f 

\ ,. -1J 

;.·1· J•y '~ \ 

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1~·i· "f I', I 

IN REPL1f REFl'R TO 

\ REF ID:A414B~. '. -, ch'('"' 

~ I \ ~/ . ' I t 

WAR DEPARTMENT 

OFFICE OF THE CHIEF SIGNAL OFFICER 

______ DIVISION WASHINGTON 

September 12, 1921. 

MEMORANDUM for Major Bender: 

l. As requested by Colonel Russell, I have set forth in brief 

·my ideas, on the modifications proposed for.making the Printing Telegraph Cipher , safe for the use of the Army. ~ transmit them herewith • ... ~ ' .. " ~ . 

. =.r; · · · Two of the modifications involve but little ·change:.· in the 

present apparatuo. The-third requires the insertion of a fourthtranemitter 

and certain changes in trpes or. re~~s • 

.. 3. . 'These recommendations· as submitt.ed are the result of experimental tests and trials· made· with the machines as they are arranged at present. 

While I feel satisfied that t&e modifications proposed.are practicable, I think 

they should be thoroughly tested out on properly equipped machines be!ore they 

are adopted. 

Lo NI n· e· troy Retu.n to h \ 

N!'A-rr.'r 0 ... h 1yvhenno"o:-i;err.eeded 

cs - ~ l\ 2- ~·--ft- ~;;~~~- l~·= 

'\0.)~~~-.i 

Code Compilation' Section0 

Declassified and approved for release by NSA on 11-19-2014 pursuant to E .0. 1352a 
/ 

"''-"1-. - -

• REF ID:A4148. ~ 

1. The Printing Telegraph Cipher System, as developed 

by the .American Telegraph and Telepho~ Company is~ in a final analysis, 

a substitution cipher involving a series of 32 mixed, reciprocal alphabets 

Which are employed in a random ll'allller determined by a non-repeating, 

unintelligible running key. The running key is produced by the interaction of ·two unintelligible revolving keys of different lengths. The 

characters on these keys, which are in the form of tapes, are numbered, 

and the relative positions in which these two tapes \vere-placed at the 

begilllling of the encipherment of each message are given in the form of a 

pair of numbers called key indicators. ';mlese indicators appear in plain 

text in the preamble to each message, so that at the receiving end the operator may set his duplicate pair of key tapes in the proper positions for 

decipherment. The processes of encipherment and decipherment are entirely 

automatic, and of an electrical nature. 

2. Any attempts to render this cipher system insolu';~):ile, 

without an understanq.ing and comprehensive grasp of the principles by 

' 

means of which it was solved, would seem to be. useless. Furthermore, it 

is necessary to know all the details of the practical application of.the 

system in order tha.t any improveimnt s or modifications proposed nay be 

within the limi t,s of practicability. It is not within the scope of this 

' 

description to do more than summarize these principles. 

The first condition which is imposed by fl\i.lita.ry 

necessity is that all stations on one circuit mu.st use the same key tapes 

·each day. To do otherwise would cause confusion. This condition thus 

automatically eliminates all modifications proposing different pairs of 

keys f~r each station. 0 

4. The second condition which mu.st be realised iS. 

the im~ of' using a single, very long tape. The reasons for 

this opinion a.re given below under paragrap'.h 10 '• The principle of two 

revolving, relatively short ta:r;es is of sufficient worth to war~.nt 

Do NI rt e~froy Return to m--

NSJ.\ 7 er."'n riit L b · ry when noionger needed 

'TL Copy No. I 

~ 
• REF-21-D : A414 B 9. 

exhaustive study with a view to nx:>difying the system so as to render it 

5. j With these two conditions in mind, let us proceed 

first to review very briefly the principles of solut~on and then to con- 1 

sider various modifica~ions which may be employed. The solution of the 

·Printing Telegraph cipher, as demonstrated in a pa.per by the ~uthor written 

when at the Riverbank Laboratories, is ach~e~ed by the principles to be 

described briefly below. 

6. Determi~tion of the length of the two key tapes is q, 

the first step in the analysis. This is ma.de possible by the fact that the ' 

key indicators for each message are given in plain text at the beginnil1g ~--- - -· •• ~--~-·---- • ~~ .,.. - • #- ... - ....... -~-~~-""~-:..,c:.--..~ 

of each message. The determination is accomplished ~a mathematical 

analysis of the key indicators for the various nessages of the day's 

activity. ,The lengt~ of the two keys, according to the original method 

'\ 

as developed by the A. T. & T. co., differ by but one unit/ b lengthS 

• 

of the two keys, according to the modified method as adopted late:r by the 

Signal Corps, differ by more than one unit, and in no case are the· two lengths 

to possess a comnon factor, nor is one to be an exact :mu.ltiple of the other •. 

It was shown that regardless of which method was UBed, _ the lengths of the 

two key tapes could r.eadi ly be determined. It was proposed to prevent 

the determination of these key indicators by the enemy by enciphering and I 

enqoding them, and a method for this purpose was qevised by the M. I. D. 

This method was submitted and demonstrated to be of little advantage, for 

the key indicators could still be read by the enemy. 

7. The method of employing two revolving key tapes 

result~ in the p:roduction of distinct cyclic phenomena, which are not 

difficult of analysis by superimposition. The cetermination of the lengths 

of the two key tapes enables the cryptanalyst to allocate each rnessage'to a 

particular cycle. When the two key tapes differ by one and only one unit, 

these cycles are produced successively with consecutive revolutions of the 
0 

REF ID:A41489f)J 

-3-

tapes, Cyclesl, 2, 3, 4 •••t being produced in regular order. When the ~wo 

tapes differ by more "than one unit, the cyc1es are not produced successively:.:· 

with consecutive revolutions of the tapes; Cycle· l may be followed by Cycle 71, 

then by Cycle 141, and so on. 

a. Solution is dependent upon the correct superimposition 

and subsequent analysis of at least three cycle;~wo.ofwhich I have called the 

EXPERD/lENTAL CYCLES, the third, the CONFiillf.IATIVE CYCLJ!:. The closer together 

these cycles are, the easier is the analysia. The easiest case is when all 

three cycles are directly sequent; such as, for example, Cycles 10, 11, 12, or 

Cycles 41, 42, 43, etc. 

9. The method of analysis is to assume plain text at 

. definite locations in the experimental cycles, reconstruct the hypothetical 

key tapes, and if the plain text that has been assumed is correct not only as 

regards the actual wards assumed, but also the exact location at which they 

are assumed to occur, the application of the reconstructed keys will yield 

intelligible text in the confirma.tive cycle. Once a small portion of intelligible text has been.found in this way, reconstruction of the key tapes goes forward rapidly until With their complete reconstruction the cryptanalyst is in 

a position to decipher a:n.y message enciphered by them, by placing the two keys 

in correct juxtaposition accord}ng to the key indicators for the various messages. 

( 

10. 

so as to render it 

There are several n:ethods of modifying the system 

more safe, and several precautions, which a proper compreI 

( hension of the principles of solution indicates, that should be observed.· It 

has been proposed by Major Mauborgne to use only a single, long key tape·. This 

vvas, in fact, the very first ~thod experimentally adopted by the A.T. & T. ~ 

co., and soon discarded on account of its impractic~bilitY.---Tiie pre:i;aration of 

a single tape 999,999 units in length is a matter requiring much time, and labor. 

It would be equiva:lent to the making of a tape of :50,000 wards each day, and 

numbering the uni ts in groups of" tens, a long drawn out piece of labor in 

itself. Furthermore, at least three duplicates of this long tape are required, 
REF ID:A;41489fl 

-4- ~ 

~ .. ~-.;'; 

~ ,.., \~ ti'~ r ' A' ' .... 

"' :" '-'. ··:_,_ " ,,,.:.\ 'I '", ''•1'_,,; ' \• \ ... ' .... \ .. ~ 

\ t ~' 

if four stations are operative on the sane circuit and the l.a;.bor in preparing the necessary duplicates rould also be very great. The handling of 

such a long tape would entail the use of a reel to wind and unwind the tape, 

and the J:atter would wear and tear very easily. The equivalent. leng~h of 

tape may be obtained by two comparatively short endless tapes', one 999 

characters in length, the other 1000. The machines have been arranged for 

the latter method,. and it awears to 100 to be unwise to discard the kbor-saving 

fe.atures which the method of two revolving, endless key tapes providei?a It 

remains, thereforev to :modify the :present method and mechanism so as to render 

the use of two continuous key tapes safe for military use. The methods Which 

have suggested themselves to me will noW',be considered in detail • ..._ 

11. The modifications of method may be divided into 

two types or classes. One type has for its purpose the interrupt,ion or 

elimination of the cyclic phenomena-produced by the revolutions of th~ ke'y 

tapes. The other type does not attempt° to interfere with the cyclic :phenomena 

but makes the reconstruction of the two key tapes impossibl~, and thus renders 

the resultant cipher insoluble. 

12. It is possible to break up the cyclic phenomena in 

the system, by interposing an interruptor in the nature Of a character which automatically &tops and· starts one of the key tapes. This character mey- be any 

arbitrarily determined letter· in either one of the key tapes, or any arbitrarily 

determined letter which is the resultant of the interaction of two letters which 

are passing through the key tape transmitters simultaneously. This would 

effectually break up the regularity in the sequence of cycles, but it would 

introduce the grave danger of the :production of 0 overlapstt, i~e., the condition 

Wherein two or more rressages or parts of them have been enciphered by the same 

resultant single key and thus very easily solvable. This danger would be all 

the greater due to the fact that four stations are operating with the same pair 

of key tapes each day. Furtherrore, even granting that no overlaps would be 

produced, it would still not obviate the possibility of the correct superimpo-
sition of a '!ew cycles which rmy eventually lead to solution in the manner 

' 

described above. 

It is, however, possible to bring into play ~ 

interruptOr Of a different nature II which WOUld achieve the same pm:p0 Se but 

without the dangers mentioned in paragraph 12. This method involves the inse:r--

tion of a third, or auxiliary, key tape, and corresponding transmitter, the 

operation of which would be intermittent and determined by any arbitrarily determined resultant of the two p+incipal my tapes. The effect of this muld be 

quite far reaching. 

14. In the first place, it would add a third key to the 

cipher without entailing any addition,al time in the enci:p:h.erment or deci:p:h.erment. 

The only additional time that would be necessary would be that involved in the 

preparation of a third key tape of 200 to 900 units in length, which would 

miltiply the length of the resrilta.nt of the two principal key tapes by an equivalent number of times. But its main function is not that in particular, for 

theoretically, the insertion of a third key tape, or even more, would not 

complicate the solution very greatly because the solution is not at all dependent 

upon any analysis of the resultant aingle key but upon the analysis of superimposed cycles, which is a totally different process. 

15. The main fU.nction of the auxiliary key would be to 

break up the cyclic phenomena of the system by introducing a key which is 

intermittent and irregular. The resultant of the two principal tapes would 

still be ~yclic in nature, but the resultant of the application of th~ auxiliary tape to that of the two principal tapes would not be cyclic. No indication of the intermittency of" this auxiliary my would be given in the final , , 

cipher messages. 'l1he emmy cryptanalysts vould never know men they were dealing 

with two keys, and when with three. Each message would be a composite of the 

interaction of two keys' at one interval and of' three keys. at another interval'; . . 

the lengths of the intervals, and their exact moments of introduction and withdrawal would likewise be unknown, and externally indeterminate. 
REE,: ID:A41489fJ 

-o- -

, I 

16. FurtlB:nnore, the da.Dger of the produ.e.tion of 

"overlaps" is entirely eliminated because the two 'principal keys do not \ 

undergo any displacements other than those nornally :produced by their own 

cyclic movement·s. Hence, no two messages emanating from any of the :rour : 

' 

stations could possibly use the same resuUant s :ingle key, and thus no overlaps can be produced. 

17. The operation of the auxiliary key tape will now 

be described. Each day this operation will be determined by a different 

character, which will be arbitrarily selected by the central station. The 

character chosen will be the resultant of the interaction of any 'One'· of-32_ different 

pairs of characters passing through the two principal key tape transmitte~s 

at the same moment. Let us suppose this resultant to be the letter K on 

a given day, and let us set down~ few characters of two hypothetical 

principal keys, designated as the "A" and "B" tapes,. and also of the hY,Pothetical auxiliary key, designated as the "C" tape. We will then proceed to 

find the successive resultants of ~he interaction of the respective units . ' 

during one cycle, by referri~ to the cipher square,~ applying to the system (Fig. 1) 

Primary 

Resultants 

Secondary 

Resultants 

Fig. 2. 

I ";!. ~ 'I- s " "t 'O 9 IO II ,.., 1'?> 14 ,, '"' n IS 19 ~o 

RPQNVOXZKVTPFCHTQORS 

DNSOZWDIVTXBBLM40GLY 

AGLH@JHQZCF®~M40@20T 

V R_9 SP NT PXSQ 

AQLHZENLU2XKMM40B5AU 

The first four letters of the message would be enciphered by the resultants 

of the interaction of the two principal keys only. Now the fifth combination 

of key letters yields'the letter K, which determines the introdUction of the 

auxiliary key tape. Immediately, the auxiliary key is entered into the reaction, and it vvill continue to interact with the tvvo principal keys until the 

same ~ombinat ion, K, is again produced by the interaction of another pair o £ 
e REE'7-ID:A41489. 

-

units of the principal keys. In this case, the auxiliary key is in effect 

for seven letters of the mess8€e, viz; letters 5 to 11, imlusive. Immediately 

thereafter, the auxiliary key is withdrawu from the interaction, and only the 

two principal keys are operative. The number of times this process of in -

serting the auxiliary key and withdrawing it, and the lengths of the intervals 

each process is in effect, is determined only by the letters or the two principal 

keys, and this determination will be totally different for each cycle of the 

principal keys, since different pairs of letters are brought into interaction 

with each cycle. _Thus, for example, in Cycle 2, with the same principal keys 

as above, the introduction and withdrawal of the auxiliary key would be deter0 

mined at these points; 

A tape 

B tape 

Primary Resultants 

0 tape 

Secondary 

Resultants 

Fig. 3 

Cycle 2 

\134s&,~9~tt~B~~~~~~~ 

RPQNVOXZKVTPFCHTQORS 

. 

N S 0 Z W D I V T X B B L_M 4 0 G L Y R 

I w@x F Q 6 ®5 A 'D®5 L M 4 FI.ls@) ,, 

P VS QR EKWOVRQP 

IWBA4IZK5ADITV3PUXDK' 

18. Letters 1 and 2 would be enciphered by the. interaction of only the 

two principal keys. With the :pro'duction of the letter K as the resultant Of the 

interaction of letters Q and o, the auxiliary key is immediately introduced, to 

be operative for five letters. From the eighth to the eleventh letters, the 

auxiliary key is not in effect, from the twelfth to the nineteenth it is 

• again in effect. These intervals and lengths of introduction and withdrawal of 

the auxiliary key are entirely different from those produced by the first 

cycle, and would be different from those in any other cycle, for at no time 

is the same pair of characters of the two principal keys ·8€ain brought into 

interaction until the entire potential leigth of the resultant single key has 

been employed. 
REF_8,J:D : A414 B 911 

-

19. At the receiving end, the introduction and withdrawal of the · 

auxiliary tape v.ould be determined in exactly the same n:anner and by exactly 

the same l'esultants of the two principal keys as· at the sending end. The , <> 

process would be automatically reversed, and no srecial treatment of cipher 

messages or key tapes v.ould,be involved, since the machine automatically 

takes care of all steps in the process •. 

20. The wiring diagram for the changes necessary to insert the third 

key tape transmitter and to effect its operation in the manner.described (;, 

above is shown in Pl~te_: 1.., · ·Clo ~ NWUL<l.) 

21. We shall now consider a pr-oposed modification in which the purpose is not to interfere in any way with the cyclic phenomena of the two 

principal key tapes but to make the reconstruction of the keys exceedingly 

difficult, if not impossible. 

22. It is feasible to provide a means of auton:atically stopping the 

plain text tape at a given point, but allowing the two key tapes and the 

machine perforator to continue uninterruptedly until the plain text ta;pe is 

again started. This stopping and starting of the plain text tape can be 

done by hand at random and absolutely irregularlyo No~inl.ication of the 

interruption will show in the c~pher m3ssage, and no correction or automatically operated interruptor is necessary at the receiving endo This is a 

most renarkable phenomenon in'cr;y:ptographic methods, and is the only case 

known to me mere an irregularly o;perati ve interruptor does not have to be 

counteracted at the recei villfj end by an identical reversal of the operations 

at the sending end. This modification would not eliminate the cyclic phenomena produced by the revolutions of the 'key tapes~ but would render the 

analysis of su;perimposed cycles more difficult because of considerations requiring too detailed an explanation t'o set forth in this brief. , In a few 

words, it would increase the difficulty of reconstructing the two key tapes 
REF _91D: A41489ji ...... 

from any assumptions of plain text in the experimental cycles, and the 

application of the thus reconstructed portions to the confirnative cycle. 

23. This method may be used for the interior of messages, but 

it is intended primarily to dis.guise the beginnings and ends of the 

messages. The reason for this differentiation in treatment is the fact 

tbat the beginnings and endings of these'messages are particularly susceptible to attack because they contain addresses and signatures which 

are always the easiest points of attack by.the cryp~analyst. Especially 

is this the case here because the n:essages are confined to communications 

. between large' headquarters where such relatively long addresses as 

"Q;tla.rtermaster General", "Chief of Ordnance", "Surgeon General", etc., 

are very common. In fact, the solution of tlie test case submitted by 

the Signal Corps was based upon the assumptions of these very addresses, 

and it turned out that the assumption of "Quartermaster General" in one 

of the exrerimental cycles and "Chief Signal Officer" in the other 

imnediately yielded intelligible text in the confirnntive cycle. If,now, 

a random, irregular interrtlption of the plain text tape oc~urs at the 

beginning and endings of messages, the enemy cannot proceed to assume entire addresses or names, for they will be interru.pted irregularly in 

somewhat this fashion: 

Q-- UAR---- T E -.- R - - - l\II. AS~ - - - - E R 

. 24. Here the dashes represent blanks which are inserted in an 

irregular manner between the letters of the plain text. The enemy rray know • < 

tbat such interruptions occur, but their location and length would be unknown. Their exact location would be unknown even to the encipherer and 

the d~cipherer, because it is done in an absolutely random n:anner during 

the enciphering process by the operator himself,• 

25. What actually happens during these interru.ptions is that the 

ma.chine perforator is punching the resultants of those pairs of characters 
REF ID:A41489fA 

-10- -,....,. 

on the key ~apes which are interacting during the 

resultants will not be differentiated in any rra.nner \\ihatsoeve~, externally, 

from those cipher letters v.hich are the resultants of the interacti.on of 

all three tapes, viz., the twci key tapes and the plain text tap~. In the 

deciphering process, when a portion of cipher tape Which is the reSll.lt 

of the interaction of onl¥ the two keys is passing through the transmitter, 

the cipher ~etters are exactly neutralized by the same resultants of the ' l 

key tapes as were involved in the enciphermento The result is that the 

printer merely stops ·printing for a corresponding number of units, until 

. , 

such a time as the cipher letters which were the resultants of all three 

~apes are going through the transmittero Then the printer immediately 

continues printing. 

26. As stated before, this irethod rray also be applied to the 

interior of ressages 11 but its employment for a considerable portion of the 

messages would soon exhaust tbe potential length of the resultant single 

key, so 'that a station w:>uld be goil:g beyond the limits set by the allotment 

before it bad enciphered all its nBssages, unless considerably longer 

key tapes are employed. This would be a disadvantage,for~nornally,key 

tapes not exceeding 999 units in length.are sufficient for the traffic of 

four. stations. 

27. It nay be well to give a diagramnat ic representation of the 

results of this method as· applied to the beginning of a message. Let the 

message be addressed as follows: 

(Note: The meaning of the figures are these: 

2 - Line Feed 

3 - Space 

4 - Carriage Return 

5 - Letters 

6 - Figures ) 

28. The encipherment nay-be in this manner: 
• REF ID: A41.4B9ii 

-11- ...... 

Fig. 4o 

A tape-0 V N K T P R X S T A P Q W V N C T P 0 I N V Q K -'13 D N C Q R I V L T M O X p 

B tape-B Q v c R I 1 A M x z p 1 K T p ·o p v N c D p 0 L y c I Q R N T p A B L M s Q 

. . . ( 

Plain- Q U A - - - - R T E R M - - - - A S T E - - - R 3 G E - - N E - - R A L 6 N 5 

text - -

Cipher-P C Z E G T 0 H D N 0 M S M C G Y A 0 Y 4 S 4 S B P I R B Q U p 4 6 R M 5 H V 

29. If now the enemy should try .to assume a plain text beginning 

for this message9_even if he did assume the correct address 9 he would not know 

how the letters are interrupted 9 and unless he knows this too, his attempts' to 

reconstruct the keys will be of no availo 

30. This modification may be applied in conjunction with that 

involving the third or auxiliary key tape, the two being independent of each 

othero If the plain text tape is stopped while the auxiliary transmitter is 

in operation, the cipher letters will merely be 'the resultants of the three 

key tapes 9 instead of only· two 9 as would otherwise be the case. 

310 The actual m:lthod of stopping and starting the plain text 

transmitter is most simple 9 and requires absolutely no changes in ~pparatus. 

It consists merely in throwing the start-stop lever ~rm of this transmitter 

to the right or left; to the right when the transmitter ;s to be stopped; to 

the left, when it is to be started. -r--

32. There is one more modification which is well worth consideringo 

As developed by the Ao T. & To Co.~ the printing telegraph cipher system emp~oys a cipher square or quadricula.r table involving 32 mixed, reciprocal 

alphabets which are constant in nature 9 and are not intended to be changedo 

The electrical circuit is so designed that when homologous selecting pins in 

e the two key tape transmitters- are kept down by the tapes, or when both pins 

are all~Ned to come through the tapes, no impulse is sent through the winding of 

the co?Tesponding relay, because no ciryuit bas been establishede Howeverg 

when a pin in one key tape transmitter is kept down and its homologous pin in 

the other key tape transmitter is allowed to come through the tape, a circuit 
I~ 

RE~, !_D : A414 B·9fii - .. ...,--- ~ 

is at once establisl:ed through the winding of the reley involved, and the 

relay operateso This arrangement is the same with respect to all five of 

the key tape transmitter relays, and an understan:ling of the phenomenon . . . 

leads to a comprehension of the n::anner in v.hich the encipherinE?; prooess is 

(fi~1) 

accomplished and the nature of the cipher square~ For example, when the 

letters B and G interact 17 we have the letter A as the resultant 

1 'a. 3 't S" 

A tape ti'ansmitter I• • •• ~ 

+ + -+-

I + ++ B tape transmitter • . • • CZ. 

t i i ~ i resultant • I•• • ] A 

t- + - - -

33. Here the first selecting pin of the A tape transmitter is 

ma.king contaQt to + battery, and the homologous pin of the B tape transmitter 

is making contact to - battery, thus resulting in establishing a circuit 

through the winding of rela;y l, and operating the relay. The same is true 

with respect to the second pair of homologous selecting pins, with reverwed 

signs in effect, and relay 2 is operated. In the case of the third pair of 

selecting pins, 'both pins are making c?ntact to - battery, so that no circuit 

is established; in the cases of the fourth and fifth pairs, all pins are majcing 

contacts to + battery, and no circuit is established. Hence relays 3, 4, and 

5 rema.in inoperative, only relays l and 2 being operated, and the printer 

will print the letter A, or if the machine perforator is operating, only magnets 

land 2 will be operated so that hoies'1 and 2 are punched in the tape. 

34. Now if we change the wiring of the key tape transmitters, 

we may effectually break up the relations established by the present connections. C.O"rn ~m~"t1ol\ ~ oi 

There are 120 different connections possible between the five selecting con- ~ ' 

tact terminals of one key tape transmitter and the five ·.homologous terminals 

of the pther transmitter. Terminal 1 oi' the A tape tr?-nsmi tter rray be 

/ 

connected with terminal 1, 2, 3, 4 or 5 of the B tape transmitter. The same 

holds true with respect to the other four terminals of the A tape transmitter., 

The number of possible combinations of connections vmich can be made is 
A 

:B 

REF ... ~p_:A4148.5 

- 5· x 4 x 3 x 2 = 120 combinations. 

35. For exaIIY?le, let us connect terminal l of tbe A tape transmitter with terminal 2 of the B tape transmitter; and terminal 2 of the A 

transmitter with terminal ill of the B transmitter. The difference in the 

circuit~ is shown in Figure 5. 

Fig. 5 

, ____ _. 

z~-------1 

3~----------' ~-------------__. 

s~---------------....1 

I 

~ 

.3 

s: 

I 

a. 

3 

., 

3& •. Now let us see wn.a.t the resultant 

l 2 3 4 5 

+ - - + + ~ l ~ .l- - + - + + 

B 

G 

J J l l l 

.- -

• 

Normal 

Circuit 

Modified 

Circuit 

of.letters Band Gare: 

37. It is seen that the resultant should be a, blank. This is, 

indeed, What the actual resultant is 9 when the indicated change is made in 

the connections. The resultant of sev~ral other pairs of letters are given 

herewith to illustrate the nature of the changes from the normal. 
Normal 

R 

z + -.+ ~ i l i ~ 

6 + + + + 

H + + 

i i .i ~ i 

N + + - i ~ i i t 

0 + + 

F + ~ + 

l i i i i 

J + + + 

t i t ! l 

I + + 

REF ID:A414Bifp 

- -14-

Fig. 6 

MOdified 

R - + + ,x ~ ~. Jt . 

z -+ + ~ t i ~ ~ 

o-- + + 

H- + + x ~ l i 

N-- ~ ++ 

l i i t i 

0 - ++ 

F+- + + . xi t ~ J + + - + ~ "" ~ i i 

s + + 

38. With another change in connections, an entirely different 

series of resultants will be produced. This would man an entirely different 

cipher square for each possible set-' of connections. Since there are 120 

different combinations possible, the number of different cipher squares would 

be 120, and the number, of alphabets involved in the system would no long-er be 

only 32, but 120 x 32, or 3,aa;o. 

39. The result of the foregoing them. is: the reconstruction of key 

tapes from assumptions of plain text in the ex.periIIBntal cycles would be 

rendered highly imp~obable, if not absolutely impossible. It is difficult 

enoUgh now, with only one cipher square inv,olved; but with 120 different 

possible squares, the exact one which is being used on a given day is unknown 

.to the ene~ and ma:.nifests itself in absolutely no way in the cipher messages, 

the problem of solution may be considered to be practicably impossible • . 40. For practical purposes, the establishing of a given combination 

could be facilitated by a panel of the nature shown in Figure 7. , 
A 

B 

e 

REF ID:A41489ji 

.. 

-15-

Fig. 7 

I ~--..----.--.--.--.-.---.--.--.--.--.~--.--.--.--.._..__,__,__,__,...,.. 

~~--. ....... ~~~--.--+-.....---.--.--.---<1--r-~--.--.--.-+-i....-----.--.--.--1~ 

3~--.1-+-.---.~~---t--.--.--.~---11-+ ......... --.--.--.-f--ii----.__,__,--t-+-

~__,__,t-+-f-~--.--.--+--+-+-,.-~--.---<1-+-+--i.--~--.~,_._....-__,__,--f--I-+..... 

5~--.r;--t--t--;r---.-t--t--1-+--r-__,__,t-+-t-t--r--.__,-+-l-+-+-t--.--.--1--+-+-f-... 

,. __ _ ~___,__,__,___,___,__,__,__,~ 

3~__,__,__,__,__,__,__,__,__,~__,__,---' 

4~__,__,__,__,__,__,__,__,__,__,__,__,__,__,__,__,__,__,~ 

5~--.--.--.__,__,__,__,__,__,__,.....___,__,__,__,__,__,__,__,__,__,__,__,--I 

'4.1. Here the combination is 4 - l - 5 - 3 - 2; 

i.e., the winding of relS¥ l is comiected to selecting pin 

contacts 4 of the A transmitter and 1 of the B transmitter; the 

, 

winding of rel~ 2 is co:miected to selecting pin contacts l of 

the A transmitter and 2 of the B transmitter; that of relay 3, 

to.Sand 3, resy;iective:cy, etc. 

42. Let us see what the resultants of the letters 

R and z, H and N, F and J will now be. 

Fig. 8. 

R -+-+-

Z .it.~ +~+ 4 4 7 .' - - --- .... 

(blank) 

H -~+ 

- - f + - t ;1; 4 t 7 

l blank) 

J 

7 

(blank) 
REF ID:A41489ji ~ 

~16-

43. It is 'seen that blanks resu.lt from e8:ch of these 

pairs of interacting letters. Other pairs ·would give different:. 

resultants. 

44. The changing of the connections between the key 

tape transmitters would have no effect upon the normal operation 

of the nnehina so far as the transmission and reception of plain 

text is concerned. 

45. It is submitted that the insertion of 

the third or auxiliary key tape transmi-tter, the· changing of the 

connections between the two principal key tape transmitters and the 

use of the interruptor as described in paragra:phs 22 to 31 will 

make the printiDg telegraph cipher ;insoluble, without impairing its 

~ 

practicability in the slightest degree. 

46. The subsequent pa.gas of this pa~r will deal with 

\ 

a phase' of the norn:al nathod of encipherment which entails precautions 

not observed heretofore, and which should be observed in the fllture. 

It deals with the method of allotting definite sections of the key 

tapes to the four stations on a single circuit. 

47. The purpose of allott :Lng definite sections 

· of the key tapes to the four stations is to preclude the possibility 

of two stations employing identical portions of the theoretical 

resultant single key. If this condition is not prevented, 

overlaps will be .. produced, i.e., two or more messages, or 
REF ID:A41489jf 

.., 

-1.7-

''\ 

parts of them, will be ~nciphered by the same resultant single key, and the 

messages are rendered very easily solvable. 

46~ The me~~od heretofore has been to divide up the length of 

the longer key into four equal or nearly equal parts, and assign each station 

a given pair of ini~ia:l i~dicators for its messages. For example, let 

us suppose that two key lengths 800 and 763 are chosen. Each station . would then be assigned 800 f 4 • 200 units of the long key; the initial 

) 

shor~ key indicators for all four stations would be the same, for example, 

001. The initial key indicators for the four stations would be assigned 

as follows': 

Station A Station B Station C Station D 

001 - 001 201 - 001 401 - 001 601 - 001 

49·., In this casfi), no overlaps could be produced, providing the 

traffic for no station exceeded its allotted number of resultant single 

( 800) , ( 7 63 ) 

key units, .in this specific instanc~ 4 , or 152,600 units• 

The reason for this is that the length of the longer key is exactly divisible 

~Y 4, and hence the allotment can be made in four exactly equal sections. 

~owever, vihen the length of the longer key is not an exact nmltiple of 4, ', 

the case is slightly different. It has been assumed, heretofore, that if 

the nearest fourth part of the length "oe allotted to each station, no 

overlaps can be produced. For example, in the test case which was submitted and solved, the lengths of the two keys were 767 and 639 units 

respectively. The initial indicators for the four stations were these: 

Washington Hoboken Norfolk New York 

126-001 322 - 001 518 ... 001 714·- 001 

:50.. . ·These initial indicators were derived by adding the nearest 

integral fourth.part of 787 to the initial long_key indicator for 

Washington. Thus: 

787 t 4 = 196 f 
REF ID:A414B~ 

-18- .,.,. 

•" \ (Initial . Washington 126 long·key indicator) 

196 • Hoboken 322 { tt tt It " ., 

196 

Norf'olk - 518 ( " II ti n 

196 

New,York - 714 { tt ft " It } 

51. It will now be demonstrated that this method is not ma.th-

( 

ematically strictly correct and that if' followed consistently will lead 

to the production of overlaJ?S• Let us suppose that these two key lengths 

have been selected: 917 and 723. These ~wo lengths are strictly legitiIIBte, 

since they do not possess a common f'actor, nor is one an exact multiple 

of the other, two conditions which must,be :rreto 'The nearest integral fourth 

part o~ 917 is 229. Assuming that the initial key indicators for Station 

A would be arbitrarily selected as 125 - 001, the indicators for the fOur 

stations would be as follows: 

Station.A Station B Station C Station D 

125 - 001 354 - 001 583 - 001 812 - 001 

:5'2~ Let us now determine what the indicators for Station A are 

after exactly 9399 letters have been enciphered. 

Initial indicators' 

Length of messages 

Station A 

- 125 - 001 

:9399 9399 

9524 - 9400 

~3, From these two totals we should now deduct the greatest exact 

multiples of the respective key lengths such as will leave positive remainders. Hence: 

9524 :.. 9400 

Deduct (917 x 10) 9170 - 9399 Deduct (723 x 13) . . 354 - 001 

.5·1=., The longer key wi 11 have c om:ple ted 10 w}l.ole revolutions, the 

shorteT one 9 130 Immediately th~reafte~, i¢ will be noted that the indicators become 354 - 0019 which coincide exactly with the initial indicator~ 

) . ..., 

• for Station Bo In other words, after 9399 letters have 
REF_,IP :A41489jri 

-.., ., 

Station A~ all subsequent traffic of Station A would be enciphered in the 

same resultant single ke~ as the traffic of Station B. 

·55. The same phenomenon is true of the traffic of Station B with 

respect to that of Station c, an? that of Station c with·resrect to that 

of Station D. 

Station B Station C Station D 

354 - 001 583 - 001 812 - 001 

9399 -9399 /9399 - 9399/ . 9753 -9400 9982 - 9400 

9170 -9399 9170 - 9399 

583·- 001 8~2 - 001 

56~. Furthermore, it is obvious that after Station A has enciphered 9399 x 3 ;; 26.197 letters,· Station B 9399 x 2 ; 16798 letters 0 ai1d 

Station q 9399 letters, the traffic of all four stations ~s enciphered by 

the same resultant single key, or in other wordsp a four-fold overlap 

would result. 

5~. The conclusion is obvious, therefore, that this method of 

allotment is not correct, and :must be modifiedo 

58~ There are two methods of allotment which are accurate, and 

can therefore never involve the danger of ov~rlaps. One is to base 

the allotment upon a correct distribution of complete cycles; the otber is 

to base it upon an exact division of the theoretical resultant single 

key. 

59. The former method is explained in det'ail in an unpublished 

paper by the author, entitled "The Mechanics of Di~ferential Prinary Keys"o 

The explanation is too long to be incorporated in this pa.pert bu.t in brief 

it nay be said tbB.t it deDends upon the solutron of two indeterminat~ or 

Diophantine equations in which the lengths of the two keys and their relative 

•. I 

displacements in consecutive revolutions play the major parto This method 

is possibly too complicated for practical purposes, and we shall proceed 

to explain the second method, which is considerably easier to apply. The 

steps are as follows: 
REF ID:A41489jip 

-20,- '19' 

·60. First, determine the length of the theoretical resultant 

single key. Let us take the two lengths given above 9 vizo, 917 and 723. 

917 x 723 = 6629991 units 

Second, divide this length by 4 

622,991 '°' 4 :;., 165;747~ 

. .$.~ This quotient represents the single key allotioont length for 

each station; .or, in other words, each of four stations rns,y encipher 

165,747 letters without causing, a:ny overlap with the traffic of the other 

stations. 

62~~ Third, add this length to the initial key indicators for 

Station A, and deduct the greatest.exact mu.ltiples of the two key lengths 

such as will leave positive remainderso Let the initial indicators for 

Station A be the same as before: 

Station A 

r-----, • 125 - 00~ 

165747 •165747 

165872 -165748 Deduc~ (917 x 180) 165060 -165567 

Key indicatars"'fort 

Deduct ( 723 x 229} 

Station B f 812 - 181 

\ 63'., The initial key indicators for Station C are derived in exactly the same nanner from those of·Station B; and those for Station D 

from those of Station c. They are all as follows: 

Station A & Station B Station C Station D 

125 - 001 /] 812 181 582 361 352 541. 

165747 165747 65747 165747 165747 165747 165147 -165747 

165872 165748 66559 165928 166329 166108 166099 166288 

165060 165567 65060 165567 165060 165567 165060 165567 

812 - 181' 1499 361 1269 541 1039 721 

·917 917 917 

582 - 361 352 - 541 122 - 721 

:6~ It will be noted that the final pg.ir of indicato.rs for 

Station D are 122 - 7210 If now'we add 3 units (which are represented by 
/ 

REF ID:A4148~ ...,. -21""! 

the! of a unit dropped by each station due to the f'act that the resultant 

single key is not exactly divisible by 4), we have this 

122 - 721 

3 3 

125 - 724 

65. Now unit 724 of the short key is really the same as unit 

001, since it is 723 units in length. Hence we have 125 - 001, which are J 

the initial key indicators for Station A, pro~ that the allotment 

lengths and key indicators for the four stations are correct. 

66. The practice has heretofore been to slip the two key tapes 

forward two units at th~ end of messages. The purpose Of this has apparently 

been to try to increase the difficu~ty of determining the lengths of the 

two keys by the enemy. This, however, fails til its purpose, unless the 

slip be different for each mess~ge, ranging from 1 to 25 units., However, 

great care must be observed that both keys are slipped e:x.actly the same 

amounts in every case, otherwise the production of overlaps will result. 

In fact, the danger is so great, and the advantages to be gained by 

slipping the tapes so slight, that it is recommended the practice be 

discontinued in the f'llture. 

• .{$ 

' .