revs. of long key) 4 

and 21 n 11 short 11 ) • • • • • • • • • • • -,...13_3._.7_2~--1-3_1_9 

Final loci • . • . • . . . • . . . • • • • . • . • • • . . . . • 522 * 161 

(3) New York Series 

Ini tia.l loci ........................ - Total number of letters enciphered •.• 714 ~ 001 

6914 6914 

Total slip ............................. . Sum ................................. " •• 76 ~I 5 6 ~I 2 

Minus 9 revs. of long key) and 10 " "short ~ )•••••······· -1083 -6220 

Fill8.l loci ............................ .. 602 * 572 

(4) Norfolk Series 

Initial loci ......................... . Total number of letters enciphered ..• 518 * 001 

5841 5841 

Total slip ............................ . 

Sum. •• • • • • •••• • • • • • • • • ••••• • • • ••• • .... . d sa15 

Minus a

9 ~eve. ~r longt ~ey) •••.•..•.... 

and " sh or ) 

P1na. l loci ........................... .. 

-622§ -~z~1. 

094 * 122 

-26-
REF ID:A516913 

In eaob case it v111 be noted that the final loci coincide 

vith tbose given bJ the individual calculations, in perfect accord 

•1th the requirements baaed upon keys 787 and 6}9 letters in 

leqtb. 

'1'be purpose or a.11 these calculations was to find euoh cycles 

aa would fora tbe basis of an attack. A table was made, therefore,, 

abow1ng all the e7oles, both plus and minus, involved in the aeries 

ot aeaaages (aee Table 1). · 

The most favorable relation of cyoles for an attack bei!lS 

tbPee sequent cyolea (tor definition see page 2 of Addendum lJ, 

an e..S.nation or thia table was made vith a viev to finding three 

sequent 01clea. 'l'hese vere round, showing first in Table 1 1n 

c7olea 415, 416, and 417, messages Hoboken 22, Norfolk 11, and 

Nev York 4, respectively. 

B7 referring to the calculations on pages 6-25, it will be 

seen that the three sequent cycles begin in reality v1tb Hoboken 

19, latent cycle 711; Norfolk 9, latent cycle 712; and New York 1, 

latent cycle 713. They end with Hoboken 24 latent cycle 415; 

Bortolk 1,, la.tent cycle 416; and Nev York 4, latent cycle 417. 

The extent of the three sequent cycles is indicated in the calculations tor these messages by the brackets. 

Had no errors been made in eno1pberment, these thl'ee sets 

ot meaaages would have proceeded along in three sequent cycles 

to the following points: Hoboken 29, latent eyole -29; Norfolk 16, 

to its completion in latent cycle -28; New York 10, latent cycle (tbeo:retical or vhat it should have been) -27. The error referred 

to on e 2 made be veen N v York 4 and ther fore outs the ' 

llUllbe:r e o n s or attac 1n ha 

c. The messages involved were immediately transcribed 

in the usual manner in the form of three sequent cycles. There 

were tvo excellent points of' attack in.these messages vhen arranged in this form. They were excellent because two messages began in 

one case at exactly the same point; in the other ease( very near 

the same point. One or these cases 1s shovn below. The initial 

points of all messages shown hereinafter will be des1gnBted by a vert1ca~ double bar surmounted by an asterisk.) 

Upper lc:•1 loci 182 186 

Lover key loci 256 260 

DBW YORE 2 -74 • • • 6XTSQWQZKWCMCPWID'Y3GD3A6JM .... Cycle 

Upper key loci w-82 186 Lover key 1001 257 261 

?fCfiPOJ.Jt 10 ••• 3XH7GMERHP3Q5NI3MCZVCTRVOU ... Cycle -75 

Upper key * loci 

Lover key loci 11186 262 

BOBOIBN 20 . . . 3C'l'FJI.XXLK3F4PKQ5LD?EQ ••• Cycle ·76 

-27-
REF ID:A516913 

TABLE 1 

D!,.stribution of Cycles 

Plus 

~0-100) 

1 Vaebington 68l 

8 Washington 39 

1

1

5 Washington 13 

8 Hoboken }2) 

25 Hoboken 5) 30 Dew York 20} 55 Washington 49) 62 Washington 23) 72 Hoboken 16) 7} ltor:folk 6) 

Plus 

(101-2001 

102 Washington 58~ 

109 Washington 27 

119 Hoboken 27l 

120 NQr:folk 16 

131 Nev York 8 

149 Washington 66l 156 Washington 37 

163 Washington 10 

17' Hoboken 2) 

Plus 

(201-300) 

203 Washington 47l 

210 Washington 20 

220. Washington 14 

221 Norfolk 4) 

250 Washington 56~ 

257 Washington 25 

26~ Hoboken 24l 

26 Nor:folk 14 

279 New York 6 

297 Washington 64) 

-17 

-23 

-28 

-29 

-39 

-46 

{

-74 

-75 

-76 

-86 

-93 

-123 

-1'0 

-133 

-140 

-157 

-165 

-171 

-177 

-1As 

-1 7 

-194 

-222 

-224 

-234 

-241 

-270 

-271 

-2ri -2 1 

-288 

-28-

Minus 

(0-100) 

New Yol'k 9) Washington 3) 

Norfolk 16) Hoboken ~8) 

Washington 25_)) 

Washington 58) New York l) 

Nor.folk 9) Hoboken 19) Washington 24) 

Washington 51) 

Minus 

(101-~00) 

Hoboken 7) 

Hoboken '3) 

Washington l4l 

Washington 41 

Washington ro 

New York 11 

Washington 6) 

Hoboken 29) 

New York 17) 

Washington 31~ Washington 60 

Minus 

(201-400}_ 

New York 4l 

Hoboken 21 

Washington 25~ Washington 52 

Norfolk 1) 

Hoboken 10~ Hoboken 34 

Washington 17~ Washington 44 
REF 

(' 

Plus 

(301-400) 

,04 Washington 3l) ,11 Washington 8 

31'&. 

321 

326 

:551 ,58 

,61 

'68 

5~ 

Hoboken 30) Hoboken l) 

Nev York 15) 

Washington 4a~ ashington l 

Hoboken 35~ : Hoboken 11 

Borfolk 2) Washington 54) 

Plus 

(401-500) 

405 Washington 25) 

{

415 Hoboken 22l 416 Nor.folk 11 

417 · Nev York 4 - 445 Washington 62l 452 Washington 32 

462 Washington 29 

468 Washington 7) 482 Washington 73) 499 Washington 43) 

Plus 

,201-600} 

506 Washington 16) 

509 Hoboken 34) 516 Hoboken 9~ 517 Nortolk l 

546 ashington 52~ 

553 Washington 25 

~~ Hoboken 21~ Norfolk 10 

593 Washington 60) 

Plus 

'601-zool 

610 Hoqoken 29) 616 Washington J) 622 New York 10 

630 Washington 70~ 647 Washington 41 

657 Hoboken 33) 664 Washington 7) 670 New York 9) 694 Washington 50) 

ID:A516913 

-29-

""""" Minus 

,201-400) 

-313 Nev York 14) 

-315 Washington 75) 

-32~ Hoboken 30) 

-32 Washington a4 

-335 

-342 

-360 

-371 

-3A2 -3 2 

-389 

-418 

-419 

-429 

-436 

-461 

-466 

-47' 

-474 

-476 

-483 

-490 

Washington 3 ~ Washington 63 

Nev York 5l 

Nortolk 1~ 

Hoboken 2 

Washington 25~ Washington 55 

Minus 

(401-500) 

Norfolk 3) Hoboken 13) Washington 20) Washington 46) 

New York 17) 

Hoboken 2) Hoboken 31) 

New York 13} 'Washington 10) 

Washington 37 

Washington 66) 

Minus 

(5_01-600) 

-sos 

-519 

-520 

-530 

-537 

{

-565 

-566 

-567 

-577 

-584 

Nev York Bl Norfolk 16 

Hoboken 26 

Washington 27) 

Washington 57) 

New York ~) 

Norfolk 6) Hoboken 16) Washington 23) Washington 49) 

New York 20) 

Washington 5) Washington 12) 

Washington 39{ Washington 68) Washington 14) 
Plus 

(701-800) 

701 Washington 24) 

712 lfortolk 9) 713 New York 1) 741 Washington 58} 7~8 Washington 29} 758 Hoboken 28) 759 Norfolk 16) 764 Washington 3) 

REF ID:A516913 

-30-

Minus 

(701-800) 
. ,\ 

r REF ID:A516913 

d. Since the messages begin with an address, it vas only 

necessary to try out all the addresses th.at ~ould be likely to 

occlll" in such messages. The modus operandi or these trials is 

given in Section 3 of this Addendum. Suffice it here to say that 

the assumption of TRAN3PORTATION3SERVICB, as the beginning of 

Hoboken 20, and ADJUTAN'l'3GENERAL, as the beginning of Norfolk 10, 

yielded LE~EQUIPMENT ror Nev York 2. There was no doubt no~ tha.t 

the messages vere broken. Subsequent work meant merely the continua t1on of plain text in three cycles and the simultaneous reconstruction ot the keys. As an aid in this precess, one of labor 

and patience, it was found necessary to decipher pe.rts of many other messages 1n oyoles as close as possible to these three. 

For example, the closest eyele to cycle -76 was cycle -86, represented by Washington 25. As soon as the first f1£teen letters or 

tbe short key bad been reconstructed, viz, 260 to 275, these in 

_conjunction vith longer key letters in loci 186 to 201 vere applied 

to Washington 25 at locus 186 in the longer key. They yielded as 

plain text 3EACH3DAY}A53THE. By applying the same steps to other 

messages, places in eyeles -93, -123, -130, -133, -141, and also 

in -46, -}9, -29, -28, -17, and -9 were deciphered, all with a 

vlev to expediting the work of rebuilding the keys, which was all 

that was necessary to complete solution since we bad no interest 

in the messages, per se. The vork was divided between two sections 

of operators, one section working forward ~rom locus 186 of the 

long key, the other working backward until the work joined. Even 

with this number of eycles to work upon, the work went slowly because of errors in the eneipherment. It was completed, hovever, 

in a comparatively short time, and the resultant keys were tested 

upon isolated fragments of new messages and found to be correct. 

It :ts ncessary to add that the messages were broken within 

ten minutes after one oi.' tQ._ose very ~Ii~t b_!:!t evei:_-present errors 

in transcribi the letters of the ori naY-three se uent e oles 

ba b~en uncovered. · s ei-l"'o.r invc-vcd the inadvertent omission, by one o'? our cierical staff, of a single letter from Norfolk 9 at 

a locus 1n advance of 186, and resulted in baffling all efforts to ~elution for every hour subsequent to the finding and the transcription of the three sequent cycles2. WHY XEY TAPES DIFFERING IN LENGTH BY MORE THAN ONE LETTER ARE 

CRYPTOGRAPHICALLY UNSAFE 

In the preliminary summary of this addendum it was stated 

that the present system of using this machine employing key tapes 

vh1ch differ in length by more than one letter is much more unsafe than the original method employing key tapes which di~fer in 

length by only one letter. The reason for this is that the present 

system not onl2 makes the production of overla2s ver~ possible, but also makes their production, under-certain circwnstances, a 

l!stt!mate function of the machine. 1n fact, the messages pre- sented fo~ test made a hairbreadth escape from such a fate! 

The point is well worth detailed explanation. 

The question which first arises in this connection is: Given 

the initial indicators ror each of four stations, can the cycles 

through vhich all messages will pass be determined beforehand? 

The answer is rilthe affirmative. In fact, tb.e cycles through 

vbich each series of messages will pass themselves go through definite cycles. Let us refer to the calculations ~or the Hoboken 

series and set down 1n the form of a list the successive plus 

cyoles involved: 

-31-
REF ID:A516913 

1iOBOXEN SERIES OF CYCLES 

321 

173 

~~ 516 

368 

220 

72 

711 

ri; 

267 

119 

758 

610 

462 

314 

166 

18 

657 

509 

361 

The numbers in this list bear de~inite relations to one 

another, relations which are absolutely determined by the displace~ 

ment, or difterenoe in the lengths of the tvo key tapes. In this 

case the difrerence between the lengths of the two key tapes is 

787 - 639 148. This means that if' we make our calculations upon the b&s1s of a stationary long key tape, the displacement of the 

abort key tape will be 148 letters per revolution of the long key 

tape. This in tllI'n means that the progression of cycles for each 

series of messages, as determined by the d1frerence between the 

key indicators, will differ by the constant factor 148. Let us 

see it this is exemplified in the series of cycle numbers given above tor the Hoboken messages. · 

Series as calculated Series as observed 

Initial cycle 321 321 

148 

2nd cycle of series 173 173 

148 . 3rd cycle of series Ts 25 

It ve continue to subtract 148, we would begin to introduce 

minua cycles, and since it is more advantageous to deal only with 

plus cycles, let us convert cycle 25 to the next higher multiple 

or tbif cycle number, by adding the length of the longer key tape 

to it. Tb.en: 

This is legitimate since all the calculations are based upon the 

revolutions of the long key tape. 

-32-
REF ID:A516913 

25 

~ 

That 1a cycle 25 is exactly the same as cycle 812. Nov let 

ue deduct 146, as before: 

812 

148 

R>4' 

1'h1a agrees vitb the cycle number given ror our list. We 

could h&Ye combined the two steps of adding 787 and then deducting 1-.S in one step, by adding 639, the length of the short key, to 

25. This vould give the next cycle number. Thus, 

Let us continue 

1. 

2. 

'· 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

25 w.. 

Series as calculated Series as observed 

321 

148 

m 148 

25 

m 

148 

wr 

148 

sro 148 

}OB" 

148 

220 

148 

m 

148 

711 

148 

~ 148 

mete. 

321 

173 

25 

664 

516 

368 

220 

72 

711 

563 

415_ 

etc. 

'l'hua, it is apparent that every cycle through which each 

aeries or messages will pass can be predetermined, provided alva:t§._ 

tba.t no errors are made in the encipherment.· For, 1r the relative 

positions or the two key tapes be changed in the slightest degree 

at an~ time in the enciphering process, the natural or predetermined series ot cycles will be modified. Such modifications actually occurred in the four series of test messages, entirely ss a result 

or errors on the part of the encipherer. 

We give in the tvo lists vhicb follov the series or cycles vbich actually resulted from the enoipherment, together v1th the 

series vbich theoretically should have resulted. Each series has 

been arranged with reference to the others in a manner designed 

to shov the production or sequent cycles. 

_,,_ 
REF ID:A516913 

TABLE 2 

'l'BBORB'l'ICAL SERIB5 ACTUAL SERIES 

Waab. 

(l!f?m>l) 

·JJoboken Noi-.folk Nev York 

<322•ooi)(~ta•oo1JC7II&•oo1> 

Wash. Hoboken Norfolk New York 

<1~01> t322*001>lsIB*o~1> c714*001> 

l~ 125 

l26 764 

616 

1=~1 468 320 321 

311 

16, 

6~ 506 

358 

210 

62 

701 

. is' 05 

257 

l~ 

~00 452 

3011 156 

8 

647 

499 

'Sl 

203 

6~ ~98 250 

102 

741 

~r~ 241 

1 9 2 

f l~ m 

321 172 173 

173 24 ~~ 6~~ 663 

515 516 517 

516 517 367 368 369 

368 369 219 220 221 

220 221 71 72 73 

72 73 710 711 712 

711 712 713 ~62 ~63 564 

i6' 564 565 1J~ 15 416 

15 416 ~417~3 266 267 268 

267 268 427 118 11§ 120 

~~ 120 279 757 75 759 

759 131 609 610 

610 770 461 462 

462 622 31} 314 

314 474 165 166 

166 326 17 18 

18 178 656 657 

657 30 508 509 

509 360 361 

361 212 

64 

703 

555 

407 

259 

111 

750 

602 

454 

306 

158 

10 

649 

501 

1Error made in sl1pp1ng the two key tapes between Washington 

7 and 8. 

2-zrror made in slipping the two key tapes between Washington 

68 and 69. 

713 

565 

417 

269 

121 

760 

612 

464 

316 

168 

20 

'srror made in slipping the two key tapes between New York 4 and 5~ 

-34-
REF ID:A516913 

r· 

A care.tu! study of Table 2 discloses some very important rscts. 

In the first place, the possibility of the production of o'V'erlaps is demonstrated ver'°1 readily. 'Washington 1 began v1th ·the 

Jce1 indicators 126 * 001, and Hoboken 1 began with the key indicatO!'a '22 * 001. Had Hoboken l begun with the long key at 321 

instead or }22, the Hoboken se~ies would bave begun immediately 

to ov~l.ap the Washington series f~om the latter's cycle 320 on 

to the end of the Hoboken messages. Again, Norfolk 1 began with 

the key 1ru11oators 518 '* 001. Had Norfolk 1 begun vith the long key at 517 instead of 518, or had Hoboken l begun with the long key at }2} instead of 322, the Hoboken and Nor£olk series would 

have overlapped for> the vhole length of the Norfolk series. 

Again, Nev York began with key indicators 714 * 001, and Norfolk 

l began vith key indicators 518 * 001. Had Nev York 1 begun vith 

the.long key at 713 instead of 714, or bad Nor£olk 1 begun with 

the long ke~ at 519 instead of 518, the Norfolk and New York 

series would have ove~l&pped. 

The beginning points for each series were undoubtedly determined by dividing the length of the long key by four (in order to 

divide the long tape into four nearly equal parts) and adding this 

number to the long key starting point for each series consecutively. ~hus, 787 + 4 ::. 196. Given the long key sts:rting point for Washington l as 126, tbe long key starting point for Hoboken l was 

126 + 196 = 322; that for Norfolk 1 wa.s 322 + 196 = 518; that for 

Bev York 1 vas 518+ 196= 714-

It is impossible, of course, to divide a prine number into 

tour equal integral parts. In the case under study the length of 

tbe long tape is 787~ The number 196 is the nearest integral fourth part of 787, it is true, but the division of the long tape 

into four parts 1s meant to be only approximate. The intention, 

as understood by us, is to allot to each station a length of the 

long key propo~tionate to its requirements as regards.its day's activity. 'With certain key lengths, the allotment on the basis 

ot equal activity of four stations will result in the production or overlaps_ Likewise, with other key lengths, the allotment on 

the basis or unequal act1v1ty will result in the production 0£ 

overlaps. Examples will be given. 

Returning to this ease, bad the number 195 been taken as the 

amount to be added consecutively, instead of 196, here are the 

starting points that would have resulted for the four series: 

'Washington 

(126 * 001 

Hoboken Norfolk Nev York 

(321 * 001) (516 * 001) (711 * 001) 

Rad this been the case a four-fold overlap would have been 

produced. Note the sequences of cycle numbers. 

-35-
• 

Washington 

(126 • 001) 

125 

764 

616 

468 

;s20 

172 

24 

663 

515 

'61 

219 

71 

710 

562 

etc. 

REF ID:A516913 

TABLE 3 

Hoboken 

(,21 • 001) 

320 

172 

24 

66, 

515 

361 

219 

Tl 

710 

562 

etc. 

Nol':f'olk 

(516 .a 001) 

515 

367 

219 

71 

710 

562 

etc. 

Nev York 

(711 * 001) 

710 

562 

etc. 

The eycle numbers would have coincided for the four series 

trom cycle 710 onwards~ and the four series of messages would have overlappe~ one another. 

That th1s is not stretching the possibilities of the situation, 

consider the results ot the adoption of 787 and 669 as the two 

lengths. 'l'b.ese numbers do not possess a coDBDon factor and are not 

multiples ot one another, so that their choice as key lengths is 

legitimate and likely. The displacement is 787 - 669 118. The 

allotment ve v111 assume to be equal; the starting point tor 

Washington 1, as 126 * 001. The starting points for the other 

aeries and the cycles are as follows: 

TABLE 4 

WashiiSton l Hoboken 1 Norfolk l New York l 

(126 661) <322 * oof) tna • 001> (714 ~ Ooi) 

Cycles Cycles Cycles Cycles 

1 125 l 321 l 517 1 713 

2 7 2 203' 2 }99 2 595 

3 676 ' 1~i ' 281 ~ 477 

4 5~8 4 4 163 359 

g 4 0 5 636 5 1~~ 5 241 

322 6 ~18 6 6 123 

~ 204 A 00 i 596 

86 282 478 ~ 67~ 9 755 9 164 9 360 9 556 

10 6}7 10 46 10 242 10 438 

11 519 11 715 ll 124 11 320 

12 401 12 597 12 6 12 202 

13 283 13 479 13 675 13 84 

14 165 14 361 14 557 14 753 

15 47 15 24} 15 439 15 635 

16 716 16 125 16 321 16 517 

etc. etc. etc. eta. 

• 
REF ID:A516913 

Not~ now that a four-fold overlap vould~te the legitimate 

result or the choice of these lengthse This case is interesting 

also because it would produce four sequent cycles in addition to 

the overlaps. In other vords, had the length of the short key ln 

the series of test messages been 30 letters more than it was, not onl~ vould there have been produced four sequent cycles but also 

a four-fold overlap! 

It may be desirable to give fu~ther instances. Let us assume 

two ke1 lengths 811 and 753, two legitimate lengths. On the basis 

of equal activity, the-allotmant vould be 811 ~ 4 ~202 letters of 

the long ts.pa per station. Suppose we start with the indicators 

126 * 001 for the first mesaage of the Washington series. The 

initial points for the other series will be as shown belov~ 

Washington 1 

(126 * 001) 

Hoboken l 

(328 * 001) 

Nor.folk 1 

(530 * 001) 

Nev York 1 

(732 * 001} 

Now let us calculate the various cycles and t.abulate them. , The displacement is 811 .. 753 = 58. 

Washington 

(126 ~ 001) 

1 125 

2 67 

3 9 

4 762 

6

5 704 

646 

7 588 

8 530 

9 472 

10 414 

11 356 

12 298 

13 240 

14 182 

15 124 

16 66 

1

17 8 

8 761 

19 703 

20 645 

21 587 __.,. 22 529 

23 ~71 24 '1-13 

etc. 

TABLE 5 

Hoboken 

(328 * 001) 

Norfolk 

(530 •; 001} 

1 "?>27 ~ 1 529 

2 269 

34 211 

153 

6

5 95 

37 

7 790 

8 732 

9 674 

10 616 

11 558 

12 500 

13 442 

14 384 

15 326 

16 268 

1

17 210 

8 152 

19 94 

20 36 

21 789 

-t) 22 731 

23 673 

24 615 

etc. 

-37-

2 1~71 

34 41:; 

355 

5 297 

6 239 

etc. 

Nev York 

(732 * 001) 

-f~7 1 731 

2 673 

3 615 

4 557 

etc. 
REF ID:A516913 

Bote tbat two overlaps vould be produced; the first cycle 

ot the lorfolk series vould overlap the 22nd cycle of the Washington aeries; the first cycle ot the New York series would overlap 

the 22nd orele of the Hoboken seriea. 

Let us nov take a case Of di:fterential allotment, assuming 

that tbe relative actiYities of four stations are in the proportion 

ot -12:1:1. 'I'heae proportions approximate the actual propo~tions 

in t.be ee~tea or test mess.ages. We v1ll adopt as key lengths 751 

&nd 651. 'I'be dieplaeement is. 100 pel' revolution or the long tape. Allotment on the bAsis or tbe ratios 4:2:1:1 gives as the initial 

paint• fol' tbe tour stations the following indicators: 

TABLE 6 

Waebington l Hoboken 1 Norfolk l lev York 1 

(100 • 001) (472 ... 001) (658 * 001) (i51 * 001) 

C7cles Cycles Cycles Cycles 

l 99 1 471 1 657 __,...1 750 ~2 750 2 371 2 557 2 650 

~ 650 3 271 ~ ~50 3 550 

~50 4 171 50 4 450 

~ 50 5 71 5 350 ~ 350 

350 6 722 6 250 250 

etc • etc. etc. etc. 

• 

!he New York series or messages overlap the Washington series 

immediately after the latter has entered its second revolution of 

the long tape. 

Bere is another instance. Let the allotment be in the proportion li: l :.1: a and let the keys be 769 and 598.. The 1n1 tial points would be as follows: 

-38-
i 

I 

1· 

.. ' 

Washington 1 

(100 * 001) 

Cycles 

1 99 

2 697 ., 526 

4 i~ g 13 

7 611 

8 440 

9 269 

10 98 

11 696 

12 52~ 

~~~ i~, 15 12 

·16 610 

i~ ~g~ 19 97 

..... ~~ g~i 

!i i~~ 25 ~09 ·26 "+38 

~~ 2~ -fl+'o 694 

31 523 

32 352 

33 181 

ete. 

REF ID:A516913 

TABLE 7 

Hoboken 1 

(355 * 001) 

-rl 

2 

~ 

~ 

~ +;;.-9 

10 

11 

12 

13 

14 

15 

16 

354 

183 

12 

610 

~§ 

97 

695 

524 

353 

182 

11 

609 

438 

2~ 

~17 694 

etc. 

Norfolk 1 

(525 .. 001) 

Cycles 

-++1 524 

2 353 

3 182 

4 11 

g gg§ 

~ 2~ -ftt'9 694 

'.""" _": ete. 

Wew York 1 

(695 * 001) 

Cycles 

-+Hrl 694 

2 523 

3 352 

4 181 

etc .. 

Here the Hoboken se~ies vould make a single overlap with the 

Wa•h1ogton series beginning with cycle 354; a three-fold overlap would be produced with the No~rolk series when cycle 524 would be 

reached; and vben cycle 694 would be reached the New York series 

would join and make a rourMfold overlap. 

Another ease where overlaps would be produced legitimately in an equal allot~ent is as follows: Let us assume two keys 917 

and 723. Equal allotments of the long tape vould give the following 1n1tial points: 

-39-
REF ID:A516913 

TABLE 8 

'Washington l Hoboken 1 Norfolk l New York 1 

(100 * 001) (329 * 001) (558 * 001) (787 ~ 001) 

C7elee Cycles Cycles Cycles 

l 899 1A2a 1 ,557 1 786 

2 22 2 134 /tc. ete 

l 628 3 857 

4~- .·4 663 I 

g 2 0 5 469 

46 6 2~5 i 769 

~~ ~ 80~ 9 9 610 

10 187 10 416 

11 910 11 222 

12 716 12 28 

13 522 iii 751 

1- 32 55 

Here we vould have a three-fold overlap; the Hoboken and 

Washington series would r1rst overlap, then the Norfolk series 

would join 1n. 

Take tbe case or the lengths of tapes involved in these test 

messages. Let us assume an allotment on the basis of 3:1:1:. The 

beg1DD1ng points and the cycles ror the four stations are as follows: 

-40-
~) 

Vaabington l 

(126 • 001) 

Oro lea 

l l~ 

i~ 

i~ 

'~ 9 515 

10 '67 

11 219 

12 71 

1:5 710 

ii m ~ 118 

19 l5~ 20 461 

21 31' 

22 165 

~ 6~ 

~ 5~ 27 212 

28 64 

29 703 

30 555 

31 407 

32 259 

'' 111 34 750 

35 602 

36 454 

31 306 

'8 158 

39 10 

40 649 

41 50 

REF ID:A516913 

'l'ABLB 9 

Hoboken l 

(519 • 001) 

Crclea 

l 518 

2 370 

3 222 

4 74 

6

5 713 

565 

7 417 

8 269 

9 121 

10 760 

etc. 

Norfolk 1 

(650 * 001) 

Cycle a 

Nev York 1 

(781 * 001) 

C7cles 

1 780. 

etc. 

The Bortolk series would overlap the Washington series when 

tbe latter enters cycle 649. 

Buch eases are not at all merely theoretical instances, but 

would be bOUDd to be.ppen. The solution of a oase involving s single overlap# even for a short distance is very easy. To demonstrate, 

let us assume that the Nev York series of messages had begun with 

the ke7 indicators 713 * 001 instead of 713 * 001 in Norfolk 9. ·A 

brief trial of possible beginnings for New York 1 would b.e.ve 

resulted in yielding the excellent plain text shovn below, when the 

address TRANSPORTATION35ERVICE had been assumed. 

-41-
Nev York 1 

. Roi-folk 9 

REF ID:A516913 

('-

Long ke7 loci 

Short key loci 

Cipher 

Assumed plain text 

Long key loci 

Short key loo! 

Cipher 

Resultant plain Text 

~ 

713 7~y- 7"~3 .. 001 OlO 020 

NTEXDRMUCIZGUH6M4YNFP5 

TRANSPORTATION33ERVICE 

713 723 1'"1J"?i 

001 010. .020 

VBUHRI4Z5DZOK76INZIW7N 

2ASSIGNMENT3T035SCHOOL 

Cycle 712 

. . . Cycle 712 

Aa bas already been stated the occurrence of such overlaps is 

not due to carelessness or errors, but is a legitimate ~unction of 

the method, viz, the introduction of a difference o~ more th.an 1 

between successive revolutions. The mathematical conditions under 

vh1cb these legitimate overlaps will be produced may be stated as 

follows: 

When, during the enciphering process :!.n two series of messages, the displacement becomes equal to the initial difference between 

the cycle numbers of the starting points, the two series of messages vill begin to overlap. For example, given tvo series of 

messages, A and B, with the starting points 375 * 001 and 765 * 001, 

respectively, (keys 787 and 639 in length), after 5ll2 letters have 

been enciphered in Series A, an overlap vill be produced with 

series B. Thus: 

Deduct (787 x 6) and (639 x 8) 

Series A 

373 ,... 001 

5112 5112 

5481 srn 

4722 3_112 

765 *~OOl 

Series B 

765 * 001 

765 ! 001 

Tb.is result could have been predicted from the rule given above. The calculations which would show the same result theoretically are as follows: 

Cycle difference of initial points 764 - 374 = 390 

Displacement after 8 revolutions of 

the short tape and 6 revolutions 

of the long tape, that is, 

(639 x 8) - (787 x6) 5112 -4722 = 390 

The calculations for the case in which the two key lengths 

vere 787 and 669 are as follows: 

Hoboken 1 

Wash. l 

322 * 001 

126 * 001 

Cycle 321 

Cycle i~~ 

787 x 13:: 10231 

669 x 15:: 1QQ25. 

Displacement ·=-I'90 

In other words, given the start!~ points of the.Hoboken and 

Washington series as 322 * 001 and 126 * 001, respectively, after 

15 revolutions of the short tape (and 13 of the long st the same 

time), the Hoboken series would begin to overlap the Washington 

series. 

Another important fact disclosed by a study of Table 2,giving 

the series of cycles produced in the test messages, is that the 

-42-
REF ID:A516913 

c7olea produced as the two ke7 tapes progress go through definite 

c1clee themselves. It 1a clear that from any given starting points, it the enoipberment proceeds without interruption or error until 

tbe total possible number of different pairs or key letters has 

been eXbauated, the two key tapes would go through every one of the 

poaa1ble c7olea, in this case 787. It would be possible in such 

a case to select any number of sequent cycles tor analysis, since 

ever7 c7cle would be included in the series of cycles used by the 

station. But.since the method ot using the tapes by allotment is 

intended to keep each station within certain limits as regards the number or cycles at its disposal, it follows that this normal 

relation does not hold, and tbe series of cycles used b7 one of 

rour atat1ons m&J or may not include two or more sequent cycles. Since the aembera ot the cbain or cycles differ by a constant 

interval (governed b7 the displacement), it is possible to select 

message& the cycles tor Which are separated by the "smallest 

poaaible interval." For example, note the Washington list in 

Table 2. In this series ot messages the smallest possible interval 

between any tvo cycles is 7; that is, the nearest cycle to cycle 125 ia cycle 118; the nearest cycle to 764 is 757, or 7 removed, 

etc·. The s•llest possible interval is a function of tvo :factors: 

(1) the displacement and (2) the allotment. The smallest possible interval 1• really determined by the least possible displacement vlthin the liaita set by the allotment as the encipherment continues. Tb.is, ve may explain as follows: 

Given 001 * 001 as the starting point, after 787 letters 

b&ve been enciphered, the long key is at 001, the short key at 

/TOOl+ 787) - 6397 = 149. The displ.Bcement of the short key is 

iheretore 149 - ?>01 :::.148. After 787 more letters have been enbered the loi? tape is again at 001, the short tape at 

'9 + 7~7) - 6:; = 297. The displacement ot the short tape is 

retore 297 - 01 = 296. Continuing this calculation. let us 

find the relative positions of the tvo tapes at the end of a few 

aore revolutions. 

Displa.eomeny 

Relative positions at end of 2nd rev. of long tape 001 * 297 296 

" n " " n }rd " " " n 001 .. 445 444 

" " n n " 4th " n " " 001 * 593 592 

" " " " n 5th " n " " 001 • t?P~.· 640=101 

Since the abort key le only 639 letters in length, then locus 

741 1• the same as locus 102. Therefore the displacement after 

tbe 5th revolution of the long tape is 101 letters. Now the 

aucceas1ve displacements as determined above may be found by 

adding 148 aucoeasively and making proper deduction for the length 

ot the short ke7. Let us ·tree what the displseement is after s 

tev more revolutions. 

-43-
REF ID:A516913 

Revolutions 

of ~ong Key 

1 

2 

~ 

g 

~ 9 

10 

11 

12 

13 

Displacement 

i48 

296 

444 

592 

101 

249 

397 

5~~ 202 

350 

498 

7 

As a check on. this calculation, note the following: 

639 

16 

383'lr 

1~ 

Displacement = 10231 - 10224 

That is, after 13 revolutions of the long key tape, during vh1oh the short tape has me.de 16 revolutions, the displacement of 

the short tape is 7. We may say, therefore, that vith the two key 

lengths given, viz, 787 and 639, after approximately 10250 letters 

have been enciphered, the cycle in which the message will be pro- ceeding at the time will be 7 removed from the initial cycle. If 

the amount of traffic for any station reaches or exceeds th1s number of l~tters, it becomes possible to select messages, all emanating 

trom the same station, the cycles for which are only 7 intervals 

apart. This is actually the case in the series or test messages. Ir only one station were eoncerned, when the long tape would have 

made 639 complete revolutions, the short tape would have ma.de 787 

complete revolutions, the displacement would be O, and every pos- sible cycle would have been represented. 

It is clear, therefore, that by allot1ng a definite number of 

cycles to each station, the smallest possible interval between any of its eyoles is a function of the least possible displacement and 

the number of cycles which bas been allotted to the station. With 

certain lengths the least possible displacement may become unit~ 

vitbin the limits or the allotment of a station, and thus sequent cycles for messages from the same station become possible as a 

legitimate :function of the system. For example, the two key lengths 811 and 753 yield the list or cycles given in Table 5. 

The list of the Washington series shovs that the smallest possible interval 1s l; for example, we have cycle 125 at the start, and 

c7cle 124 as the fifteenth cycle in the series. The follov1ng list gives the series of displacements for these two key lenths. 

-44-
REF ID:A516913 

Revolutions 

or Lopg Tape 

1 

2 

~ 

g 

~ 9 

10 

11 

12 

13 

Displacement 

s8 

116 

174 

232 

;~ 406 

464 

522 

580 

638 

696 

754 

Tb.at is~ after 13 revolutions of the long tape the net displacement would be 1, and the cycle upon which the message would 

then be about to enter vould-be directly sequent v!th the initial 

c7ale. After 26 revolutions of tbe long tape, there would be 

tbree sequent cycles, and the series of messe.ges would then run 

along in three sequent cycles. 

It vould be very easy to find a great many cases where the 

least possible displacement within the allotment limits is 2, 3, 4, 

or 5 intervals. In another section of this Addendum we shall show 

bov the possession of three seguent cycles is no longer absolutely 

essential before a solution can be achieved. Cases where the 

cycles are separated by the same interval reater than 1 or by 

different intervals (v1th1n certain limits are susceptible of 

solution. -

'· METHODS FOR EXPEDITING THE TRIALS :NECESSARY TO MAKE THE 

INI'l'IAL BREAK IN THE DECIPHERMENT 

It is quite true that there are difficulties in making the 

tirat break, but these are by no means so great as would seem. 

It ia necessary, before the decipherer can make the first 

break, that he find the correct plain text at the correct loci for 

tvo cycles. He may have the correct plain text for both cycles, but unless be applies it at tbe correct loci, all his efforts are 

of no avail. 

Nolf, in the original explanation it was shown bow the correctness ot the assumptions of plain text for two cycles, herea~ter 

to be designated as the "Experimental Cycles," vas tested on the 

third, hereafter to be designated as the "Confirma.tive Cycle." Thia step necessitates the reconstruction of the long and short 

keys tor the points vhere the plain text is assumed in the tvo 

experimental cycles and testing the reconstructed keys upon the 

third or con1"1rmat1ve cycle, at the proper loci. This process is 

ver7 laborious and time-consuming, and vhere a great number of 

trials must be made, the recovery of the individual key letters 

by the process illustrated in Plate 1, Fig. 1 of the original 

paper 1s out of the question, unless a very large force of operators is at band. 

Bovever, it is possible to reduce the process to such simple 

te:rma that a single operator can make as many as tvo thousand 

trials in three to four hours. 

-45-
REF ID:A516913 . 

0 

The eaaieat vay to explain the process is to discuss the 

actual example afforded by the following three sequent oyelea, v1tb messages beginning at the points indicated by the stars and 

bars, as was the ease with Norfolk 10 and Hoboken 20. 

Upper ke7 loci 186 196 

Lover ke7 loci 260 270 

DW YORX 2 6X'l'SQWQZ.KWCMCPWIDY3GD3.A Cycle -74 .. Upper k&J" 1001 

Lover ke7 1~186 196 loci 261 271 

llClRPOU:: 10 ••. 7GMERBP3QSNI3MCZVCTR . . . Cycle -75 .. . Upper ke7 loci 11186 196 Lover lce7 loci 262 272 

HOBOIU 20 . . . 3CTFJIXXLK3F4PKQ5LD • • • Cycle -76 

In this case it is necessary to assume beginnings for Norfolk 

10 and Hoboken 20, the experimental cycles, then test the assump- tions upon Rev York 2, the confirmative cycle. 

Thia testing may be done through the agency of reconstructed 

ke7s, but it 1s patent that the keys so reconstructed are of value 

not in them.selves, but only insofar as they do or do not yield good plain text tor Nev York 2. We may, therefore, omit the step 

ot reconstructing the keys, if ve can test whatever assumptions 

are made with respect to the exnerimental cycles directi~ on the 

conf'1r.mat1ve c{c1e without their 1ntermect1acy,, and tbus save a 

great deal of 1me and labor.. · ____ ,,, 

In order to understand the method, it v111 be necessary to 

consider the relations existing between certs.in sets of letters in 

the long and short keys in three sequent cycles. In the subsequent discussion~ for the sake of clearness, tbe long and the short keys v111 be designated as the upper and the lover keys, respectively • 

Upper key . • • • ARQNV .. • • . CYCLE 1 Lower key • • ,, • ZXTPOR N • .. Plain text • . • . I N G 3 T • • . • 

Cipher " • . .. H6XVP. 0 • • 

... Upper key ARQNV • • • • 

CYCLE 2 Lower key XTPORN. • • 

Plain text COMMA • • 0 0 

Cipher T Z X 4 Q. • • • • 

Upper * key r R Q NV • n • 0 

CYCLE ;, Lover key TPORN • 0 0 • 

Plain text ADJ UT • 0 . 0 

Cipher TY} E 2 . . 

Note· that in Cycle l the plain text letter G is enciphered 

by the conjunction or the pair or key letters Q and T; in Cycle 3, 

the plain text letter D enciphered by the conjunction of the pair 

ot key letters R and P. Now these two pairs of letters, viz, Q, 

T, and R, P form a single set of letters which encipher two adjacent 

letters of the plain text 1n Cycle 2, in criss-cross fashion. That 

ia, in the second cyele, Q of the upper ke7 in the first cycle unites vith P of the lower key in third cycle; while T of the lower 

ke7 in the first cycle unites with R of the upper key in the third 

c7cle. Now the nature of the enciphering square, being completely s~etrieal, is that no matter in vb.at manner the letters of a 

set are united, the final or resultant letter is ·the same. For 

-46-
REF ID:A516913 

example, taking the :f"our letters Q, T, R, and P, no matter how 

these letters come into juxtaposition o~ in what o~der they are 

taken, the result of' the summation of the four of them will be "6". 

The result of' these relat.ions 1s that the second or middle cycle 1n an7 tb?-ee sequent cycles represents a series of' sets of letters 

Whieb form a B?Jllll8trical or balanced system v1th certain sets of 

letters in the upper and lover cycles. It is analogous to the 

manner in which the two extremes in a proportion balance the two 

means. Such a set of letters will be designated herea:f"ter as a 

"Balanced Set." This balanced relation holds true not only for 

the ket letters; 1t holds also for the correct :e..lain text letters 

viatb t e1r respective cipher letters. because in every case the~ 

p In text with its cipher letter 1s balanced or is symmetrical '-.~ 

with the two key letters involved. For example, the resultant of 

Q and T, viz, U, coincides with the resultant of G and X, viz, U. 

Therefore, the balanced or symmetrical relation existing between 

the key letters in the three sequent cycles, as pointed out above, 

exists also between the plain text and respective cipher letters 

involved. 

Just as in the case of proportion (in mathematics) one can 

determine the unknown mean or the unknown extreme trom the given relations between the three known quantities, so one can determine 

rrom these relations, without the intermediacy of the key letters, 

the unknown pl&in-text letter in the fourth set, assuming the 

correct plain-text letters in the proper loci in the other three 

sets. When the correct asswnptions are made for the e~perimental 

cycles, therefore, the correct plain text must ·result in the cont1rmat1ve cycle; the key letters can be reconstructed afterwards. 

Let us apply the obvious steps to the example above, giving only the cipher letters first: 

CYCLB 1 

CYCLE 2 

CYCLE 3 

Contir~~1ve.Cycle 

Experimental Cycle 

Experimental Cycle 

In the following explanation ve shall indicate by the Greek 

letter Sigma (i:) that the summation of the series of letters is 

to be taken. Thua: 

I 2 

2: 

Base -

The resultant series of letters B Q K 4 ••• , vh1ch ve have te~ed the BASE, forms the framework upon vh1oh the assumptions 

are made and the results noted. Let us assume that the message in one of the experimental cycles, viz, Cycle 2 begins COMMANDING, 

and then let us try all other :possible beglnnJ.ng3 for the othi?J' 

experimental cycle, viz~ Cycle 3, in conjunction with it. First, 

it is necessary to "add the letters of COMMANDING to the base, 

in the manner shown below, which gives the resultant of the first 

assumption, or~ as we shall term it merely, the FIRST RESULTANT~ 

-47-
REF ID:A516913 ~ 

Base 

plain text } ~ Q K 4 

Assumed M M A 

for one experimental · cycle 2 

FIRST RESULTANT 

l

K !4 ... M - M ..,,, -.1 

-· .M --· A 

K' Q 

We are ready now to try in conjunction with the first resultant 

all possible beginnings for the other experimental cy~le (Cycle 3). Let us assume that this message also begins with COMMANDING and 

t1nd the second resultant. If the plain text assumed for both expe~imental cycles is correct, and in the correct loci, then the 

second resultant must yield intelligible plain text. 

FIRST RESULTANT K W K Q 

Assumed plain text for ) other experimental cycle 3) _c ___ o ____ M~_M_ 

SECOND RESULTANT E J w J 

This gives E J W J as the second resultant, or the plain text of 

the conf1rmat1ve cycle {Cycle 1), s.nd we realize at once that one 

or both of our assumptions for the experimental cycles are incorrect. Let us retain COMMANDING as the beginning of Cycle 2, and 

assume THE3 as the plain-text beginning of Cycle 3, instead of 

COMMANDING. The results are as follows: 

FIRST RESULTANT K W K Q 

Assumed plain text for } T H E 3 

other exper1mental cycle ) 

SECOND RESULTANT 5 u c w 

This, too, is clearly incorrect. Thus ve proceed until the trial 

or ADJUTANT : 

FIRST RESULTANT K W K Q 

Assumed plain text for ) other experimental cycle ) A_,_ __ D~__.J _____ u 

SECOND RESULTANT N G 3 T 

Here 1s a good possibility, and we proceed at once to add to it. 

Now all these trials can be made very rapidly by the use of 

certain sliding alphabets. These are prepared by cutting ape.rt the columns of the cipher square, accompanying each alphabet by 

the straight alphabet including the "functions;" a.nd arranging 

the letters as shown below, 'where only the first five and last 

five pairs of the A, B, and C alphabets are given, (Fig. 20). 

-48-
REF ID:A516913 

Tak1Qg the sliding. alphabets indicated by the first resultant, 

viz, K, W, K, and Q alphabets, we slide them in such a manner as 

to align the letters of the assumed plain text, using the upper (normal sequence} member of each pair of letters for this, whereupon the resultant plain text for Cycle 1 (the second resultant, 

or the text of the conf"irmative cycle) appears on a line made up of the other (mixed sequence) member of each set of letters composing the pe.1rs. Thus, the trial of the first four letters, 

ADJU, of the assumed plain-~ext beginning for the one message, would 

place the sliding alphabets in the position shovn in Fig. 21, 

wherein the tour letters of the resultant plain text for tbe other 

mea1&ge 1a immediately apparent: NG 3 T. Thus, by sliding the 

alphabets, all the possible beginnings ~or Cycle 3 are tested with 

the assumed beginning, COMMANDING .. for Cycle 2. If no good results 

are obtained, then one assumes some other beginning tor Cycle 2 

and goes through the same steps again. If no errors ·have been 

made in calculations, when the correct beginnings have been assumed 

in the correct looi of the experimental cycles, the correct plain 

text must appear in the confirmative cycle. 

Let us go through the solution of the test messages, as it 

actually vas achieved. The three messages involved are New York 

2, lorfolk 10, and Hoboken 20, of which the last two mentioned 

are· the experimental cycles; the first, the eollfirmative oyele. Thia is one of the two excellent points of attack referred to on 

page 27. The steps are summarized below: 

Upper ke7 loci 

Lover key loci 

NEV YORK 2 

Upper key loci 

Lover key loci 

lfORPOLK 10 

Upper key loci 

Lover key loci 

HOBOKEN 20 

186 196 

260 . 270 

••• 6XTSQ.'WQZKWCMCPWIDY3GD3A ••• Cycle -74 (Conf.1rmat1ve) 

fl 186 196 

261 271 

••• SXH7GMERHP3QSNI}MCZVCTR .•• Cycle -75 (Experimental) 

. . . 

Base 

* 

II ~~~ ~~ , 3CTFJIXXLK3F4PKQ5LD ••• Cycle -76 (Experimental) 

WQZKWCMC .•• 

GMERHP3Q. o o 

MERHP3QS ••• 

~ C T F J I X X o • • 3RMGGLE. o· .. 

Since in Norfolk 10 the first letter which enters into the 

balanced relations discussed above is G1 we must place the letters 

ot whatever we assume tor that message in their proper loci, viz, 

the 5th letter of the assumed beginning must go under ite cipher letter G; the 6th,, under M; etc. Assuming ADJUTANT3GENERAL for 

tbe beginning of Norfolk 10, we must add-the proper letters as 

shown below: 

-49-

• 
REF ID:A516913 

Q 

A B c -- x"r 

BC 

! A A A c:s i 1 G , l TN i 

' EP i B B B FG 

a 7 Q OF 

' HA 

I 

c c c rz 

p Q. 1 JM I K KO l D D D -AN LS l. R T lJ BP MJ I 

CE N6 I 

! 

I E E E DI OK I 2 ·o lt EC .PE j 

! . 'W F2 Q7 

'1."r GY RX i • 4 

• BR H6 SL 

• • K ex ID TU (A D J U -xr 00 J} UT • 0 - "('NG 3 T ' 3 3 BP gi;- 'K1 Vi5 . . . u x R . CE FV LX w3 

DI GD MW XR 4 4 4 EC HU ?lA Y2 

J z 1 F2 IY OQ ZI 

GY JO PB 2Y 

5 5 5 H6 KM QO 3w 

M I z ID 1£ R8 45 

J3 MK SR 54 6 6 6 X7 N5 TS 6N 

0 2 y LX OJ U4 7Q 

MW PS vz 

7 7 7 NA Q3 WM A B c OQ RB XL 

PB SP YG 

QO TA zv 

RS UH 2F FIG. 20 5R VF 3J 

TS W7 40 

U4 xc 5'1! 

vz Yl 6H 

WM Z2 7K 

XL 2Z 

YG 3Q 

zv 46 

2F SN 

3J 64 

4U 7W 

5'1' 

6H 

7K 

PIGo 21 

-50-
REF ID:A516913 

(': ~ 

Base z 3 R M G G' L E • 

Assumed plain text~ ror Worfolk 10 T A N T 3 G E N E • experimental cycle 

Base z 3 R M G G L E • 

~ssumed plain textj T A N T 3 G E N 0 0 0 

tor llorfolk 10 A N T 2 G E N E • 

1st resultant 2 J p 4 3 E 5 }l 

Let us nov set up the sliding alphabets 2, J, P, 4, 3, E, 5, and N, and then try out the various possible beginnings for 

Hoboken 20, the other experimental cycle. When TRANSPORTATION 

!a tried, the results are as shown in Fig. 22. 

2 

Al' 

B6 J rt CN 14 BX AX: • 

DJ BL CR E BY EA cs DF X2 Ai 02 F~ D2 4 ES BO DS GO BR AJ FD CK BI EF HP FI BZ GV D4 CZ PE 13 GZ CI HT E7 DP GP JD H5 DE I2 FN EV HO 

KF IF ED JK G6 FL IR 

L'l' J7 PS KJ HY GS JU 

WI K3 GL LP IU HJ KA NC LB 'HM MO JR IB LV OG MQ IC N4 KC JH MT 

i'H NU JA OM LW KT N7 ~y ow KU PL MX LF OH R4 PX LG QW NF MA PG \"' ~., QM p MH RC OB NW Q6 a.)i.J 

'TL RE lY N3 SE PQ.. OU -B.1 - fT R A N S P 0 R 

'CS SC BK OT TH QP PD SD - LEY3EQUI 

VM T6 co PV UA RJ Q4 TM .¥1;(,, UN D5 Q5 VG 83 RY UJ •i! VY EQ R2 'WQ TZ SG VL 

'j ;,. .WO F6 SF XB UI TK W5 zw XP GN TO yz V5 uo xz '21 YV H2 UK ZY WL VE YB 3·1 zo IT VP 2! XM WN zx ~R 2D JX W6 37 YH X2 2C rjX }K KB XY 4N ZT YR 34 6B 4A L3 YX 56 2A zc 43 72 5H MR ZB 65 lS 2X 5'W 6T NG 2R 73 4D 36 6Q 7J oc 3N 5V 4Q 7N 

P7 47 6G 57 

QE 5Q 7E 63 

RM 6W 75 

SW 74 

TI 

uz 

V4 FIG~ 22 

VS 

XJ 

YA 

zu 

2H 

3L 

4V 

SD -51- 6F 

7P 
REF ID:A516913 

From the sequence L E Y 3 E Q the vord EQUIPMENT soon made 

itself apparent. A fev more letters (PMENT3) were tried out to 

naake &Ul'e, and very soon, since the8e yielded good plain text in 

the other tvo cycles, it vas clear that the cipher system had 

indeed been solved and the challenge successfully met. 

The keys were then reconstructed, additional messages being utilized to expedite the process; they were then tested on new 

aeaaagea and found to be correct. 

It should be clear that this method ot using sliding alpha- bets can be applied to a case where the beginning points of two 

messages are not close together. In such a case, given one of 

the experimental cycles as involving a beginning of a message, possible beginnings are assumed for it and then the sliding alpha- bets are brought into play by assuming high frequency polygraphs 

tor the interior or the other experimental cycle and testing the 

results on the third eonf1rmat1ve or third cycle. 

* * * * 

In the preeed1ng method it was necessary to assume plain text 

for tvo c~clee and test the assumptions on the third. We sb.811 

now show how plain text m&T be assumed for only one cycle and the 

eorrectaeaa ot the assumption tested on the other two cycles simultaneously. We shall use for examples Nev York 2, Norfolk 9, 

and Hoboken 19. 

Upper key 

BEW YORK 2 Lover key 

Cycle -74 Cipher 

Upper key 

BORPOLlt.9 Lower key 

C7cle -75 Cipher 

Upper key 

HOBOD:N 19 Lover key C1ole -16 Cipher 

The base is as follows: 

loci i 179 

loci 253 . . . TNPWBQFVLRG6XT 

' ~ loci l 179 

loci ,._.{, 254 

. . . 2EPQU23UN I 

loci l 179 

loci 255 

• • • WDPZMCZWHEA 

PWBQPVL 

PQU23UN 

BPQU23U 

DPZMCZW 

,J 

Base 4 3 0 C 8 N H 

. . . 

Let us assume for the plain text or Norfolk 9 the likely ending, 'OFFICER. and find the first resultant. In order to apply the assumed text to the base in this case, it vill be necessary to ~ind vhat we have termed the MEAN VALUES of the assumed text. 

'l'hese are s1mpl~ the sums of the successive letters of the plain 

; text taken 1n pairs. They have been termed mean valu~s because 1 the7 constitute the means in oUl' balanced sets or proportions. 

Por example, the mean values of the word 30FFICER are as 

t>ollows: 

Plain text 3 ~ f. F I C ;E l \. ,/\ I\.;\ /\1 /'\ r/\ 

Mean values ~M Y 7 J 4 X ~ 
REF ID:A516913 

The mean values are nov applied to the base 7 yielding the 

first resultant as follows: 

Base 

Mean values 

First· resultant 

4 3 0 C 8 N R 

MY~J4KJ Rz SFAE 

The sliding alphabets are now brought into play, and an attempt ia made to produce intelligible text on tvo lines made up of a 

pait' of letters on each alphabet. Note the folloving set up in 

Pig. 23 and the plain text given by the lines indicated. 

This method or making an initial break into three sequent c7eles makes it very praetieable to work with the case where the 

beginning points or two messages are not close together. Given 

one ot the experimental cycles as involving the beginning of a 

:message, assumptions of probable addresses are made 7 and then the 

sliding alphabets are brought into play by assuming for the 

interior or the other experimental cycle high frequency polygraphs 

such as 442333,3, 6M533, 6N53, 3THE3, 30F3THE3, etc. The results 

of the assumptions are tested on the confirmative cycle. 

* * * * 

The relations existing between the experimental and the conr1rmat1ve cycles may assume three general eases: 

1. the two experimental cycles may be the first and 

second of three sequent cycles, whereupon the confirmative cycle 

is the third of the series; 

2. the two experimental cycles may be the second end 

third. of tbree sequent cycles, whereupon the conf1rme.t1ve cycle is the first of the series; 

3. the two experimental cycles may be the first and 

third of three sequent cycles, vbereupon the confir.mative cycle 

is the second o~ middle one of the series. 

To continue the analogy with the relations in a proportion, 

in the first ease, the upper experimental cycle constitutes one 

·of the extremes; the second experimental cycle constitutes the 

two means; and the confirmative cycle constitutes the other 

extreme. The second case is the same as the first. In the third 

case the experimental cycles constitute the extremes, the confirmative, the two means. The third case is therefore considerably different from the first two in that in the first tvo cases we 

have given (or rather assumed) one extreme and both means, leaving 

only one unknown, viz, the other extreme, to be determined; whereas 

/in this ease ve have given (or rather assumed) both extremes and 

l still have two unknowns, viz, both means, to be determined. Were 

it the ease that one and only one isolated balanced set were concerned in Case 3, there vould be no vay of finding both means; but 

the fact is that a series of balanced sets is involved, and that 

taet coupled with the fact that the two unknown means of each 

balanced set combine with the adjacent pair of unknown means to ~orm intelligible text enables us to select from thirty-two pairs 

of unknowns for each balanced set the pair which, when united 

vith one of thirty-tvo pairs for its neighboring balanced set 

forms intelligible text; and this process continued results in 

the production of plain text for the confirmative cycle. Exactly 

what is meant vill become clearer in an example. We shall give 

the correct plain text for all three cycles first, and then take 

up the cipher letters alone. 

-53-
('. REF ID:A516913 I-\ 

0 

I'6' p 

BE m OP BB 

DZ CA A 

EB D} rr 

FY El BG 

G2 P7 CF 

BN OQ DR 

IV XB E2 

JW I.J FC 

H KQ. JI GB l<r IB K2 HQ E 

BF IC L5 IS A2 

CG N.fl l4Z J4 BO 

DX 07 D XN CK 

BY PO oY LZ D4 

FB QK P6 M5 E7 

GC RL s Q.G NK FN 

H7 sx rr RU 06 G6 IL T4 BM 5.tf. PY BY JS us CJ 'l'X QH IU lt6 VI DN UB RD JR LI WJ E3 vw SI KC M4 XS F4 WV TW LW 

NO YF GS X'l' U3 MX OB z ZD HZ YO vx NF 

P2 JI; 2G IA ZM W1l' OB 

QA BA 3M JC 21.: xv PQ RV cs 4T KR 3D yp QP 

~~~Jg 48 iJ RJ fT E 6 M ~ 2 8 • <i> .3U ~ . . E ·~·· '::" '=-- 3TAB E3 . . . FM 70 ND 

VR GJ OX 1F 4J UI 

WU HS PW 5M V5 

XD IQ QL 60 WL 

Y.E JG RX 7A XM 

ZS xv 37 'YH 

2P LA. TY ZT 'T MF U2 2A 4M NX V6 3S 5J OD WP 4D 

6K PU XO 5V 7H QI YT 60 

R6 ZH 7E 

5H 2U 

'l'E 3E UP 4F 

VK 5G W2 6V 

XN 78 

Y3 

Z7 

2W 

}Y 

4B 

50 

6R 

7Z FIGo 23 

-54-
~~; .......... ~ 

0 

,, 

lJpper ke;r 

OYCLB l Lover key Plain text 

Cipher 

Upper ke7 

Lover key Plain text · OYCLB 2 

Cipher 

Upper ke;r 

Lover ke7 

OYCLB ' Plain text 

Cipher 

* 

C7cle 1 lBxperimental~: C7cle 2 Cont1rmat1ve : 

07cle ' Experimental : 

REF ID:A516913 

MESSAGES -'( I OBNTOKABD s Q !I' p B v R 

* 

'ZONB3FI 

.. NPTUTMK 

SQTPNVR 

BNTOKABD 

RTMENT3 

PJMXXFQ 

~T P NVR 0 x· AB D 

CH l BF 

.!FDIC 

... * * 

nN PT UT MK 

PJMKKFQ 

Ill F D I C 

• 

Base: 

* 

Assumed plain text for Cycle 3: 

UTMKo o. 

K K F Q .... 

M K K F •• o 

I F D I o • o 

LXQW'o ... CHIEFz. 

MDZL o

1 First resultant: •• 

·~ 

To the tirst resultant let us add ZONE3FINANCE, the assumed 

plain text of the other experimental cycle, viz, Cycle 1. The 

tirst letter vhlch enters into the relations is the E of ZONE. 

First resultant:, 

Assumed plain text for 07cle 1: 

Second resultant: 

MDZLooe 

E' ' F- l o o .. 

XFMH •• o 

Let us consider now the first tlutee balanced sets in our rela- tions: 

CYCLE 1 Cipher UTM EXPERIMENTAL CYCLE Plain text 4 E3F 

CYCLE 2 Cipher MKKFQ CONFIRMATIVE CYCLE Plain text plp2p3p4p5 

X F M IfCYCLE 3 Cipher IF D EXPERIMENTAL CYCLE Plain text CH I 

The letters ot the •econd resultant are ahovn in their proper places in C1cle 2. The first letter of the aeries, viz, X is the 

aua ot tvo plain ttzt letters represented b7 P1 and P2 ; the second 

letter ot the aeries, viz, P, 1a tbe sum ot tvo plain text letters 

repreaented by P2 and P3. If, therefore, ve assume P1 to have any 

value, say A, we can derive, auoceaaively, the values of P2, P3, P4, P5 •••• Thus: 

-55-
REF ID:A516913 

, It P1:A, then P2:A.,.x -c!,; p,=V.,.F:. W; P4 ::.W+~l.:::K; P5:K+H:.§. 

Upon this assumption the pl.a.in text of the eon!irmative cycle vould. ~ead A V W K 6, which ia. obviousl7 incorrect. 

We could proceed to find the value of this series based upon 

various assumed initial values of Pi, taking the letters or the 

alphabet 1n auoceas1on. Let us see what we get vhen ve assume 

P1:. M. 

Here ve bave excellent plain text, M B N T 3. 

• We may el1m1DBte all the trials necessary to find the value 

ot P1 b7 t~e uae ot eliding alphabets. Assuming P1 to b.ave the 

value of 7, the value ot P2 1 P3 .•• is found in the following 

manner, starting with the second resultant X F M H derived as shown 

on iage 55: 

.second r,eaultant 

Third resultant 

x 

t 

F 

x 

" 

M 

'l' 

ff 

H 

N 

() 

or 

Setting up the letters indicated in the third resultant on 

the ordinary al1d1~ alphabets of the cipher eguare, ve have ~hat 

is ahovn in Fig. 24. 

1 X T 1' 0 xf'trro 

B'DYB 

cw v 2 p 

DBB.SZ 

EMZFB 

F 'l' X B Y 

GURP2 

B D 3 0 N 

I 6 PR V 

JP6UW 

EL5AQ 

I f-f~ i 

OS4ll7 

P J 1 G C 

Q R U 6 lt 

RQGIL 

SOYDX 

'l' F 7 M 4 

U G Q J 5 

VA CL I 

'W C A 5 J 

X7PZS 

Y4SBP 

Z If B X D 

2 5 LC G 

3 B H 4 .M 

4 Y 0' T 

52KWU 

6 I· Ji A 

71'1' 0 

PIG. 24 

Here the correct generatrix becomes visible 

almost instantly by giving intelligible text. 

The choice of 7 as the basic or assumed value 

of P means nothing in itself, for any other of 

the thirty-two letters of the alphabet might be 

used as a base, vith the same results. For 

example, supposing, as before, we start with a 

as a base, ve get the third resultant shown 

below: 

Second resultant 

Third reeultant 

Setting these alphabets up, we find that the 

generatrices are exactly the same as those produced above, but they are in a different order, as shown 

in Fig. 25. 

'l'be mechanics of the process should be clear. 

E4ch of the letters of the second resultaht, X, F, 

M, H, ••• represents the union of a pair of means . in the proportions mentioned on page 52. The 

pair ot means of adjacent proportions have one 

member in common. This fact, together vith the 

tact that the succession of means must form 

-56-
.' " 

,,-... REF ID:A516913 ~ 

1ntell1g1ble text, make a the process capable of yielding 

4ea1red results. 

AVWK6 

f X-if i ?> 

GU RP 2 

FT X·E Y 

RQGIL 

2 5 LC G 

CWV2P 

B3DYE 

QRU6K 

SOY DX 

4 Y 0 3 T 

IZM7H 

ZNEXD 

52KWU 

XL5AQ 

6 I J QA 

Y45BP 

HD 3 0 N 

DHBSZ 

I 6 PR V 

WC A~ J 

'BH M 

X 1 F Z 5 

TP7MA 

VA 0 LI 

P J I G 0 

Llt2VR 

EMZFB 

U G Q J 5 

JP6UW 

~lfi~1 

PIO. 25 

* * * * * * 

SLIDING OF ASSUMED PLAIN TEXT 

TO FIND ITS CORRECT LOCUS 

the 

It baa been stated above that not only must the correct plain 

texts be assumed in two different cycles but also these texts 

must, of course, be assumed in the correct loci in those cycles. 

' Proceeding upon the theor7 that messages emanating from 

Norfolk, Bev York, and Hoboken are more likely to go to Washington than to other points, it seemed feasible to assume as the plain 

text or tbe beginnings or certain messa.ges WAR3DEPARTMENT2WASHINGTON 

3DC3# the problem then being to find the correct loci of the phrase in each of two cycles. An example will serve to make the process clear. Note the three sequent cycles below, in which WAR3DEPART 

MENT2WASHilfGTON3DC3 is assumed to occur 1n experimental cycles 2 

and 3 near the beginning ot the messages. 

-57-
REF ID:A516913 

Upper ke7 loci 192 202 212 

Lover ke7 loci 266 276 286 

K.Y. 2 (C7ole -74) ••• 6XTSQWQZKWCMCPWIDY3QD,3A.6JM3ZE6n'l'D4PZRLR .•• Con. 

\Jpper k97 loci 

Lover keJ' loci 

!Km. 10 {Cycle -75) 

Upper ke:r loci 

Lover ke1' loci 

HOBo 20 (CJ'cle -76) 

1

*1 192 202 212 

267 277 287 

Sll70MKRHP3QSNI3MCZVCTRVOUOMVNUS4'1'64AAZY. . • Exp. 

~ 192 202 212 

268 278 288 

'CTPJIXXLJGP4PKQ5LDYEQUGEPWGVOL34VVV. • . Exp. 

It 1• po111ble, ot course, to begin by placing WAR,DBPARTMENT2 

WASHINGTON at any or the likely loci ot Cyclea -75 and -76, reconstruct the ke7s and tr7 them on Cycle -74. If no good text 

results, the phrase would be moved one epa..ee to the lett or right in one or the cycles, say the second, and the keys reconstructed 

again. Thia process would be continued until the phrase had been 

shifted to all possible loci in Cycle -76 (within the section under 

examination), keeping the locus of the phrase stationary in Cycle -75. Ir no good results vere obtained, then the phrase in Cycle -75 vould be shifted one space to the right or lett and the whole 

process ot shitting the same phrase iri Cycle -76 would be gone through again. In a section or 25 letters in length vtth a p~sse 

25 lettera 1n length also, 50 x 50 or 2500 trials vould be necessary to exhaust every possibility. The labor and time of me.king such a teat•beins very great, a short cut vas devised, vbich 

reduces the vork enormously. Sliding alphabets or a special kind 

&Jle used. They consist or a simple rearrangement of the horizontal 

lines ot the cipher square, aecording to the order of the letters 

or the phNae to be teated. If the phrase be WAR}DBPARTMENT2 WASHINGTON, then the W row of the cipher square is written f1rat, 

followed by the A row, then by the R rov,-etc., until all the rows 

bave been arranged a.ecordingl7. The modii'1ed cipher square then 

bas the tolloving form: 

WAR}DBPARTMENT2WASHINGTON 

~ABCDWFGHIJKLMNOPSRSTUVWXYZ2a4i6~ TRiOLVDUfoMll-5JS38PXRP7~!2z 6 4 

A7GPR2CBQS4NZSK6YHDIW}XTVPLIUJMOARDW3AJUTVNESOPILMX7KGFHBQ564C2YZR 

3UXRPSDVT2KJP04MLWCEHAGQBZYI7E653 , DRTU74}WXX2I6YSZ5VANBCQGHMOJFEPLD 

B20K47N6YURCWXFBQPJ3ZI5LMHTASDVGR 

PYK05Q6N2TXB}RGC7EMWIZ4SJAUHLVDFP 

A7GPR2CBQS4NZ5K6YHDIW3XTVPLEUJMOA 

RDW3AJUTVNE50PILMX7KGFHBQ564C2YZR 

TWDVBZXR}P652NM4IUGY7QCAF8ELHOXJT 

M5SLYXZI4GQWC7T3RJPBN62KBDFVOHAUM 

B20X47N6YURCWXFBQPJ3ZI5LMHTASDVGE 

NKY25FEPORUAVT7HG6IDMJL5ZBXC43WQN 

TWDVBZXR3P652NM4IUGY7QCAFSELHOXJT 

2E6NJAKOP3DPTVCGHY4ULSMZ5QW7IRXB2 

WTRXGLVDUYOMEK5JS3BPAHF7CI2ZQ6N4W 

A7GPR2CBQS4NZ5X6YHDIW3XTVPLEUJMOA 

SIXJN345ZACRQBDXWLK7Y26POTHUEFGVS 

BQFGXYBC7L56I40N2AVZ3WRUDESPTMJKH 

IS54XUJML7FDHGRVTZNAPEOY6WQ32CBXI 

N 1t Y 2 SP E P 0 RU AV T'7 HG 6 ID M J L 5 Z BX C 4 3 W Q N GBABW6QTCMZY4IP2~FT5RX3DUKJOVLSEG 

TWDVBZXR3P652NM4IUGY7QCAF5ELHOKJT 

06BPZBY2NVW~R3H7CKLX45IJ5FDGMTUAO 

NKY2SPBPORU~VT7HG6IDMJL5ZBXC43WQN 

FIGo 26 

-58-
REF ID:A516913 I~ 

The columns are then cut apart, and mounted on strips in the 

form of sliding alphabets, ready for use. The method of use, emplo7ing the principle or balanced sets, will be illustrated in the 

case of the three cycles forming the basis of the preceding analysis. We shall start by assuming that the phrase WAR}DEPARTMENT2RASHINGTON 

.is in locus 192 of experimental cycle -75, as the beginning phrase 267 

ot Norfolk 10. The base and the first resultant are derived in the 

usual manner, and are as shovn below: 

NEW YORI: 2 

CYCLE -74 

(CODPIRMATIVE} . Nc&POLK 10 

CYCLE ·75 

{BXPERIMEN'lAL) 

HOBOXEll 20 

CTCLE -76 

(EXPERIMENTAL) 

Base 

Assumed plain 

text t'or NOR. 10 

First resultant 

Upper key loci 192 

Lower key loci 266 

Cipher •. ~6XTSQWQZKWCMCPWIDY3GD~A6JM}ZE6EKTD4FZRL •• 

Upper key loci 

Lower key loci 

Cipher 

Assumed p. t. 

Upper key loci 

Lover key loci 

Cipher 

192 

267 

•• • 3QSNI3MCZVCTRVOUOMVNUS4T64AAZY ., .. • · • WAR•3DEPARTMENT2WA5HINGTON. · · 

192 

268 

.•. XXLK3F4PKQ5LDYEQUGEPWGVOL34VVV* •. 

MOPWIDY3GD3A6JM3ZE6EKTD4 

Q5NI,MCZVCTRVOUOMV~U34T6 

3 Q 8 N I 3 M C Z V C T R V 0 U 0 M V N U S 4 T 

XXLKiF4PK~iLDYEiUGEPWGVO hf K; l~Ii iif~Nf~if~g~~ AR 3 DEPART MEN T_g. WASHING T O.N 

24A64JG3720IGRWMH40P4FUK 

fhe sliding alphabets indicated in this first ~esultant are 

then set up in a "staggered" me.nner, as shown below in Fig. 27. 

If the hypothetical phrase in Cycle -75 is really in the locus assumed, 

and if it also is contained anywhere vi thin the ·section included in 

CJcle -76, then intelligible text must appear on some generatrix 

or the set-up. 

Should it happen that the locus of the first letter of the 

phrase in both cases falls v1th1n the same column, that is under 

the same "long key" letter, the uncovered plain text for Cycle -74 

will oceup7 the longest generatrix; that is it will begin vith 

the second letter on the first strip (the letter immediately below 

tbe latter designating the alphabet) and will continue all along 

the generstrix, provided no breaks occur in the phrase VAR3DEPART 

MENT2WA5HING'l'ON# as assumed. If a break should occur, for example, should the phrase be WAR3DEPARTMENT6N53WASHINGTON, then the uncovered plain text for Cycle -74 will appear on two generatrices, 

separated by four letters giving unintelligible text~ 

Should the phrase in Cycle -76 begin one letter to the right 

or where it begins in Cycle -75, the plain text vill appear on the 

generatrix which begins v1th the second letter on the second strip, 

and so on upwards until, if the phrase in Cycle -76 should begin 

under the next to the last letter of the phrase in Cycle -75, only 

one letter of the plain text for Cycle -74 will be given by the 

set-up, viz, the second letter on the last strip. Should the 

-59-
1:. 

2~ ll 

7~ a. 

9L 

10~ 

11;~ 

12. 

13J 14. 

15. 

16. 

17. 

18. 

19. 

20.' 

21. 

22. 

23. 

24. 

25. 

REF ID:A516913 

It 

v 

~ 3 8 

p 6 0 p J 

G JUAT 

D?2DCC 

BMN3IB 

U J T L E If 2 N 

!K Q 2 V 5 D 6 3 5 

R75VNWQVCP5 

B T P T E 6 7 J U Q 'W 

IDDBOXDNY2X6C 

YB7QYYVBMOZIA 2JSTCGX2JTIHN~5 

Z6NVALRQ2RRDEQF 

3 EL2WJS5VOIQ3X5M G A4MK6MTP3H6GOKHN 

DURIZUNDBN4DPIRV3R 

OBC,JBTB7A7Y3RH6C26 664T7DACSTGKXOOOSJ4WD 

JEVPEH6NRPLT3RDYFBEA 

T02KWSPELPIJ5NP6BWMJJY 

67ZN26LA44G6IAVUJ52CE15 

ZJDSERNURL3UPGZKQPCT3QQQ 

E2ULDXBCTVBRR475ZMMGLX5A 

4NRGV4THMAHPOBTB7CPNOYJ 

IE2FJEROEC43DDPAL37ITE 

JDY026I5NLGYBKUGOLRC3 

AV7ZOQ64T7J85VYTC02G 

H J D J H R P H 2 Z 6 A C N 5 I 3 T P EZWUDURIVEXLMIDNN~ 

4 0 5 G 3 6 0 Q. A U N 7 P T A 3 0 

LH2QODDUSPVR7GJT 

VDKJROBEH3HMRL5 

A 3 W B 6 4 5 T I C 2 P 2 I 

·c 0 E 4 J 0 0 2 N 0 4 V P 

LRTCF5M4GL7R 

767VMFPVTGH 

Z J I K C U 7 H 0 C 

EFQX3ZRMN 

UMSQL624 

PCKEOWP 

33BJTU 

CL WA 3 

0 0 6 Q 

L 'l' K 

G 3 

c 

FIGo 27 

phrase in Cycle -76 begin one letter to the left of where it begins in C7cle -75. the plain text will appear on the generatrix which 

begins v1th the third letter of the first strip and so on downvards, 

the reverse of vhat vae set forth above. In other words, by keeping VAR3DEPAR'l1MEN'l'2WA8HINGTON in the locu~ sbovn in Cycle -75 in the 

textual diagram above, this one set-up of the special sliding alphabets is equivalent to having slid the same phrase in Cycle -76 

-60-
REF ID:A516913 

. (" ~ 

t1tt7 times. Examin.J..ag Fig. 27 in the light ot "&tte foregoing discussion, no good plain text ie discovered on any generatr!x, nor 

do we tind even a fragment or intelligible text sufficient to justify :turth•r experiment with this set-up. We proceed thereupon to move 

tbe pb?t&se one space to the right in Cycle -75· 

. Going through the same steps as shown on page 59, · -. vi th 

the same aaaumed pbraae 111 Cycle -75 (WAR3DEPARTMENT2WASHINGTON) 

but beginning under the letter Q instead of 3, we have the following: 

Upper ke7 loci 192 

Lover ke7 loci 

B.Y. 2, C7cle -74 

266 

6XTSOMOPWIDY3GD}A6JM3ZE6EK'l'D4FZRLR 

Upper ke7 loci 

Lover ke7 loci 

N<RPOLE 10, Cycle -75 

Upper key loci 

_Lover key loci 

HOBOED 20, Oycle -76 

BASB 

192 

267 

3QSNI3MCZVCTRVOUOMV'NUS4T64AAZY 

VAR3DEPARTMENT2WA8HINGTON 

192 

268 

XXLK3F4PKQSLDYEQUGEPWGVOL34VVV 

Z30FBOO\ilHDPJ3YX25BCHZSWO 

OONFIRMATIVE 

EXPERIMENTAL 

EXPERIMENTAL 

If the second generatr1x, omitting the first letter 1 of the 

preceding aet-up o:f alphabets (Fig. 27) be united with the phrase WAR,3DBP.ARTJllEN'l'2WASBING'l'ON, we get-the same base as is 1nd1eated 

bere when the phrase is moved one letter to the right in Cycle -75. 

Thus: 

2d Gen. Of Fig. 27 

Assumed plain text 

Derived new base 

(E)2 UL DX B 0 TV BRR 4 7 5 Z MM G L X S'A 7 WARjDBPARTM~NT2WA5HINGTO r30 HOOWHfiPJjTX25BCHZSYo 

This means that once a set-up such as that of Fig. 27 is made, 

new or additional write-outs of cycles as the assumed phrase is 

slid, need not be made: the proper bases can be derived as shown 

by the foregoing example from a single write-out of cycles and 

assumed plain text. 

The sliding alphabets indicated by the foregoing derived base 

( 1 t ._ is really a ":first resultant") are then set up as before, and 

the various generatrices are examined vith a view to finding plain 

text. The set-up given in Fig. 28 shows a generatrix containing 

intelligible text consisting o:f a sequence or eight letters, 

N G 3 T 0 3 S 6. Note the generstrix which is underscored. It 

means that we have struck the correct loci of at least a part of 

our hypothetical phrase in Oyole -75 and Cycle -76. We can ascertain what parts are involved from the position of the plain text 

in Fig. 28. For the fact that the plain text, viz, N G 3 T O 3 S 6, 

begins immediately arter the "letter" 2, designating the generatrix, 

aeana that the b.J'pothetieal phrase in Cycle -76 begins with 

WAR3DE ••• etc. The fact that this generatrix is the 16th or the 

set-up means that in Cycle -75 the hypothetical phrase begins with t~6th letter, which is the W of WASHINGTON.. In other words, 

the loci ot the hypothetical phrase are as shown herewith: 

-61-
REF ID:As16913 

• 

~. 

0 

22: 8~ ~ 21. z_JP T L 

20. fx1!i I .B M 19. L K Q Z 

18. B Q 6 E G B 

l"Z. : ~IBP V Y N L C 

;L6. .. - - - - - - - - - - - - - - - - - -> .ING fi T 0 _, 5 6 15. z M V x if tr '1' t 

1-. Y C B Y X U Y 0 I B 4 

l,. I V 4 6 T K 2 L K A 3 

12. Q P Q I P 0 0 Q 6 Y X B 

ll. 0 U 5 B J V K F V E B L H 

ro. D 5 4 c z B A D G 3 3 F 3 5 4 

9. H G Y E 7 M M B M W V 4 T D A G 

8. U ft M K F H J E Y D L Y X Y Z J 

7. 7 QA L 2 SA V 4 K 8 K 0 EU 7 6 

6. 0 J 'l' V F 5 R L P Q L A 0 2 3 W P T X 

5. H J 6 B T 7 Q X U 5 F V V Y V P 2 I P N ~. F06LQX474C8BAWDNUL7UV 3. V Q L .M G Y 5 Y E H D M C K 6 X Q H Z Y H 

2. J 0 V M Z L 2 R M 6 0 H Z L X R F Z 5 A 5 2 

1. ~Q 6 U T Z B S Q A I Q 8 B P 1 N G J 7 Q D D 4 

2ULDXBCTVBRR455ZMMGLX5A7 

LOM3YC6B3YQUHQCEGF40JYJH 

67ZN26LA44G6IIVUJ52CEX5 .. YPB6QL4XYSIDQPOPBYH3DD 

OSOOV43LOBHOUTD3WAVNX 

'l'L6U,3B 53J54EE6CSDP 0 

UULX4BHAPGYCTWZOKE~ 

LC4ZYH4ZURW52BULUY 

6H}N04G7QN2F4KFGW 

E OBE 3GJ'l'ZXTUV S 50 

F 5 H X P J 6 P 7 lt G Z H F Z 

'1'44XU6XULSN6MB 

X B G V Q X N Y 0 W I W ·4 

BIJOZNY5CBCU 

WQ647VHD3ZG 

2UXBLH2AN5 

L E B J 0 2 4 J 0 

HTVBC475 

52BQ37H 

Q42XNH 

XV4YO 

JH7E 

BMH 

D 4 

X FIG 28. 

-62-

1 
REF ID:A516913 . ·"' 

NEW YORK 2 Upper key loci 186 196 206 216 

CYCLE -74 ·· Lower key loci 260 270 280 290 

{CONPIRMATIVE) Cipher ••• 6XTSQ'WQZKWCMCP'WIDY3GD3A6JM3ZE6EKTD4FZRLR ••• 

Plain text ... NG3T03S6 ••• 

lf ORPOLX 10 

.QJCI.a- -75 . (EXPIRDIBNTAL) 

BOBOID 20 OYO~ -76 

(BXPBRilmBTAL) 

. Up]>6r key loc1

1

* 186 196 206 ,.· 216 

Lover key loc1I 261 271 281 291 

Cipher lsxu7G.MERHP3QSNI}MCZVCTRVOUOMVNOS4T64AAZY •.. 

Plain text ••• WASHI_NGTON .•. 

Upper key loci 186 196 206 216 

Lover key loci 262 272 282 292 

Cipher lf3CTFJIXXLK3F4PKQ5LDYEQUGEPWGVOL34VVV ... Plain text i ... WAR}DEPARTMENT ••. 

Vitb this as a start, the keys can be ~econstructed and the 

decipherment continued. 

• * * * * 

. A var~ation of the roregoing method makes use of special eliding •lpbabets based upon the hypothetical p~ase, the presence of which 

ie suspected 1n both experimental cycles. These sliding alphabets 

are built exactly like those based upon the phrase WAR3DEPARTMENT2 

WASHINGTON, except that instead or using the sequent letters of this 

phrase in constructing the alphabets, the mean values of the letters 

of the assumed plain text ~re used. The mean values of the phrase under discussion are as follows: 

~~· .... ........__ Mean values . 

V A R 3 D E P A R T ME N T 2 'W A 8 H I N G 'l' 0 N 3 D C 

AR5DEPARTMENT2WASHINGTONiDC) TD P4~YDGNxrMLZTIZL~PR~H FUR 

Sliding ~lpbabets are now made by first constructing the square ehovn in Fig. 29 and then cutting the columns apart. 

tABCDEPGBIJXLMNOP~RSTUVWXYZ2i4f6~ Vbv!zlR~P652NM4? GY·7~CA)SEL o J 

DRTU74,WXX2I6YSZSVANBCQGHMOJFEPLD 

CFQ7U~AHG4SEML2POB3JVDTXW65NRIZYC 

FCHA3N7QBJI25ZEY6GU4XRWVTOMKDSLPF 

~JZIEDSLMCAUGH3TV52FOKP6YXBRN7QW4 

QBCBVPGFAZMOSJ6KE7XLUTD}R2IYW54NQ 

YPfi6MBOKEWVGUDBFA25TSLJI473QZXROY 

DRTU743WXK2I6YSZSVANBCQGHMOJFEPLD 

GBAHW6Q7CMZY4IP2NFT5RX3DUKJOVLSEG 

NKY2SFRPORUAVT7HG6IDMJL5ZBXC4;WQN 

XV3WHMTUD6PLKEZ3JRQOFG.AC7AN4BY2IX 

FCBA3N7QBJI25ZEY6GU4XRWVTOMKD5LPF 

M58LYXZI4GQWC7T3RJPBN62KEDFVOHAUM 

LZJM6W54IHBX7CVR3SOQ2YNEKUATPGFDL 

ZL450TMJSQGVAFXDUI6HEPK2N37WYBCRZ 

TWDVBZXR3P652NM4IUGY7QCAFSELHOKJT 

IS54XUJM~7FDHGRVTZNAPEOY6WQ32CBXI 

ZL450TMJSQGVAFXDUI6HEPK2N37WYBCRZ 

LZJM6W54IHBX7CVR350Q2YNEKUATPGFDL 

RDW3AJUTVNESOPILMX7KGFHBQ~64C2YZR 

PYK05Q6N2TXB3RGC7EMWIZ45JAUBLVDFP 

RDW3AJUTVNESOPILMX7KGFHBQ564C2YZR 

4JZIEDSLMCAUGH3TV52F OKP6YXBR N7QW4 

HQFGXYBC7L56I40N2AVZ3WRUDESPTMJKH 

4JZIED8LMCAUGH3TV52FOKP6YXBRN7QW4 

PCHA3N7QBJI25ZEY6GU4XRWVTOMKDSLPF 

U3VDCIRXWEN4Y6J5ZTF2Q7BHGLPSAKOMU 

RDW3AJUTVNESOPILMX7KGFHBQ564C2YZR 

FIG. 29 

-6;-
REF ID:A516913 

• 

f"1 ~ 

Then by setting up the alphabets indicated by the letters of 

the base in staggered fashion as before, the successive first 

resultants will be found in successive generatrices. Note th&t 

the tvo generatrices used in the preceding discussion appear in 

the set-up in Fig. 30. 

6 

K J 

U 5 L 

I y 

C C E P 

N Q. D 2 W 

BOYTRUN 

L ELWKOC 

N 2 T I Z P T G L 

M6QSHDLIE 

LSMH7JJCYQ 

I J25Z5DQ.XAI 

J P Z N E G C X Y 3 J L P 

5 KPK3SNEILG2U 

Y24YR6UTLTARllD 

VNSJTYB6A3E'W6XR 

FRUJICKQS4YYZ2YVJ 

W74AZFJPV357NP5X 

53HAFMWZ07KHHCKQDR 

NIAQILVK2CZ 5SGFCEVD 

TYE 1 LB T 2 MH 5E CJ B N 0 PX Z 

ZIDL2SF6NZRSKT740GKYSF 

iocsczuGKUSU6YVVADCFNFBZ 

~IZ30FHOOWHDPJ3TX25BCHZSW 

2 4 A 6 4 J G 3 7 2 0 I G R 'W M H 4 G P 4 F U K 

6K7VQDIQPW4QHDLRAJ2RHK6W 

MN5EYYYEUABBQ43X7WVPPWUP 

5DGADIATQLQGPVWVOK2HRK2M 

GP 0 5 G T,L 7 IM H 6 7 D TI 3 W 7 4 PR 4 Z 

S H 3 N N E 2 Z 4 5 Y F Q R 4 G O Z M H W 7 S 

U4QGXZWSJVAGHLHIGF7ZBF 

66EJF7XMR4HBNC43IZ36H 

4FT6MOVXM5QETLROGBKP 

VM7RLF5JJMKXNTP35V2 

KNZ3ZNDM43WECNREYW 

5XSUTGV5TOKALTKJO 

CWMIIFXUN3F5CYSI 

1 T X T Z C S 6 T I Z A J 5 4 

AZJULPBULGFIEL 

2UM3RRSSCI4BN 

H'1'5MPPUBLA2E 

AWU7RH6SQDK 

1 J 6 M 4 4 U 7 X 3 

OQUVHBqRT 

3J824Z4U 

ODBVF6S 

GYS6UP 

ID 7 ZR 

GNRM 

5 I U 

y J 

0 FIGo 30 

• 

-64-
REF ID:A516913 

In the preceding example the assumptions for the plain text 

involved the hJ'pothet1cal presence or the same phrase in both 

experimental cycles. We shall now proceed ~o a consideration or 

the case where the 888Ull8d plain text 18 not the same ror both 

experimental CJ"Cles. The procedure is basically the same as in 

the preceding case. The messages to be used for the demonstration 

are three actual messages ot the aeries. The base baa been derived 

in tbe usual 111.nner. and to it is applied the assumed beginning, TRAl8PORTATIOK}SERVICE. ~or C7cle -76, one of the experimental c1cles, 71elding the f1rat resultant shown below: 

• 

Upper ke1 loci 11'9. 5

9 • • 403 Lover ke7 loci 46 477 

B.Y. 3 (C~ale -15) •• Z T D M 7 J X U P K X 

403 

478 

• • • 

.Upper keJ' loci 

Lover Jcet loci 

DOR. 10 (Cycle -75) • • .• D4G7QYMK7H7F •.. 

Upper ke7 loci 

.Lover kef loci 

BOB. 21 C7c le 

Aaaumed p.t. 

* 

-76) 

Base ••••••••••••••••.•••••• 

Assumed p.t. for) ••••••••••• 

.cycle -76 ) 

403 

479 

GTXAQXNNUFRT ••• 

T R A N 5 P 0 R T A T I 0 N o 

ZTDM7JXUPKK 

D4G7QYMK7H7 

4G7QYMK7H7F 

GTXA~XNNUFR 

R L c 4 5 2 3 s P 4 

TRAN5PORTAT 

lat resultant •••••••••••••• G 0 F 3 TD G CY YO 

• • 

Since Nev York begins somewhat in advance of the locus where 

Hoboken 21 begins, ·and since it is probable that the former message 1a going to 'Washington, ve assume that the phrase WAR3DEPARTMENT2 

WASBINOTOD3DC3 occurs som.evhere in the vicinity of loci 395 to 425 

or the upper key. 

The special alphabets based upon the phrase WAR3 etc. are set 

up in the manner shovn below in P1g. 31. Of course, no plain text 

can be visible aa yet because the con1'1rma.tive cycle in this case 

is tne middle cycle, and ve must apply the principles elucidated 

on pages 53-56. 

The steps are the same for every generatrix of the set-up, a~d ve vill take only the correct generatrix for the demonstration f 

or the method. The correct generatrix is, of course, found only b7 trial. The method in brief is as follows: 

Taking the correct generatrix, which is as follows: 

OJCE3KPHSFH 

and going through the usual steps, to detel'Dline the series of 

unknown means, ve have: ' 

P4 P5 p6 P7 P9 P9 plO pll pl2 

C E 3 K P H S F~ H 

X M 0 Q E Y T X 

-65-

\ 

\ 
REF ID:A516913 

Setting up this aeries ot letters in the ordinary alphabets we 

have the tollov1ng' FIG, 32l: 

1. 

2. '· 4. 

5. 

6. 

A: 

9. 

10. 

11. 

12. 

l.}. 

14. 

15. 

16. 

0 

y J 

YI 6 

C I P L 

GXP5M 

DDFSZZ 

TGB3ZMB 

3ARTRMHC 

PQWAVUHA6 

OVUGPWKAPL 

G J C C B 7 6 0 P 5 4 

D 6 lJ 7 B .If. N F 5 S ' 

BLDPZSB3SDB 

TM3SIBTVDHH 

VZNLWARLHB4 

WB6tJOBIXBSG 

6 0 0 C 7 Y 6 2 B Q J 

N6UBN4PVQ16 

BLXOZSRNIPX 

T4ZSMBOXP'l'N 

R3N47JDFTEV 

IBBHLGBJEWH 

6BXIAR5GWB2 

P ·4 X Q W N 0 4 B X 4 

ROVUYXM2KS7 

OJCEJKPBSFB 

I16'ttPS7VFB 

BXB2MWRPB 

5NJ4RB22 

CVBV7ZP 

MHQB4S 

P2XMM 

7 4 y 4 

R7E 

2H 

p 

FIG. 31 

tOWXMOGEYTXD 

6ifv56B2PW'i7R ~ B E R 3 5 E C 0 N D } T "--·-

C PX W LP BK 6 V WU 

DZGHYZV4MBH7 

EBLMXBP7HZM4 

FYVTZYGNOX'l'3 

G2DUI2F6KRUW 

HNUD4NAYB}DX 

IVY6GVZU'WP6K 

JWOPQWMRV6P2 

KQMLWQOCG5LI 

LREXCR5WU2K6 

M3KE73JXDNEY 

N H 5 Z T lI 6 F B M Z S 

0 1 J 8 3 1 X: B F 4 S Z 

PCSJRCEQAIJ5 

OK3RJK7P2URV 

RLBQPLXJ5GQA 

5XPOBXL3TYON 

T4AFN4UZS7FB 

U5HG65TILQGC 

VIFA2ID5JCAQ 

WJ7CKJ3LIACG 

XSC7ESRM4P7H 

YFIJl.DF2H7S4M 

ZD2NPDIT3BNO 

2GZ5VGYAQL5J 

3MQBOMW5ZHBF 

4T6YHT5DXOYE 

5UN2AU~VRK2P 

6A4IUANGCJIL 

70WXMOQEYTXD 

PIG. 32 

The plain text BER,SBCOND'T stands out very prominently. Counting down the t1rst alphabet of the set-up shown in Fig. 31, 

ve .find tbat it is the 16th letter ot our phrase WAR3DEPARTMENT2 

VASHING'l'ON, vh1ch begins the hypothetical phrase in Cycle -74, 

1.e., the vord WASHINGT01' occurs in Nev York 3, beginning vith 

locua 405. With the section BER3SECOND3T as a start, it is not 

difficult to add to the plain texts of all three cycles. The keys 

can be reconstructed simultaneously with the building of the plain 

texts. The proper placements of the initial texts are shown 

herewith: 

-66-
,. , 

: ' 

, 

Upper key 1001 ~f 95 Lover kV loci 469 

J.Y. 3 (C,-cle -74) •. 

l'la1D text •. 

Upper key loci 

Lover kef loci 

JIOR. 10 C7cle -75) • • 

Plain text . . Upper 1ce1' loci 

Lover kef loci 

HOB •. 21 Cycle -76} . Plain text 

... 

REF ID:A516913 

!Jo' 

477 

• • ZTDM7JXUPXX ••• 

• • 2 W A S H I N G T 0 N • • • 

403 

478 

• D4G7Q.YMK7H7P. • • .BER35BCOND3To • • 

ir03 479

GTXAQXNNUFRT •• • TRANSPORTATION • 

* * ... 

Upon prope~ occasion it 11&7 be desirable to slide tvo different 

pbraaea against one another. For example, WASHINGTON against liBW3YORK. 'l'be methods discussed in the tvo preceding cases have 

been elucidated su.rr1c1ently, it is believed to show that auch s 

process would be perfectly practicable. Special sliding alphabets vould be prepared and kept on tile tor use vben the occasion arose. 

B7 means or this J>!'OCess, it 1s possible to test all sorts of 

pbraaee 1 such aa na.11ea of persona or places likely to occlll' in 

addreaaea or signatures. Given a autticient number of messages favorable to the application or aueh a test, the process becomes 

a ver7 valuable adjunct to other methods of attack. 

4. SOLU'lIOB OF CASES NO'l' INVOLVING THREE SBQUENT CYCLES 

The possession or three c7eles in unbroken sequence ia no 

loQ.ger absolutely essential to solution. We shall discuss the 

tolloving tour cases likely to arise in practice. 

A. The tvo experimental cycles sequent, the conf'irmative 

cycle at a short diatanoe removed trom either of the experimental 

cycles. 

B. The experimental and conf'irmative cycles equidistant. 

O. The distance between the eon1'1rll8t1ve cycle and the 

nearer experimental cycle is a multiple or the distance between 

the tvo experimental cycles. 

D. Cycles at irregular intervals from one another. 

'!'he tour cases vill be studied in succession. 

A. (Caae 1)--Tb.e tvo experimental cycles sequent, the eonf"1rmat1ve 07cle at a short distance removed trom either of the exper1-

aental c7cles. 

'lhe solution ot this ease is dependent upon tvo factors; first, 

how tar removed tbe con1"1i-mative cycle is rrom the two experimental c7clee; and second, the length ot the assumed text. Let ua study 

three actual measage8. 

-67-
'Upper ke7 loci ~011er keJ' loci 

BOB. 10 (Cycle -75) 

Upper k91 loci Lover ket loci 

BOB. 20 {Cycle -76) 

Upper key loci 

Lover ke7 loci 

WASH. 25 (Cycle -86) 

REF ID:A516913 

Messages 

/: 

i. 186 196 206 

; i 261 271 281 ii SXH7GMERHP3QSNI3MCZVCTRVO Experimental 

186 196 206 

262 272 282 

\13CTPJIXXLK3F4PKQ.5LDIE ••• 

.,, 

Experimental 

186 196 2o6 

272 282 292 

••• KCF7TRQJU3NRMOZJ6SXXQ ••• Confii-ma.tive 

In tb1a case we have Norfolk 10 beginning in Cycle -75; Hoboken 

20. beginning in Cycle -76; and 'Washington 25,, in Cycle -86,, or 

ten c7cles removed from Hoboken 20; that is,, the eonfirnative cycle 

is ten cycles removed from the nearer experimental cycle, instead 

of being directly sequent, as bas been the ca·se in all the examples discussed heretofore. It.vas des~rable to obtain a method by means 

ot Which possible beginnings for Norfolk 10 and Hoboken 20 could be 

tested very rapidly on Washington 25, and the folloving method vas d~viaed. 

R•conatruct the tvo keys without reference to any plain~text 

vbatever, using the series of cipher letters only in C7cles -75 .. ~ 

and -76 for the first 15 letters, beginning vith 7 as a base ~n 

loci 186 * 262,, C7cle -76. Thus: 

Upper ke7 loci 

Lover ke7 loci 

Upper key (hypothetical) Lover key n 

Borfolk 10 (C7cle -75) 

Upper key loci 

Lover key loci 

Upper key (hypothetical} Lover key n 

Hoboken 20 (07cle -76) 

Upper kej' loci 

Lover ke7 loci Waa~. 25 (Cycle -86) 

186 196 ,,.,. 261 271 

I

! OQFHDJEBUCC5BVK I 3PU75KPMJ4RAQ;KZ lsm7GMERHP3QSNI3MCZV •.• 

186 196 

262 292 ·~ 70QFHDJEBU:C05BVK I: 3PU75XPMJ~QIZO '.~ 3CTFJixxupF4PltQ •.• 

186 196 

272 282 

••• KCF7TRQJU3NRM02J •.• 

Experimental 

Experimental 

Por example, starting with 7 as the upper key letter or locus 

186 in Cycle -76, the resultant ot 7 and 3 ia 3,, which becomes the 

lover key letter or locus 262. Thia then becomes the lower key letter above M in Cycle -75. The resultant of } and M is o, upper key letter 187, Which is nov placed above C, the second letter in 

OJ"cle -76, etc. The process ie exactly the same as that in reconstructing normal keyal except that no plain text is used as 7et. 

Xe7e produced in thi~ manner,, we have termed IMPERFECT KEYS, because 

the7 are not completed,, or made SJlllDletrical by the plain text letters 

which appl7, and will therefore not produce plain text when shifted. 

Normal keys. or keTs which vill produce plain text ve have termed 

PERFECT ltEYSo . 

Since Washington 25 is ten c7cles removed from Hoboken 20, then 

the lover imperfect keys of the latter beg1.nn1ng with R A Q. K z 

(atter the bar in the diagram) must be united vith the upper imperfect keys of the beginning point or Hoboken 20, and these must 

be applied as shown below, to the cipher in Washington 25, beginning 

-68-
REF ID:A516913 

vith KC F 7 .... The series ot letters vb1ch n~~ protluc9d 

ve term. aa before, the BASE: 

Vaah1ngton 25 

(C7cle -86) 

Upper key loe1 

Lover key loci 

Upper 1mpertect keys Lover 1mpertect keys 

Oi;pbel' 

s.rae •••••.•••••.•• 

186 

272 

70QPHD ••• 

R A Q K Z 0 • • • 

XCPITR 3 ... 

SYP2Y6 

11ov it 1a patent that 1£ we bad included the asstaDed plain 

text tor Bor~olk 10 and Hoboken 20 in constructing the keys, the 

b&ae vould bave become the plain text ~or Waeb1ngton 25; and bad 

the aea1Dled plain text been the correct plain text for those two c7cle•~ then the base vould have-to be intelligible plain text. 

However. whether ve include such aaeUJl8d plain teJn; in the :fi~st 

steps. working vith perfect keys,or apply it arter imperfect keys have fielded the baae~ the final result will be the same, providing 

ve go through tbe correct steps. 

It 1• alao patent that although. the assumed plain text consists 

ot tvo distinct parta, one applying to Norfolk 10, the other to 

Hoboken 20, it 1• perfectly correct to test the e:ffaot of' these t~o 

parta separately. '!'bat is,, ve Jl8.y as21ume one pbr11se as the begin- ning or Hoboken 20 and try it in combination vith all possible beg1DD1~a for Norfolk 10, exactly aa was done in 3eet1on 3. 

tfov as tar as the first few locl of Washington 25 are concerned, the assumption ot pl.sin text for Hoboken 20 v111 have two 

effects: tirat, upon loci 186 & 187 ••• of the upper keys, and 

secondly, upon loci 272 & 273 •.. of the lover keys. Let us 

analyze theae etrects in detail, ae~nm1ng Hoboken 20 to begin with 

'l'RAl'fSPORTATION3SKRVICEo 

Locus 186 or the upper key is unchanged, since we still retain 7 

as the base for reconatruotion of the ke7s. Locus 262 or the lower 

key 1a atteeted by the first letter ot the assumed beginning, viz 1 

T. It vould result in producing a letter d1ffe1•ent than the one 

ahovn (3) for locus 262 of the lover key and this in turn would 

g1ve a different letter in locus 187 of the upper key. Locus 263 

ot the lover key would be affected again by the second letter of 

tbe assumed plain text beginning for Hoboken 20, and this in turn 

would a.f'feot locus 188 of the upper key. In short, the effect is 

ruo5ess1ve and cumulative. This series of effects Y!ll be pro~ 

uce 6,- the toi!ovlng series of letters: 

TTTTTooo 

R R R R ,, • o 

A A A o o • 

N N ., .. o 

a • o • 

'l'"GBYT ••• 

5uoh a ael'.'ies of swmna tions bas been termed the PIWGRESSIVE 

VALUE o~ a phrase, and the integral sign placed before a series of 

letters vill indicate tbat the progressive value of the series is 

to be taken. Thus, f TRANSPORTATION means that the progressive values, letter by letter, are to be taken. 

-69-
/ 

REF ID:A516913 

This p1·ogreasi Vt3 value ~rust be applied -C.o the L!Sae 1 ~:tnd since 

the f . .h•st locus ()f tb.a upper k~y to be. e::.f'fec ted by i;he plain text 

assumed i-3 ltl7, '~e G.?ply t.hfJ progreBsive vn1ue a.s ~houn belo\1: 

Upper I~ey loci 

Loe-i:Jr key loci Bas~ 

Prog.ressi v1~ vs.lua of 

ass1.imed plain text 

for Cycle -76 · 

Suma 

186 

2·r2 

s 

s 

187 188 

2?3 2'{4 

y F 

T G .... -···-""'=-- -

s Q 

189 190 ic·. ~· ~. 

2'75 2~(6 2T? 

2 y 

B y T __.-.,,....,_...,,,,...,, 

6 7 J 

.We have so far found the effeet of the assum.pt5.on or plain 

text .tn Hoboken 20 only upon ·the upper key loci 186 to 190. Now 

ve nrnst find the effect upon the lower key loci frcm 272 to 276, 

for they, too, are involved in the process of fin.ding the pl~ii.n 

tex~ for Washington 25. J 

'rhe !irst lover key 'locus affected is 262,, by the letter T of 

TRAl'lSPORTATION o The next is locus 263, by the lett~,1., R, and so on. 

The efrect is likewiae progressive and cumulative. It vill be as 

follows, in detail: 

262 263 264 265 266 267 268 269 2·70 271 272 273 r-: .. ~ 4 c. i ' 275 276 277 

'P T T T i' T T T Ill 

... T T T T T T T 

R R R R R R R R R R R F'. R R. R 

A A A A A A A A A A A A A A 

N Ii N l\! N M N N _r1 .. !i 1\' A1 N N 

$ s s 8 s s s s "' .. , s s s 

p p p p p p p p p r p 

0 0 0 0 0 0 0 0 0 -o 

R R R R R F. R R R" 

T T T T :11 !JI ir T 

A A A .f. A A A 

T T T T T T 

l l I I I 

0 0 0 0 

N N N 

3 3 

3 --:-r=-=!f---B-,...=y=---~;--·- r· -.. -v -· B: 3 u-=-·-cr~"~z -~rr -~ ---=- ... E 3 

B:!nc1' th~ !'i?~t lo~ei- key locus inlrolve0 il ~a f1hi!1et,,n 25 is 

272:, ve begin.with the letter Q or tlie progressive value, 

the series to 

Thun: 

the bas&·- already corrected a.a 1•egards upper 

Upper• key loci 

Lover key loci 

Baser corrected for l 

imperfect upper keyf Corre~tion fo~ i.m- ) 

perfect lo-wer key J 

First resul t.s.nt 

186 

272 

~.J 6~=1=~L~-!~ 

-i ~ f ~ ~-t=~~~ 

a.nd apply 

keys. .-..._ 

· Tbis series or letters, corrected f'or upper and lower key letters 

as .::i.f'fected by the plain text assumed for Hoboken ~:O i• we t.erm, a.s 

before, the !i'IRST RESULTANT • 

-70-
REF ID:A516913 

'\ The steps illustrated above are summarized below in standard 

torm: 

Upper ' ' 

key •• 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 

loci 

Lover 

key •• 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 

loci - T R A N S P 0 R T A T I 0 N ) ~ 

Progres-} .J, /.·~ / ·l /~ /~ /·~ /i \~/!"' ,.;.,i ,../1/.t.. /J,. /"~ /"1 /JI/I~ ' sive T G B Y T I V H 3 U Q Z D S E 3 

value 

Upper key loci 186 187 188 189 190 191 . . • 

Lover ke7 loci 272 273 274 275 276 217 . . . Base S Y F 2 Y 6 . . • 

Correction fOl' im-t T G B y T perfect upper key 0 0 . Correction for imperfect Q z D s E 2 lower key • • • 

Fii-st ,resultant L H v v E -K 0 0 • 

We are now ready to assume beginnings for Norfolk 10. We may omit 

the incorrect trials and proceed at once.with the correct pbl'ase, ADJUTANT3GEN!RAL3ARf«. The steps are practically the same as above-. · ~b.e progressive values are sought, beginning with the second A or 

Al>JUTABT, since it talls under upper key locus 187, and is therefore 

the t1rat letter which enters into calculation. 

ADJUTANT3GENERAL3ARMY ••• 

!!~~esaivet i~ 5 6 E 7 N F U 3 P L Z 6 U L • • • 

Upper key loci 186 187 188 189 190 191 • • • 

Lover key loci 272 273 274 275 276 277 • 

-Second resultant L H v v E It . 0 • 

00l'rect1on for 1•-i A K 5 6 E perfect upper ke7 • • • 

Correction for 1m- ' p L z 6- u 0 • • - pertect lover key Plain text p E A T E D • • • 

Having tound intelligible plain.text for Vasbington 25, per1"ect keys are constructed in the normal manner and the decipherment continued. 

The process described above bas been carried out in full detail 

to demonstrate its mechanics. It may be s'UDllD!Lrized below: 

Upper ke7 loci 

Lover key loci 

Base . Correction ror assumed l 

plain text or Cycle -76) 

Firat resultant ••••••w••• 

Correction tor assumed t 

plain text of C7cle -75) · Plain text tor) - C7c le -86 . ) • • • • • • • • • • • 

t' 

186 

272 

SYP2Y6 

.T GB YT 

QZDSE3 

LHVVEf 

AK56E 

3PLZ6U 

PEATED 

-71-

(.)TRANSPORTATION3S ••• } 

( TGBYTIVH3UQZDSE3 ••• ) 

(ADJUTj ANT3GBNERAL3ARMY) ~ AK56E7NFU3PLZ6UL) ' 
REF ID:A516913 

' ·"' 

This process takes longer to describe than to perform, naturally, and compared vith the time it vpuld take to try out all possible . co•binations of beginnings by constructing perrect keys in each case, 

it is several hundred times more rapid. The progressive values for ~11 possible beginnings, once having been determined, can be kept 

on tile so that v1th all the data at band the process is extremely rapid. 

B. (Case 2)--Experimental and eonfirmative cycles equidistant. 

Given three cycles which are equidistant, vith tvo or them begi~ng near the same locus, a solution is possible, provided that 

the assumed text contains three or tour more letters than the distance betveen the cycles. 

Bxample 

Message 1 - Xe7 1nd1ca tr.,ra 300 4 309 (Cycle -9) · , 

XBCPRAQ40XP6NOXVZAKDNXZ 0 0 • 

Message 2 - Xe7 indicators 303 * 316 (Cycle -13) 

WLL02AXD·YRJ2WSPOU4BJOQ 

lleaaage 3 - Xey indicators 100 * 117 {Cycle -17) 

• 0 0 • 

The section beginning with 303 * 320 is as tollovs: · 

• o oGDACIWSUUUP2TY5KC6 . . . These -saages are arranged as follows:· 

300 303 313 . 

Message 1 (Cycle -9) 

309 312 322. 

XBCPRAQ40XP6NOXVZAXDNXZ. 

303 313 

316 326 

• • 

WLL02AKDYRJ2W3POU4HJ •.• 

303 313 

320 330 

Meaaage 3 (Cycle -17) .... GDACIWSUUUP2TY5XC660 ••• 

W~ must t1rst prepare these cipher letters properly so as to 

be able to make trials quickly. The reconstruction or the two im- , perfect keys 1a first carried out. Inasmuch as the steps are somewhat different from the ordinary ones in constructing key8 from 

sequent cycles, ve vill shov them somewhat in detail. 

Cycle -9 

C7cle -13 

C,.ele -17 

~03 

312 

X BC PR A Q 4'0 KP 6 N 0 XV ZAK D N X Z 

303 

316 

WLL02AKDYRJ2WSPOU4HJ 

303 

320 ,, .. GDACIWSUUUP2TY5XC666 

-72-

0 • • 

~ 0 • 

• • a 
\ 

' 

\ 

REF ID:A516913 

I" 

These cycles are four apart. Let us divide up the three lines 

into sections of four letters, beginning with the letters falling benea·th upper key 303. Thus : 

303 :307 . 11 15 19 

312 16 20 24 28 

C7cle -9 X B CPR A 4 0 K 6 N 0 V Z A DNX . . . 303 07 11 15 19 

316 20 24 28 32 

Cycle -13 WLL 2 AX y R J w 5 p U 4 H . . . 303 07 11 15 19 

320 . p24 28 32 36 

Cycle -17 .GDAC.IWS u up TY 5 c 6 6 

Since these cycles are four apart, then the construction of 

the two keys from Cycles -9 and -13 must be carried out in intervals o~ periods of four. That is, if we assume the upper key for the 

first o? Cycle -13 to be 7, then the lover key would be W. This 

·letter W, the 316tb letter of the lover key must then be placed above the letter 4 in Cycle -9, that is in the locus designated as 307~1n Cycle -9. The resultant of W and 4, viz, 6, is then 307th 

316) . upper key letter. Applying 6 to loous{307 in Cycle -13, ·we get B 

320 

for the 320th letter in the lover key. 'This letter applied to tQe 

locus;311 in Cycle -9 gives 2 as the 3llth upper key letter, etc. 

1320 

The result is as follows: 

Cycle -9 

·1~~ 1~t 1~5 ~~~ J~~ XB PRA ~OK ,iNOJ~ZA iNXZ 

I 03 I 07 rll f 15 rl9 16 20 24 28 32 

7 6 2 D W 

W B Q G H 

WLL 2AKDYRJaWSPQU4HJ 

03 07 }' 11 j' 15 }19 20 324 28 332 36 .~.GDA IWS UUP TY5 C660 

.; 

. . . 

We have been dealing so far with the first position letters 

·1n these sections of four letters, or as we shall term them the 

first elements of the periods. Let us now take up the second, 

third, and.fourth elements of the periods, beginning, as before, 

with 7as a baae, that is, as the upper key letter in loc1~304,;305, 

. ~317 1318 and~306 1n Cycle -13. Each set or series of letters is entirely 

~319 

independent of any other set, and that is why it is absolutely immaterial with what letter as a base each series is begun: the ulti..,ate result, viz, the interaction of certain letters in Cycle -17. 

will be the same regardless of the initial letter in each set of 

elements. The four reconstructed, and independent.series are as 

shown below, and the manner in which they interact~in the third message is also indicated. The result of applying the keys to the 

cipher letters is marked BASE. or course, no plain text appears 

as ·yet. 

-73-
I ' 

C7cle -9 

Cycle -13 

Cycle -17 

Upper key loci 

Lover key loci 

REF ID:A516913 

303 

312 

307 

316 

' 

I~ . 

311 

320 

315 

324 

319 

328 

Upper key loci 6 R X C 2 S R G D V 2 Q W Q D V . • 

Lover key loci W L L 0 B D L U Q K E 0 G 6 H K • • 

Cipher X B C P R A Q 4 0 K P 6 N 0 X V Z A K D N X Z • o 

Upper key .loci 

Lover key loci 

Upper key loci 

Lover key loci . Cipher 

pper key loci 

Lover key loci 

Upper key loci Lo~er key loci 

Cipher 

BASE 

303 307 311 315 319 

316 320 324 328 332 

77776R~C2SRGDV2QWQDVo o 

WLLOBDLUQKEOG6HKH5XY •• 

WLL02AKDYRJ2WSPOU4HJ •• 

303 

320 

307 

324 

311 

328 

315 

332 

319 

336 

7 7 7 7 6 R X C 2 5 R G D V 2 Q ·w Q D V ~ • 

BDLUQKEOG6HKH5XY 

GDACIWSUUUP2TY5KC660. o 

A 7 Z DIR P B Z!5 B 4 QtF H 7 Ff 

{•) . (~ (!) (<t) 

We are ready nov to try out various beginnings. As before, ve 

vill assume one beginning, keeping it constant, and trying all other 

beginnings vith it. Let us assume Cycle -13 begins with ADJUTANT3 

GENERAL, and proceed to apply corrections for imperfect keys for 

Cjcle -13 first. The upper keys for the first period of Cycle -17 

are unarfected by the plain text assumed. The lover ~eys are affected 

by the letters ADJUTANT. In the preceding section we corrected the 

ke7s b7 adding the progressive value of the plain text, and this 

value vas determined by adding the letters of the plain text in their 

direct sequen~e. But in this case, since the four elements of the 

periods are independent, ve cannot apply merely the progressive value but must apply what shall be termed the PERIODIC PROGRESSIVE 

VALUE, found by adding in progressive manner every nth letter of 

·the assumed plain text, n being the period. Or, put in the form of 

an expression, the sign_r/4 is understooQ to indicate that the 

progressive V$.lue of every fourth letter of the ser:tes is to be 

taken. For the first period of Cycle -17 the correction for imper- fect lover keys vill therefore be the fo11oving: 

J/4 

{ 

1st rriod AD u 

TANT · WRUQ 

'l'hia correction applied to the first period of the base gives the following: 

Base 

Correc-tion tor im1st period 

A 7 Z D 

perf'ect·-upper key - - - -

Correction for im-} perfect lower key f V R U Q 

First resultant T R P V 

-74-

2nd period 

R PB Z 

3rd period SB4Q 
REF ID:A516913 

. The corrections tor imperfect upper and lower keys for the . ·second and third periods are as follows: 

( 

2nd period 

Upper kez Lover kez 

ADJU 

)

,.

4

. A D J U 

TANT 

&GEN T 1 6 

3rd period Upper key t(,wer key 

ADJU 

TANT WRUQ 

I 

)4 

A D J· U 

TANT 

3 GEN 

ER AL 

Pa SD 

~hese corrections are applied to the respective periods as follows: 

1st J?eriod 2nd ;eeriod 3rd J?eriod 

Base A 7 Z D RP B Z 5 B 4 Q 

Correction tor im-t ADJU WR U Q pertect upper key ---.-

Correction for 1m- WRUQ Q. T I· 6 PG 5 D pertec~ lover key · 

Pirst resultant TRPV VKHF GDRD 

Having determined the first resultant ve are nov ready to test 

all po.asible beginnings for Cycle -9. Let us proceed at once to 

the correct one 1 v1z 1 COMMANDING3GENERAL. The periodic progressive corrections are found as before 1 beginning with the letter I of COMMANDING since it is the first one to enter into the calculat1ons 1 

tba.t 1a f /4 ING:;GENERAL is to be taken. 

lat period 

UPJ>!r ker Lover kez 

Bo correc- I N G 3 

tion necessary 

2nd period Upper key Lover ke.z 3rd period Upper key Lover key 

ING3j ING3 (j ING3 (j ING3 

4 G E N E .)4 G E N E ) 4 G E N E 

· M F P s M· F P 3 R A L 6 Pc 3V 

These corrections are applied to the second resultant and yield intelligible plain text. Thus: 

1st l!eriod 2nd Eeriod 2rd J?eriod 

First resultant TRPV VKHF GDRD 

Corffctioo tor im-1 ING 3 MF P 5 perfect upper key ___ .,_, 

Correction tor im~ ING~ MF P s· pc 2 v perfect lover key Plain bext · PIN q 3 C ON TR 0 L 

All tbese steps may be simplified and sunmarized as shovn 

belov·. It vas necessary to go through all the steps above in order 

·to sbov the mechanics of the process in detail. But it these steps be anal7zed carefully 1 it 'Will become apparent that certain repe- titions or plain text periods cancel out, being duplicates, so that 

the final result is achieved just as vell by going through only the following steps: 

-15-

'---------------------------------------------------------------
I. 

REF ID:A516913 

1st }!eriod 2nd period ~rd 12er1od 

Base A 1 Z D RP B Z 5B4Q Co~rection for plain! ADJU TANT 'GEN 

text of C7cle -13 TANT f GEN ERAL 

Pirst resultant TRPv KHF a D R1'.f 

Correction for plaint ING 3 GENE RA L 6 text ot C7cle -9 

Plain text for} PING ' C 0 N TR 0 L Cycle -17 

Bo further comment 1s necessary in regard to the rapidity of th~ process. Once intelligible text is found, new keys are con- -atructed employing the deciphered plain text and taking into account 

the fact tbat the period.a consist of four independent elements. 

'l'be reconstructed keys will not be perfect keys,· but they will 

o¥'rate In eyer{ case where the eJcle involved is four or a multiple 

o four lnterva s avay from any o the·ezcies Which entered intotheir reconstruction. • 

C. (Case 3)--The distance between the co.nf'irmative cycle and 

the nearer experimental cycle is a multiple of the distance between 

the tvo experimental c7cles. 

In the case just discussed, the cycles were equidistant. The 

proceaa can be applied likev1ae to those cases in which the distance 

between the conf'1rmative and the nearer experimental cycle is a 

iaultiple of that betveen the tvo experimental cycles. The practical appl1eat1on of the method is dependent upon the same two factors 

as berore, viz, the distance between the cycles, and the length 

·Of the plain text assumed~ An example taken from the series or 

test messages will serve our pul'poses. The messages have been 

/arranged for decipherment: 

Upper key loci 

Lover·ke;r_loc1 

l.Y. 20 lCycle -~09) 

Upper key loci 

Lover kef loci 

·BOB. 32 (Cycle -621) 

-upper ke7 loo 1 

Lover ke7 loci· 

WASH. 13 (C7cle -624) 

Messases 

014 

623 

••• VQVY4 3VG36. • • Contirma. ti ve 

I

., 002 014 

623 635 

NT48JOVVCX73RSOFEY2HI07l/PBo•• Experimental 

* 

11

002 014 

626 6,8 VCC8GUPWMUDY2NR 02GHPIB. • • Experimental 

Hoboken 32, and Washington 1,, the experimental cycles, are 

ttu-ee cycles apart; while Nev York 20, the confirmst1ve cyele, and Soboken 32, the nearer exper~ental cycle, are twelve cycles 

apart; in other vords, the distance between the first and second 

cycles is the fourth multiple of that between the second and third. 

Let us reconstruct imperfect keys employing the principles 

ot periodicity just elucidated. The period, being the distance 

between the'experimental cycles, is three. The keys, using X, Y, 

and Z as bases, are as follows: 

-76-
: . 

! 

I 

I . I . 

;, 

REF ID:A516913 

\ . · { Upper key loci 

N.Y. 20 Lower key loci 

Cycle -609 Cipher 

~ Upper ke7 loci 

Lower key loci 

HOB. 32 Upper key loci 

Cycle -621 Lover key loci 

Cipher 

{

Upper key loci . Lover key loci 

WASH. 13 Upper key loci 

Cycle -624 Lover key loci · .Cipher . 

014 

623 

••• VQVY4 3VG36 

002 014 

* 623 635 

l

.l X'YZXYTOJXJ7NFM66PDARS 

PFKA650KQCOENDBK'l'ZAHW T4SJOVVCX73RSOFEY2HI07VPB 

002 014 

626 638 

JI

XYZXlTOJXJ7NFM66PD 

A650KQCOENDBKTZAHW · ~ VCCSGUPWMUDY2NR 02GHPIB 

Appi71ng to Nev York 20 upper keys 014 ••• and lower keys 623 ••• 

ve have the tolloving: 

1'. Y. 20 

Cycle -609 

Upper key loci 

Lover key loci 

Upper key loci 

Lover key 1001 

Cipher 

Base 

014 020 

623 629 

FM66PDARS. 

PFKA650KQ~ 

VQVY43VG3. 

SIRFSLS5P. 

. . • 0 

. . . . Let us assume tor the plain text of Hoboken 32, SURGEON3GENERAL6 

R52WASBINGTON, and determine the first resultant. We must begin v1th the E ot SURGEON, since that is the first letter which enters 

into relations. 

lat period 

Upper.kez ~Lover kez 

3 GE E 0 N 

NER 

AL 6 

m f 3 

. Nev York 20 

2nd period Upper. key .. Lower ke..z 

3GE No corN:BR rection ,. 

AL 6 necessary ) 3 

N 5 2 

~4i 

3rd period UPJ?er key Lover keJ 

3 GE 3 GE 

NE R 

AL 6 

N 5 2 

WA5 

m 

Base lat ¥er1od 

s R 2nd ~eriod 

P t ~rd ~er1od 

s 5 p Correction for 1m-t perfect upper key . UPL HYF .u R 4 

Correction tor 1mperf'ect lover key · E 0 N - - - 'GE 

First resultant · A 4 H B T 5 R K 5 

Let us now try as the assumed plain text of Washington 13 the 

correct beginning, DEPARTMEN'l'3AIR3SERVICE. · 

-11-

• 
REF ID:A516913 

lat period 

Upper ker tower key 

DEP 

ART 

MBN 

m 

No correction neces-(. 

sary ) 3 

Flrst resultant 

Correction tor im-i perfect upper key Cor~ection for 1m-

.perfect lover key Plain text 

New York 20 

2nd period Upper key LOver kez 

D-B P 

ART 

MEN 

T 3 A 

.uL.2 

m 

DEP 

~d period Upper key Lower key 

DBP 

ART 

MEN 

T3A 

IR 3 

SER 

8 3 u 

f DE P 

3 ART 

R J I 

1st ieriod A H 2nd friod 

B 5 

3rd teriod .R 5 

IC D 7 3 F s s u 

- .. - DEP R JI 

SIX TY 3 SEV 

The appearance of the words S_IXTY3SEV ••• gives the beginning of 

excellent plain text. _The keys are reconstructed aid the decipherment continued. 

The short-cut, eliminating all details, for this process is summarized below. The plain text letters are the summations of the 

letters in the columns. 

Nev York 20 

Base 

lat period s IR 2nd ~eriod 

F L 2rd ~eriod s p 

1 

E 0 N 3 GE NER 

Assumed plain text J 3GE NER AL 6 

tor Hoboken 32 NBR AL 6 N 5 2 

AL 6 N 5 2 WA 5 Ni2 W A !2 Iii \ D P ART 

Assumed plain text} ART. MEN T3A 

for Washington 13 MEN T 3 A IR 3 

T~A IR 2 8 ER 

Plain text for Nevt 5 IX TY 3 SEV York 20 

D. (Case·4)--The three cycles at irregular intervals. 

We have been leading up> step by step~to the solution of the most 

important case of all, viz, that in which no sequent cycles, or 

cycles at any regular.distances apart are available. This case is, 

of course, the most valuable trom the practical standpoint, and 

warrants restatement. It means that given tvo messages separated 

by 2, 3, -· ... up to say 15 cycles, plain text may be assumed and 

tested upon any other cycle th.at may be available, providing only that the keys applying to this third cycle fall within the sections 

of assumed plain text • . Let us study an actual example taken from the series or test 

messages. We shall choose as the experimental cycles Hoboken 32 

and Washington 13, which are three cycles apart. For the confirmative 

-78-

, 
REF ID:A516913 

cycle we shall take Washington 39. In the diag~am below the.messages have been arranged for decipherment; imperfect keys have been 

C'lnstruoted and applied to Washington 39. 

Hoboken 32 

Cycle -621 

Upper1Cef loci 785 

619 key 

I I 

602 012 022 Lover 623 633 0 key loci' 

Iaper.tect upper 

Im:per:teet·lover 

Cipher key,l\ 

<' 

NT 4 

XYZXYTOJXJ7NFM66PDARSCT 

PFKA650KQCOENDBKTZAHWQM SJ 0 V V C X: 7 3 R 8 0 FEY 2 HI 0 1 VP Bl~ 

Washington 13 

C1cle -621 

Upper key loo1-

Lover key loci 

Imperfect upper key Imperfect lover key Cipher 

002 012 022 ' 

626 636 ' 007 

XYZXYTOJXJ7NFM66PDARSCT 

A650KQCOENDBKTZAHWQMAQZ 

ft. V C C S G U P W M U D Y 2 N R 0 2 G H P I B B 

• Waaliington 39 (Cont~ Cycle I -631 

Upper k6y ioe1 

Lover key loci 

Im.perfect upper key Impertect lover key Cipher 

bo2 012· 022 

. . "' 

Baae 

33 004 

XYZXYTOJXJ7NFM66P 

OENDB TZAHWQ.MAQZ 

UDL65 DXRAG7FL6AH 

2X KWTEUHMD6MF 

Before ve can proceed, it vill be necessary to introduce into 

the diacuasion a feature vhieh presents itself here tor the first 

time •. 

014 

RSC T 

5 T 7 • 

The distance between the tvo experimental cycles determines 

the period and the periodic length ia simply the sum of the number 

ot its constituent elements. As regards the upper key, the periods, and there.tore all their constituent elements, tor all cycles, coincide, since all or our analysis is based upon the fiction of 

a stationary longer (=upper) key. But as regards the lover key, vhioh in our analysis is regarded as the moving key, any period 1.n 

one experimental cycle b&s a homologous period in the other experi- mental cycle, both periods being com.posed naturally of the same 

elements and in the same order. In other words, the first, second, 

third ••• ele•ents of a given period of one experimental cycle coincide vith the first, second, third ••• elements of a homologous period ot the other experimental cycle. The case is somewhat 

analogous to that in wave motion, when two waves of similar period reach their ma.xi.Jllum magnitude s1llultaneously, the two waves being in a condition termed as "in phase.n . 

Now, in the case of three equidistant cycles, the lower key periods of the eonf'1rmat1ve cyele are in phase with those of the 

experimental cycles. The same is true of the case where the distance 

betveen the confirmative cycle and the nearer experimental cycle is a multiple of the distance between the two experimental cycles. But in the case vhich conforms to neither of these eases, that is, 

where the distance between the confirmative cycle and the nearer 

experimental cycle is neither equal to nor a multiple of the distance between the tvo experimental cycles, the lowe:r key periods of tbe conf1rmative cycle are not in phase with those of the 

~79-
REF ID:A516913 

0 

' 

experimental cycles. The condition, to continue the analogy with 

wave motion, exhibits a "difference in phase"; and in this case, 

with a period of three, the difference is either 1/3 or 2/3 of a 

period. That isJ the periods of the confirmative cycle are either 

advanced or retarded 173 or 2/3 of a period. When this is the case, 

the application of imperfect keys derived from the two experimental 

c1cles Will not result in the production of intelligible text in 

the confirmative cycle unless a correction for the difference in 

phase is applied. The reason for this phenomenon is obvious when 

one considers the origin of imperfect keys as contrasted with that 

or perfect keys. In reconstructed perfect keys, adjacent letters 

or both the upper and the lower key bear a definite relation to· 

one another--they are the individual successive links of a continuous 

single chain which bas been made~link by link)from the plain text--. 

cipher text relations. But imperfect keys that have been constructed 

'from experimental cycles not directly sequent consist of several 

independent chains which "dovetail" in such a manner as to produce intelligible text only where the periods of' the confirma.tive cycle 

are in phase with those of the experimental cycle. These chains 

are independent because they are generated by independent, unrelated 

base letters. 

The difference between keys ~r these two types is comparable 

to that between a single phase and a polyphase alternating current 

ot electricity, and we have termed a key of the first type a 

MONOPHASE KEY, and one of the second ·type a POLYPHASE KEY. The 

difference between them may be shown diagl'amm&tically in the following sketch: 

1 2 f l 2 f t ~ f 

Monop~se 

Polypb&se 

Difference in phase in a polypbase key may be shown likewise 

in diagrammatic manner: · 

1 2 3 1 2 3 1 2 3 l 2 3} t-H--mttt~-,-~-1;··1- 1/3 'i-f-1-fT+f/r-i··f·· l 

2 l 2 3 l ? ~ ).. 2 3~-J ~r-r-r· 1~-t1 2/3 I a3 23J23.·· 

1 , ·T-r-T 

phase difference (1200) 

phase difference (240°) 

It, after a polypbase key bas been constructed, we can establish a · relationship between the letters or elements o:f its period (:.the 

phases Of the period), then the independent chains Of the polyph&se key may be merged and converted into one continuous chain vh1ch 

v111 then constitute a perfect monophase key. 

Let us proceed now to decipher the message~. For the beginning or Hoboken 32, one experimental cycle, ve will assume SURGEON3 

GENERAL6N52WASHINGTON. The corrections to be applied are shown 

-80-
/ 

i 

1. 

REF ID:A516913 

below. The upper keys being constant, its periods are in phase · throughout all cycles. The lover key periods ot Washington 39 are 

out or phase vith those of tpe experimental cycles, being retarded 

l/' ot a perJ.od. The elements of the periods of Washington 39 are 

in the order 2-3-1, instead or 1-2-3 because the first elements or . . the periods ot Washington 39 are the second elements of those of 

the exper!Jaental cycles. For this reason the correction to be 

applied to Washington 39 takes the following fora: 

Vaah1pgton 39 

lat period Upper ke1 LOier ke1 2nd period Upper iey LOVer key 

3rd· period Upper key Lover k.!J: 

No correction necessary 

2-3-1 

•• 3 

GBN 

BRA 

6 J J 

1-2-3 

3 GB 

4th period Upper key LOver key 

1-2-3 2,-3-1 

3GE . . 3 

BER GEN 

AL6 ERA 

JDT L6N 

5?W 

ffi 

2-3-1 1-2-3 . . :; 3 GB 

GEN NER 

ER A 4 6 J 

L6N 

D !' tt 

5th period UPR.er ke_z. ~over key 

1-2~3 2-3-1 

3 GE . • 3 

NBR GEN 

AL6 ERA 

N f 2 L6N 

u t 52w 

A 5 5 

tt : ~ 

2-3-1 

. • 3 

GEN 

ER A 

L 6 N j£: 

lat Per. 2nd Per. 3rd Per. 4th Per. 5th Per. 

Base 2XK It w 'l' EUH MD6 MFQ 

Correction tor ~ -- - 3 GE 4 6 J. JD T UP L iap. upper ke7 

Correction for 6 J J D 'l' U PLH YPJ R 4 5 imp. lover key 

let resultant B P 3 2 BP 5 c J 2 F 7 ZWG 

Let us assume tor the beginning ot Washington 13 the phrase 

DBPAR'l'MENT3AIR3SERVICB. The corrections are as follows: 

-81-
REF ID:A516913 

lat period 

Upper ke1 Lover kez 

2nd period 3rd period 

Upper key Lover k~ Upper key ~r k~ 

No correction necessary 

2-1-3 

• • D 

EPA 

RT M 

ENT 

lrR I 

1-2-3 

DE P 

4th period ue12er key Lover key 

1-2-3 2-1-3 

DE P . • D 

ART E PA 

MEN RT M 

PR R ENT 

3 A I 

R 3 5 

ERV 

8 u 6 

2-1-3 

• • D 

EPA 

RT M 

ENT 

3 A I 

c D 7 

1-2-3 

DE P 

ART 

R J l 

5th period Upper key tover key 

1-2-3 2-1-3 

DE P . • D 

ART E PA 

ME ·N RT M 

m ENT 

3AI 

R 3 3 

ERV 

I C D 

AD G 

Let us nov apply these corrections to the first resultant: 

lat Per. 2nd Per. 3rd Per. 4th Per. 

1st resultant BP 3 2 B "P 5 c J 2 F 7 

Correction for l DE P R JI PRR imp. upper key . - - - Correction tor R R I C D 7 3 F S s u 6 imp. lover keyj 

2nd resultant WM 2 8 z 7 ~ 4 4 z 7 z 

2-1-3 

• • D 

EPA 

RT M-"' 

ENT 

3 A I 

R 3 S 

3 F s 

!2th Per. 

z 'W G 

I C D 

AD G 

H HD 

We are ready'nov to apply the correction for difference in 

phase. Our.imperfect polyphase keys consist of three independent chains 1 generated·by the initial letters ·X, Y,and z. Let us designate by the letters ki, k2 , !~nd k~ those letters in perfect monoph&se keys which occupy the pos1t1ons of X, Y, and Z of our imperfect polypbase keys. Nov k2 and kl are related insofar as k2 is derived 

from ki by means of the plain text-cipher relations which intervene; 

and k3 1s related to k2 1n the same manner. If ve could convert X 

into kl, Y into k2 and Z into k3 , our imperfect polypb.ase keys could 

be converted into perfect mcSnopflase keys. Now X plus an unknown. 

letter c1 would equal k1 ; Y plus an unknown ~etter c2 , would equal 

,;k2; and Z plus an unknown letter c3 , would equal k3 . These three 

uiiknovn letters c1 , c2, and c3 , whlch would constitute the corrections for pba@e difference, vould repeat themselves periodically throughout the imperfect keys. We can transfer these relations 

directly to the second resultant. 

/ 

Second resultant - W M 2 8Z7 Z44 Z7Z HHD 

W plus tne unknown letter c1 would give the correct plain text 

tor that locus; M plus c2 would give the correct plain text letter to~ the second locus; and 2 plus c3 would give the correct plain 

text letter tor the third locus. The cycle would repeat itself 

throughout- the second resultant. 

-82-
'REF ID:A516913 

~) Z} 't e1 = correct plain text for 1st letters of periods 

iJ 

fl• c2 - correct plain te:xt for 2nd lette:rs of periods 

:

7z2} ... 

T c~ ~ correct plain text for 3rd letters of periods 

The correction being constant for the three elements of the 

periods, we may set up the respective elements of these periods on 

the ordinary sliding alphabets, whereupon the correct plain text 

for each set or elements will appear on one generatr1x vb1cb can 

be selected from all ,others by inspection, since it will be the 

one which contains tht? best assortment of high-frequency letters. 

The correct generatr1x will be different for each set of 

elements, ~f course, but by selecting the most likely generatrices, 

the corrected elements will now form intelligible plain text. 

Thus: 

GEN. 

-r 

B 

c 

D 

E 

F 

a 

H 

I 

J 

K 

L 

M 

N 

0 

p 

Q 

R 

S. 

T 

u 

v 

w 

x 

y 

z 

2 

3 

4 

5 

6 

7 

W S Z Z H 

.TILLQ 

RM 4 4 F 

X J 5 5 G 

G N 0 0 X 

L 3 TTY 

V4MMB 

D 5 J JC 

u z s s 7 

YAQQL 

0 C G G 5 

MRVV6 

E QA A I 

KB FF 4 

5 DX X 0 

JXDDN 

s \{ u u 2 

3 LI I A 

BK66V 

P7HHZ 

AYE E 3 

H 2 PP W 

F6KKR 

7 p 2 2 u 

C O N N D 

I T 3 3 E 

2 H 7 7 5 

z u w w p, 

QEYYT 

6FBBM 

N G C C J 

4VRRK 

W S Z Z H 

M Z 4 7 H 

SLJAQ 

S 4 Z BF 

L 5 I C G 

Y 0 ED X 

XTDEY 

Z MS F B 

I J L G C 

4 SM H 7 

G QC IL 

Q GA J 5 

WVUK6 

C A G L I 

·7 F H M _4 

TX YN O 

3 D T 0 N 

RU V P 2 

JI 5 QA P 6 2 RV 

B HF S Z 

NE 0 T 3 

6PKU'W 

2 KP V R 

K 2 6 WU 

ENYXD 

D 3 X YE 

F 7 B ZS 

V'WR2P 

0 Y N 3 T 

H B 7 4 M 

A C Q 5 J 

U R W' 6 K 

M Z 4 7 H 

-83;;. 

2 7 4 Z D 

EAJLR 

6 B Z 4 T 

N C I 5 U 

J D E 0 7 

A EDT 4 

K F SM 3 

0 G L JV 

PHMSX 

3 I C Q K 

DJ AG 2 

F KU ·v I 

TL GA 6 

VMHFY 

C N 3 X S 

G 0 T D Z 

HP VU 5 

YQ5IV 

4 R 2 6 A 

US F H N 

LTOEB 

SUK PC 

MVPKQ 

Z W 6 2 G 

SXYNH 

QYX3M 

W Z B 7 0 

7 2 R W J 

I 3 NY F 

R 4 7 BE 

x 5 Q c p 

B6WRL 

2 7 4 Z D 
i 

REF ID :.A516913 

• ~ I 

Note' that in the set-up of the first elements .the Y generatrix le composed entirely of high-frequency letters, I T 3 3 E. In the 

set-up ot the second elements the T generatrix is composed of bighf'reque:ncy letters, N E 0 T 3. Uniting the .first and second elements 

in the third resultant we have the following: 

1 2 3 4 5 1 2 3 

Third resultant: W M 2 

1 2 3 

8 z 7 

TE 

1 2 3 

z ,~ 4 

1 2 3 

z 7 z 

3 T 

l 2 .3 

HHD 

Plain text; I N 3 0 E 3 

In the set-up of the third elements the 3 generatrix is composed entirely of high-frequency letters, but they do not combine 

well-with the plain text found thus fer. This generatrix vhen combined vitb the other tvo gives: 

1 2 3 4 5 

1 2 3 1 2 3 1 2 3 1 2 3 l 2 3 

WM 2 s z 7 . z 4 4 z 7· z H HD 

I N I TE 3 3 0 N 3 TY E 3 F 

The correct generatrix is the S generatrix. It given the following: 

1 2 3 4 5 

1 2 3 1 2 } 1 2 3 l 2 3 1 2 3 

WM2 s z ·r z 4·4 z 7 'i~ HHD 

IN U TES 3 0 F 3 T JI E 3 N 

In all subsequent cycles the ~orrection for the difference in 

phase is the period indicated by the genera.trices determined above, 

viz, YT S. In other words c1 ::. Y; c2 ~= T; c3 ~ S. · 

"For exa•ple, in Washington 68 the stepa without going through 

the explanation above give the base sho·wn below: 

Hoboken 32 

Cycle -621 Exp. Upper key lo'ci 

Lower key loci 

Iap. upper key 

Imp. .lover key 

Cipher 

Washington 13 

Czale -624 Exp. Upper key loci 

Lover key loci 

Imp. upper key 

Imp. lover key Cipher 

Washington 68 

Czcle -638 Cont. 

Upper key loci 

Lower ke7 loci 

Imp. upper key 

Imp. lover key 

Cipher 

Base 

' . 002 012 019 022 

623 633 001 OQ~t 

X Y Z X Y T 0 J X J 7 N F Iwl 6 6 P·· D A R S f 0 T 

PFKA650KQCOENDBKTZAHWQM 

NT4SJOVVCK73RSOFEY2HI07VPBN 

002 012 016 022 

626 636 001 007 

·XYZXYTOJXJ7NFM66PDARSCT 

A650KQCOENDBKTZAHWQMAQZ 

VCC5GUPWMUDY2NR02GHPIBE 

002 012 022 

001 011 021 

x y z x y T 0 J x J 7 Np M 6 6 p DAR sic T 

ZAHWQMAQZ I 

LMXT7EYH05U4S4F26YZDTR 

VROV2FC4H 

-84-
REF ID:A516913 

Assuming for the beginnings of Hoboken 32 and Washington 13 the 

same addresses as before, viz, SURGEON3GENERAL6N52WA5558HINGTON 

and DEPARTMENT3AIR3SERVICE, respectively, ve apply the proper "corrections to the base derived above. 

Since the first period of the lover key of Washington 68 is 

affected by the assumed plain text for the 2nd, 3rd, 4th, 5th, and 

6th periods of Hoboken 32, and also by that for the 1st, 2nd, 3rd, 

4th, and 5th periods of 'Washington 13, we must be guided accordingly in making the corrections for imperfect keys. _Again, since the 

flrst element of the 1st period of Washington 68 is the third 

element of the 5th period of Washington 13, then the relative order ~f the elements or the periods of Washington 68 is 3-1-2, as compared with their order, 1-2-3, in Washington 13 and Hoboken 32, 

the experimental cycles. The order of the elements of the upper key is the same for all cycles. The corrections for the first three 

periods of Washington 68 take the following form: 

Correction for assumed plain text for Hoboken 32, SURGEON~/3 GBNBRAL6N52WA5555HINGTON= 

For Upper Key 

Period 

1 2 3 

No correction necessary 

1-2-3 1-2-3 

}GE NER 

3GE~m 

2 3 4 

~ 

3-1-2 3-1-2 3-1-2 

ENE RAL 

-:--ycr -+ 0 g ]f""li:"O _.. E 4 6 

For Lover Key 

Period 

5 

3-1-2 

6 N 5 

6 

3-1-2 

2 WA 

J'JD~JJD 

TU'.P-+TUP 

7 

3-1-2 

.5 5 5 

8 

3-1-2 

S H I 

LHY~LHY 

FJR->FJR 

4 5 N 

Period 

l 2 3 

Base V R 0 V 2 F c 4H 

Correction for 1m-i .. 

perfect upper key - - - 3 GE 4 6 J 

Correction for im- L·H Y F JR 4 5 N perfect lower key First resultant NVF Q 'W I C NW 

-85-
REF ID:A516913 

Correction tor assumed plain text for Washington 13, (/3DEPART JIDT}AIR3SBRVICE ~ /' 

1 2 

3-1-2 3 .. 1-2 

.DB PAR 

.!Sl-..DB 

1 

For Upper Ke1 

Period 

2 3 

No correc-· 

tion neceaaary 

1-2-3 1-2-3 

D_E P ART 

DEP-.DBP 

R "J I 

3 

3-1-2 

't M E 

Por Lover Xey 

4 

3-1-2 

N 'l' 3 

Period 

5 

3-1-2 

A IR 

6 

3-1-2 

3 SB 

7 

3-1-2 

RV I 

P'RJ.+PRJ 

IPR4IP:R 

R I C~ R I C I>' 3-+ DH1_3 

F55-tF s 5 

8 

3-1-2 

CE 3 

u 6 A 4U 6 A DGU 

Period 

1 2 3 

Pirat resultant NVF Q WI c NW 

C01'1'ect1on tor 1•-1 - - - DE P R J I _ perfect upper key 

Correction for im- F 5 5 U6A DGU perfect lover key Second retiultant B 6 4 BDW FXL 

/ 

We are re&dJ nov to apply th~ correction for the difference in 

phase. We have found that c1 = Y; c2 = T; and c

3 : S. Since in this 

case the third element of a period of the experimental cycle becomes 

·the first element of that ot the cont1rmat1ve cycle, then the correction to be applied becomes S YT to correspond with the order 

3-1-2 of the lettars of the confirmative cycle periods. 

Washington @ 

Second resul t&nt· 

lat Period 2nd Period 3rd Period 

164 Bl>V FXL , Col"rec-tion for phase\. ditterence J SYT 5YT SYT 

Plain text 3co MMA 442 

· It is desirable, c.t course, to construct perfect monopb.ase keys, in order to eliainate tbe corrections for differences in phase in 

subsequent vork. The method is as follows: 

Take the tirst three letters upon vb1ch the reconstruction or tb~ 11lperrect keys vas based. In this ease they are X Y Z. 

-86-
REF ID:A516913 

Take any pair of equivalents for Y, the first letter of the 

9orrective period, such as U L. Place these two equivalents beneath X Y Z and find the resultant. Thus: 

Basic letters 

Equivalents of Y 

Resultant 

x y z 

UL 

Gu 

Take the resultant of L (the second member of the pair or 

equivalents of Y) and T (the second letter of the corrective period), 

which is 2; add this letter to Z, the third basic letter. Thus: 

XYZ 

UL 2 

(j u w 

These three letters used as a base in connection with the 

correct plain text for the two experimental cycles will give two 

perreot monopbase keys such as will apply to any cycles produced through their interaction, without the 1nter·vention of a correction 

for phase differences. The steps diagrammatically for the conversion -0f polypbase keys to monopbase are as follows: 

Corrective period 

Base for polypbase keys 

Base for monopbase keys 

YT S 

UL 2 

x y z 

GUW 

Beginning vith these letters as a base for the construction 

ot perfect keys from the tvo experimental cycles ve have the follov1ng: · 

002 

623 

1,. G U W Q ·M S X D L 

· TUEF4JZNL 

Hoboken 32,,N T 4 SJ 0 V V CK 7 3 RS OF E Y 2 HI O 7 VP B N . 5 U R G E 0 N 3 G E N E R A L 6 N 5 2 W A 5 5 5 3 H I 

002 

626 

GUWQMSXDL 

~ F 4 J Z N L Q 6 2 

Washington 13 

f

'l V C C S G U P W M U D Y 2 N R 0 2 G H P I B E 

DEPARTMENT3AIR3SERVICE3 

Comparison of these keys with those given on pages , shows 

that they are identical vitb the monophase keys1and will therefore 

apply to·any message enciphered by their means. 

1 I was unable to find, in my manuscript, where these monophase 

keys bad been reconstructed. Evidently some page or pages must 

be missing and ve will have to take it for granted that the 

statement made is correct.--W.F.F. ('48) 

-87-
. , 

I 

I c 

. . 

\ : ,,.. 

\. 

REF ID:A516913 

'· R'8uMI 

In the origill&l brochure the basic principles for the analysis 

ot this cipher were set forth. The analysis vas based upon a careful 

stud7 of the method of encipherment in vhich two key tapes differing in length by ,but one letter ver~ used. In this method sequent revolutions of the key tapes produce what ve have termad sequent cycles, the analysis ot any three o.f'vhich is sufficient for a complete solution to be achieved. It vas also shown, first, how the 

slightest carelessness in the operation of the machine would produce 

messages enciphered by means of the same single key letters, and 

second, bow such messages, termed overlaps, are particularly easy 

to solve. 

In Addendum. l it vas shown how the same principles of solution 

apply to the system when the tvo key tapes differ in length by more 

than one letter. The dangers or using two keys whose lengths possess a.factor in comm.on vere also demonstrated therein. 

In Addendum 2 the correctness of the principles set forth, and 

the truth of the statements and claims made vere demonstrated by the actual solution of the series of test messages submitted. The 

method of determining the lengths of the key tapes vas elucidated. 

The mathematical relations existing between various lengths of key 

tapes and the resultant cycles were demonstrated, and the untrustworthiness of the adopted method of allotment of the key tapes indicated. The various types of solution were given, and their 

feasibility discussed. It vas then shown hov solution was no longer dependent.upon the finding of tbree sequent cycles, a discovery which completed the demonstration ot the vulnerability of the 

system. ( 

William F. Friedman 

\ • 

-88-
REF ID:A516913 

ADDENDUM 3o 

(he ot the p-erequisites to the solution or this cipher being the knowledge ot tho ke7 indicators tor the varioUB mD8&agr:tBJJ there if88 submitted for 

Olr consider a'\; ion a met hod ot encoding and enoiph <ring the indicators. 

!bl result ot 1nvestigatioo shows that (1) the method as sul:mt tted does not, 

to m appreciable degree, aai to the satety of the :system; (2) the possession of 

thl code book is not essential. to solution. 

A list or enooded and enc~hered key indicators for 80 messages •1as dram 

up b.r one set ot operators and mbndtted to another. Within ten minutes after 

cert.ain tables had been made, the exact length of the t-w keys were det.ermined; 

an1 within three hours the key indicators in t.he form or numbers for any message 

could be read at will. This list follows: 

Jleaaage Iangth Indicators Message length Indicators 

l m IDB ...:.EJJ 4l .392 AGJ - CAG 

2 ~ JEE - AID 42 156 r:EC - :OO@i 

3 81 FGC - IEJ 43 721 FGI - GAD 

4 ~l PFF - CBC 44 890 JHI - IFC 

' 949 JCG - EEF 45 312 EAA - CFC 

6 152 OOH - IDE 46 260 DBE - HBJ 

7 275 JDJ - AJH 47 89 CHH - JAB 

8 SOl JDG - ABJ 48 l2l AAE - OOC 

9 'RO GEJ - DEF 49 363 FJA - HIC 

lD ll08 PHE - Jm 50 405 DJF - DEI 

u 47J CIG - EAR 51 560 AIA ~ BDD 

12 191 CIJ - EEJ 52 703 GGG - JJC 

13 312 JEI - CII S3 1009 DDJ - BHA 

l4 2!Tl FAP - CIB 54 004 AAJ = BDJ 

15 45i CIJ - GIH 55 462 BIA - GIA 

l6 902 CFF - OOJ 56 791 FIC - mt: 

17 79 JCE - l1JJ 57 920 GGJ - IGD 

18 2lD CDE - JFJ 58 201 GCI - CJG 

19 506 COO - BFC 59 52:! DCE - FDC 

3:> 7f¥'/ ICB - OOA (:D )!6 &1F - FFC 

21 :B> EJJ - DAJ 61 747 FCE - IIA 

22 170 <EB - DJE 62 920 CIH - GFA 

23 S42 DID - GHF 6.3 1780 JHB - JJJ 

24 108) CEI - GFA 64 )')9 DHA - HJH 

2S u,7 <EB - GHJ 65 187 HltH - GFC 

26 392 GJE - HDI 66 '' EFB - DHF 

Zl 468 ~ - IGI 67 209 AOO - BIG 

28 554 DHC - EGH 6S 867 FFl> - JBE 

29 93> FFC - !HF 69 729 EFI - GGJ 

~ 387 FBE - DBG 70 Y/2 CDC - EJF 

:n 542 HJH - GBB 7l Z'.l FDF - HAF 

32 659 CJB - DFF 72 183 FCD - CAG 

33 36.5 FDA - EBE 73 l49 JEE .;... BDB 

31. 1162 BBH - A!C 74 540 IM ~ JNJ 

'35 293 AED - GED 75 Z'/4 JED - AEA 

36 lSO BAA - EBE 76. 963 JEI = LAJ 

37 297 ACB -.JCF 77 582 JOO - BAE 

38 326 BEA - CDI 78 91 ~TJIH - GJC 

~ 8(;0 BJH - JIJ 79 355 HAG - ACE 

4D 47l GGI ... GEG 00 79 CFD =·JIA 

l 
REF ID:A516913 

Tia -'Md ot anaJ1'Z1ng the enaoded and emipherect in:licators was as follows: 

Thi 1J19tem at encoding am enciphering thD irnica tors is such that mv key 

indiaator 'Illich ia repeated will have the same final torm. For e:xamp1e1 suppose 

om 11•aage 'baa the ke)' indicators oSO * 2Bl. The plain code graip tor 050 ie GJJ. 

low1 ina•>ch as cmlJ' 3 enciphering alphabets are usecl1 cne ror each lett«E- of the 

. tJree oode let.ten 1 whatever be the cipher equivalents tor G

1 , ~ 1 and J3, both 

msaages 1l:lll show as the long key indicator the same combinatioos ot letters, 

tar ellBJllple. using the tables given in the code bo«*, me. 

What has been said as regards the long key indicators applies likewise to 

.th• shart keJ' indicators. 

Two sets of tables were therefore drawn up in the form or indexes or the 

let.t.er 1rld.1catore, one set apNing to the long key indicators,, the oth!r set. 

to the ahart. key indicators. 

*************** 

Rolf note that 1n a eerioa ot only 80 DDSsages there are several instances 

1n 'lflich the 1etter indicators are identical. aa regards both the long key and the 

abort IClfl7 indlxea •· For examp1e, the long k07 indicator ror messages 12 and 15 

IN 5dent1cal, CIJ. 

Row there is only one circumstance under which t~ messages in the 3BID9 

eeriea, that is 1 trom the same station, can have the ssne long or the same short. 

le7 ind.ieator, and that is when the nunber or letters intervening between the bfo 

massages is equal to or is an eact multiple of the length of the lo~ key or tb! 

short. ke;y respective:q. 

Reter to the series of test .uessagee subm1.tted and note tm key indicators 

fer Washingtcn 42 and t'lashingt.on S3o They are 020 * 100 and 020 * 261 respectiv~a 

Row the tat.al nmi>er of letters from the beginning ot Washingtcn 42 to the beginning of l'Uhington 53 is as fallows: 

t'IASHDCTON 42 - Z'l5 

43 - "514 

44 - 206 

45 - Yf 8 

46 - 421 

47 - 319 ~ - 359 

49 - 400 

j) ... 326 

S1. - 582 

52 -...m 

Tota1 - 3913 

2 
REF ID:A516913 

!low t_hllre are eleven messages 1\-om 'ah1ngton 42 to Waehingt.ai 53.. Since th!t 

e11p 1s condstentl.7 2. we must add 11 x 2 ar 22 letters to the total.. Thi.s gives 

""'as the grand total.. The f'actore or this nunber are 5 x 7870 The length or 

the long key is clearl7 m 0 The carrectness of this number can be corroborated 

tmm oeVeral nore instances. In the same manner, taking the distance between 

msssages 12 ond 15 in this series we have the following: 

Message 12 - 191 

13 - 312 

14 -1il 

Total - - "8X> 

How it is clear that the length of the long key is at least 800 letters.: We 

have ;yet to take into aoco'l.Ult the slip between mes sages. Ir t:e assmie the slip 

t.o be 11 then the length of the long key vwuld be 80J; if 2, it 1'«Juld be 806; if' 

'• li. 11C>Uld bo 8091 U' 41 it would be 812, etco Let us refer to another :repetition 

'ds·• ttat betwun n:essages 42 an:i 811 :indicator EE. The total number of letters 

intena'ling is aa Eolloms 

'Jl!1u1age 

42 ... 156 

43 - 721 

44 - 890 

4;- - 312 

46 - 2lll 

47 - 89 

48 - l2l 

49 - 363 

50 - 405 

.51 - 560 

52 - 703 

53 -1009 

54 - 004 

55 - 1.62. 

56 ... 791 

57 - 9itJ 

58 - 201 

59 - 529 

00 - 386 

Total no. or mes sar.e = 390 

61 - 747 7l - 222. 

62 - 920 72 - l8 3 

6) -1700 73 - 149 

64 - '$)9 74 - 540 

65 - 187 75 - 274 

66 - 99 76 - 963 

67 - aJ9 77 - 582 

68 - Bill 78 - -·11 

69 - 725 79 - 355 

70 - 372 80 - . 19 

Total - - - - 19332 

Since the long key is ot least 800 letters ~length• the number of 

re-t0lutions it has made between messages /~ and 81 is 2.4 (19332 - 800)" Trial or 

a slip or 1,,2.3,4 letters is then made o Ir the slip be 1, then we must add 39 x 1 

to 19332 and see if the total is exactly divisible by 8030 It the slip be 2, then 

we mmt add 39 :x 2. or 78 to 193.32 and see if the total is exactly divisible by 806, 

etco mien we try a slip er 4., and add 39 x 4 = 156 to 19332 \'le have 194880 A slip 

ot 4 'll)uld mean a ke3' of 812 letters and aa.lculation shom that 812 is the 24th 

Jllil.tiple ot 19'881 and indicates 24 conplete 1'6V(llutions between messages 42 and Slo 

-J- . 
REF ID:A516913 

• 

ThB length of the abort by wae aacertaincd b:y t1tactq the sane principles,, 

exaep' that tho amunt to ba ackled tor alip rae not knolWl. The length ot the short 

Jm;r 1B8 f'omd to be 693. Thus,, meesa.e;es 41 and 72 showed repetitions ot the short 

lllJ' hKIScatora, CAG. 'lbe calculations are as foll.oms: 

41 - 392 

42 -156 

43 - 72l 

44 - 890 

4S - .'.312 

46 - 2ilJ 

47 - 69 

48 - 121 

49 - 363 

SO - 4DS 

'l'ot al l1D. or mes sages 31. 

51 - 5(:0 61. - 747 

52 - 70.3 62 - 920 

53 -1009 63 -1 ?eJJ 

54 - 805 64 - 309 

55 - 462 65 - 187 

56 - 791 66 - r1J 

57 - 9~ 67 - 2J9 

58 - 201 68.- 867 

s 9 - 529 69 - 725 

f:/J - 386 10 - m 

7l ... 221 

Total - - 16SQb 

Slip---~ 

16632 7 24 = 69.3 : length or short. key. 

As tar ae the solution of the messages is concerned we need have nothing 

H' to do with the encoded and enciphered indicators, for \'ill!I can proceed to find 

the md:loatore tor tho series of messages,, assuming as the beginning points any 

pair gt 1nd1caton we please. bec8Uf1e solution is based upon the relative eositions 

ot ml!!• not tbe1£ absolute llWl!bo£ o For eDmple, tho cycle number of any two 

ololes 11181' be 72 and 75, OZ" 133 and 136, er 2 and 5: the distance between the 

two qclee is the same, vizo, 3. hloth~ way of pointing out the relativity of 

the calculations is this: the two ,key tapeo are contirwous eml.ess chs.iM. It 

is therefore ot no :Importance whether we call a given locus ai one of the tai;:ea 

001 ar 201,, so long as we a.re consistent throughout 1n designating the otmr locio 

'l'tN.s, the locus inrnediatel;r fallm'ling ocn. would be called 0020 If' we designate 

locus OCD. as 201, then the next me is 2021 at.co r!e lll\Y start. in therefore, to 

tird the relative key indicators for our series of messages b,. basing the calculat:.loms upon the indicators 001 * 101 for measage 1.. These calcula.tioo.s are 

as toll.awe: 

-4-
REF ID:A516913 

Solut;ion mq- now be achiem by fltaat:.l.y the same principles as those given 

1n t.he ~ broclmres. It ia apparent, theretore, &om a considarat.5Dn ot the 

J3"9oed11'1g paragraphs that the possession ot t.'ie code book ia not. easent1al to 

-aolutiC111. 

Ro111Y91'" 1 it we desire we can cletemine the S>solut.e kll7 indicators. The D1Bt.hod 

U eiaple and Se &8 foll.CMS I 

Fran the relatiw calculat1ona move, tables are made or the long key indicat.«'11 and the ahort key iniicators similar to those made at the beginning or the 

i:rob1-. .wit~ the letter indicators. This index 1B ae tall01at: 

* * * * * * * * 

We loak 1n the 89 tables tor an unbroken •quence ot indicators in which the 

mt.8"81.e bet.we aicesai.T• key im1cator numbers are smal.1o In tile index tor the 

ahort U, indicat.ora we haw a sequence 488 ... 491, 492 ••• 506, ap.PJ.71ng to messages 

91 J.S,,s.36. Let us est dom t.be short; k87 letter indicators for these mesa.gee, 

md their ftl.atiT• positions. Tl1J8 : 

llesaage 9 .o. DBI" - 488 

******* 

15 - GIH - 491 

SS - G!A - 492 

~ * ** ~* * * 

36 - EIE - SC6 

The on4' repetitions of lef;tera in the letter indicators ar~ the pair of 

l.ett.ere G, and I. This means that in the cod9 list of equivalents for indicator 

nunbera there are two sequent mmbers the r:l.rst two letters or Yb.ose code 

equbalents are the same. There are ~ such cases in the code book, so we 

must t'md some further points or oontact to enable us to pick out the correct pair. 

For e:xample, we find that tho sh<rt key indicator for message 11 is EAE:i value 58So 

Let us add this to t.he table. 'lhua: 

lies aage 9 - IU - 488 

******* l5 - GDI - 491 

5S - GIA - 492 

* * ** * * * 36 - ~-- 506 

***~*** ll - 14 - 588 -·-

-s-
REF ID:A516913 • 

• 

Tit have now tflo mare points or contact. The absolute equivalents of the 

relative J.Ositions .506 and 588 must. agroe in the .fii:e.t; and third letters, and they 

must be 82 intervals apirt;., since 588 - 506 = 82. 

Search 1a made throughout the code book to tlnd all the cases. Examine the 

tal.l.ow:l.ngs 

Bile. Code 

Xeeeage 9 IEF 

l5 GIH 

55 GtA 

36 iiiE ll~ 

Relative position 

a~; 

lM 

491 

492 

S06 

588 

Plain Code 

GFJ 

AGD AGB 

cDii 

Cm 

Absolute Position 

388 

391 

392 

406 

488 

The agreement is g:><>d. " B.r . rafering to otm r rmmbers as given by the index, 

·if t.he letters of the encoded and enciphered indicators fit in with the set alrea~ 

drawn up, we may assume that tte have struck the correct. absolut.e positions of the 

_1 1 2 2 in:l1aato~a. For cmample., if, accor~ to the move cp = Ee J F P = Ee ~ and 

~ • 1 thin 1n moeae.ge 51 sho:Jt. key indicator EEF = CJ:"J plain oode = 574 

abaalute position. The interval. between 488 and 574, absolute. lll.lst be the same 

ae that between the relativo equivalents. i,e fim that. L,88 absolute = SSS relative 

and that the abort key indicator for message 5 as calctil.ated relatively is 6740 

'1'ha proof iB complete. 

Chee a short. section like the above is determined, the rest follows very 

eaa~. 

-6-
REF ID:A516913 

• 

1b illustrate how ca:ietul the officer in charge must be, note the relative 

poelt!one of the k91 tape• at the end ot meaaags 2 1 viz., 648-623. His next 

IUllRIJI containa approximately 70 word811 he notes, and he tiguree that 350 letters 

•Ul be enciphered,. or, including f'llllctions, approx1mate4' 400 characters will be 

neceeea17 tor the mes saga. He then finds thnt t~ a<kiit.ion of 400 characters to 

the point where l'Ql9ssage 2 left oft will throw him "rut. ot bounds.rt Thus: 

648 - 623 (a) 

kOO - 400 (c) 

i0-48 - 1023 

-~00 iU -· · ~3 6~ Di!terenee equals - 5o 

In other words, tB ldll be enc:roachmg upm n region reserved tor Station 4. 

He rmat therefore shift. his key tapes back a lollt distance, and he moves them into 

the position 418 - 362, ar a difference or 56,, and then proceeds t,o encipher. ~ 

haa lad to do this several tines during the course of the day, and the greater the 

d1tterenaa m lengt.h bet.lleen tho key tapes,, the more often vd.11 such shifting tack 

be neaesearr. 

law note tJBt in t.hitJ sories ot all.)" 17 messages wo have five sequent oyclea. 

Using maaage 2 as a baee, because it shows the greatest <iif'terenae in the series 

ot S •naagoa 1n the soquont cycles, the &J:Tangement is as :fallows: 

Cycle l - Mossage 2 Key" Indicators 442 - 4171 Difterenoe 25 

Cycle 2 - Message 12 Key Indicators 260 - 236, Diffei"enos 24 

Cycle 3 - Jleseage 17 Key Indicators 22; 202, Dii'terence 23 

Cycle 4 - )(es98B9 4 Key In:licators OSO - 068,, Difference 22 

Cycle 5 - Message l Key J'ndicators 076 - 055, Difference 21 

These messages have been arranged graphically in F:ig. 19, and ere now 

ready to be attacked in the manner described before, using the beginnings am 

taki~ advantage or the fae?t. t.mt encipherment begins with name am addresso The 

tact that messages carry in plain text the pl.ace from which the message emenates, 

limits the llW?i>er of i;:ossibilities tor assumption or a signature, granting that 

the OJ'lelQ' baa a good intelligence system ard a close liaison exists between the 

o~ attice and tho intelligence bureau.. Unless all messages passing over the 

llm ar • enciphared, addresses and signatures in plain text in ordinary ma ssa.gss 

would torm a valuable body ot information for the basis of asaunptions of plain 

text. 

-7-
I REF ID:A516913 

• 

'Cbo9 a at.art is made to•rd deoililermri• the rest. 1'oll.CN1e quickly became the b)' indicatol"8 tar other meeaagea will enable the deci}i'lerer to shift. 

tha 1aQ11 al.Nady partial~ reconstl'llcted into at.bar positions aid ~ badlding up 

noUme of the kl!LY t..,ea t.he sectic:ms can b9 united in the proper DBnl'l9r and 

time the maplote kqa r-.u.t. P'cr e:aq>le. note the kBJr' irl:licators fer message 

3 •. TS.s •• 418 - 362. Qranting that l'2 have reconstructed the lo~er k91 from 418 to 

1161 1.50. and the shorter key from 362 to sa;r 395,, :in cne ot these five eycles1 it 

m onJ¥ necess8J7 to bring toget.ha- these series of longer and sharter Je7 

let.ten tran 418 to 450 on the one, and ft-om 362 to 395 m the other to produce 

the decipheuueut of the beginni~ ot messar,e 3. By contmuing such procedure~ 

the ent.Jre ke;rs my be pieced together and coq>letely reconstructed. 

It; shoul.d be noted that an excessive ditference in 1ength between the two 

k91 tapes 1B l~ to cause great difticulties,, tor the gt"eater this dittermce 

the aoaner does one station become "out of bounds,, n tor t.he range of the kB7 

~IP•• becomea mere limited as the diftorence between them increases. For example,, 

we haw given two tapes,. 700 and 600 letters, a difference ot 100 let.terse The 

diaplacement 1a therefore 100 letters per revolutioo of the longer tape. This 

means that att.s- only •ven revolutions of the longer tap one has rotumed to 

the starting point, and further enc:lpher.ment without resetting the tapes would mean 

an owrlap. Caapare this with the case whe~ the tapes d:if'ter by ooly one letter, 

tar example• tapes ot 700 and 699 letters., Here, only art.er the longer tape has 

made 700 revolutions does one get back to the starting point. In at.her words, one 

cm micipler 700 x 699 or 489, :J)C> letters before an overlap v.t1uld ~ producedo 

* * * * * 

It is clear, therefore, that the modified m~hod ot using the ma.chine affords 

no better protection against decipherment than tm orjginal met! od• and it is also 

i:atent that the principles tor the solution ot this cipher as first laid down 

according to our original understanding or the method or ushlg the machine apply 

with equal. val1dit7 to the modified method as subnittedo 

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It mq bo thought; that the occurrence of' sequent cycles can be avoided by 

at.rl~ supervision. Thero are some things to be said on that po:into 

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REF ID:A516913 

Supemaion could UD:loubted~ be exercised in each of the or rice a 

:1n'9'0l.Ted in a quad,. but it would ot necessity have to be supervision ot the 

met careful nature by of'1"1cers special:q quali£ied. Granting thi.81 there 

mlg!C be two methods ot eliminating tm possibility of the ocwrrence of seque& c;ral.ee. <be would be to have an absolutely raidom choice of ley indicagora (within t.he limits or the region aasigned ror the station) but with the 

restrict:k>n that no two messages are to ba in sequent cycles. The other method 

waald be to deVise soce system whereby 21 3 or more cycles are skipped regular:cy. 

hi -11 tratf1c. 

Ai"ttr considering these alternat.ives- we may say that the solution of 

caees in which one Ql" tao mterverdng cycles are miss~ can be achieved with 

no &Nat dif'!kulty. The solution or cases in which sq five intervening cycles 

are missing JIEt" be more ditticult to achieve, but the necessity of skipping arw 

ambm- of eyclea ab are !'ive in the caee of random choice or indicators• and sq 

ti•e replar~ 1n a systmatic choice of indicators is eo involved with practical 

ditftcult.iea that the entire s~tm l!Ould be mak. For, :1r at least five cycles 

mst int_."'18, ard it a station be allotted 200 eyal.es £or its dl\f 1S traf.f'io, 

then the greatest lllDi>er or cycl• actual]¥ available would be l/J, er in the 

case ot a longer tape ot 700 letters in length, a limit ot 28t000 letters would 

be imposed upon the &Gr's activity for that stationo In the case of a etat:Wn 

th& mat transact a large vol\11119 or tusines a every d;q this vould ne,,-er be suf'-

f'icient. snd the tapes 110uld rave t.o be inareased very greatly in length.. All or 

this is aside &om the da~er of a misunderstandir:g of the rules and of carelessness in operation. 

Purthermre, in the case or a single very long message, unless the message 

be brokml up into :im-ts,, the mcipherrrent of such a message is bound to extend 

into two ar IOOre sequent cycles. Of course, without a. knowledge or the lengths 

ot the tapes this would afford no clues to the decipherer. But the decipherer 

can tall apJrcacimatel.y the lengths of the ta.pee by stud\Y'ing the indicators for no 

.messages pass b91Qrd 695 for the longer tape and 690 for the shorter. he can 
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REF ID:A516913,.._~ "' .. ~ 

feel reuonabl.7 cert.a~ that the tapes are in the neGborhood of 700 lotters 

' in length. lt would take considerable experimentation to determine theh- exact 

length, but. li could be done within a iracticable length ot t.i.Jte by a COJ'll9 or 

deoipherera 1t t.he remlts to be expected .,uld warrant the expenditure ot the 

the and ld::Jcr. 

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A1191at 19, 1919. 

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