(classification} 

Exempt from GDS, E. 0. 11652 (category '"Z--- ~ A. 

Declass date if determinable:=====-----

Preliminary Remarks 

an Invest ion(?) 

Isomorphs in 

R. Fisher I Declassification Officer "?-.~] v~ 1'< 

Initial: £~r((1;(; The0a@xperi enced cryptanalyst very frequently has occasion 

to use the rtprobable word method", that is, he assumes the presence 

of a word in the text and tries to find it by one means or another. 

The word for which he is searching usualiy contains several repeated letters the identities and positions of which impart to the 

word a characteristic or peculiar "pattern" or "formula". Such 

words are termed idiomorphic. For example, the words BATTALION, 

DIVISION, and ARTILLERY are idiomorphic, and each has a distinctive 

formula of composition. The formula for the word BATTALION is 

representable by a sequence of arbitrarily-assigned digits standing for the different and the similar letters, as shown herewith: 

BATTALION 

l 2 3 3 2 4 5 6 7 

In other words, the idiomorph is "coded" in the sense commonly 

spoken of in connection with the use of tabulating machinery 

operations. 

2. Suppose the cryptanalyst suspects the presence of the,......_~-a 

word BATTALION in a message. Having established the formula fo 

the word, he goes through the text, beginning with the first 

letter and sliding the formula against the text one step at a Cf\ ·~ 

time, until he finds a place where the formula for a sequence \ > 

of nine letters in the text is matched by or coincides with the~\ 

formula 1 2 3 3 2. 4 5 6 7 t- BATTALION). In this process the 1 ,._,,. 

cryptanalyst must either indicate on paper, or see with his ()\ .~ mind's eye, the textual formula that is at the moment in ju.Xta- oc-. 

position with the formula of the word for which he is searchin ~ 

·3. .Again, the cryptanalyst may not have· a definite word 

in mind for wbich he is searching, but is simply desirous of 

locating two formulae which arte identicahl andtwhb

1

icihhare techni- JS. 0 , 

cally called isomorphs. In his case, e es a s es a con- fl ., tinuously changing series of formulae, beginning with the first ~ I~~ letter of the text, and tests each of them against the remainin 2 : 

text of the same message or against the text of another message ~ i 

For example, he may start with the first ten letters of the 

message and note the formula for these ten letters. He then ' 

applies this first formula to another part of the text, beginn~·~......,....,~ 

at a given point and sliding the formbla against this text one 

step at a time to see if he finds another sequence with an 

identical formula. If not, he starts with the second letter 

of the message notes the formula for a sequenoe of ten letters, 

and repeats th~ search. When he encounters a formula which 

coincides with the one ·he has set up, he has found a case of 

isomorphism. The two isomorphs may or may not correspond to 

the same plain-text word. For example, the three wor~s, WARRANT, 

LETTERS, and. MISSION have identical formulae and. are isomorphic. 

Declassified and approved for release by NSA on 10-20-2014 pursuantto E.O. 1352a 

I'-/ ~ I q s7 . -

1- c &' s. ~ .-.:/,,.~ :'l11-m -~ Cr) ~ 
REF ID:A4146524 

In searching for isomorphs, if the cipher text should contain all 

three of these words enciphered monoalphabetioally, the cryptanalyst would not know whether the isomorphs he finds in the message represent three occurrences of the same word, or two occurrences of one 

word plus a different word with the same formula, or a single occurrence of three different words. These alternatives would be 

determined later, by further analysis. At the moment, the important 

fact is that he has located cases of isomorphism. 

4. The present "hand" methods of locating idiomorphs and 

isomorphs are very tedious, slow, and subject to hwnan error. 

Automatic machines for locating them would be quite useful. and 

it is the purpose of this invention to provide such machines and 

to describe the method of their use. Basically, the invention 

employs the comparison circuits used in the "coincidence coUn.ter" 

described in another paper, in combination with additional mechanism to be described. 

5. The text in which idiomorphic or isomorphic sequences are 

to be ·located is prepared in the form of perforated Baudot tapes. 

Several copies of the text tapes are prepared, the number depending 

upon the length of the sequences for which a given machine is con~ 

structed. Machines for locating 6, 7, 8, ••• letter sequences may 

be constructed. This description will deal ·with machines for 

locating sequences up to the length of ten letters. In general. the automatic locator goes through exactly the same steps as does 

the human operator at present. but at a much greater speed, and 

without overlooking possible places where sought-for sequences may 

exist. 

B. The idiomorph locator. 

6. First to be described will be the idiomorph locator. Let 

us assume that we are searching for the word BATTALIONS, the ·presence of which is suspected in the following text: 

APDMNG~AAFVQZ;RIQVVWZMAZXQOPA 

7. The machine consists primarily of 10 Baudot tape transmitters, each being wired for comparison purposes, in a manner 

similar to that employed in the "coincidence counter". In this 

case, 10 tape copies of the message are prepared and.these tapes 

are placed in the transmitters so that the successive starting 

points on the successive transmitters correspond to the successive letters A, P, D, M, ••• of the message. . . . 8. Closing a starting switch, the first letter of the message, 

A in·transmitter l is tested successively against the next 9 let- t~rs of the message, in transmitters 2, 3, 4, 5, 6, 7, 8, 9 and 10. 

This is done by means of a motor-driven rotary multiple switch, ~r · other means which successively connects the whole set of comparison 

contacts of'transmitter 1 with those of transmitters 2 to 10.in turn. 

-2-
REF.ID:A4146524 

.. 

The comparison circuits in this case merely serve to operate supervisory high-speed telephone relays to drive a series of 

10 rotatable indicator wheels, the peripheries of whioh are . divided up into 10 equal segments, numbered from 1 to 10. (This 

corresponds to the "coding" function referred to in Par. ·l.) At 

the start all indicator wheels are at their reset or initial 

position, with segment 1 showing through a window or aligned at 

a bench mark. Indicator wheel number 1 is always set to position 

1 and need not change; it may in fact be a "dummy" wheel. If no 

ooincidence is encountered when transmitter 1 is compared with 

transmitter 2, indicator wheel 2 advances to segment 2; likewise, 

when transmitter 1 is co~pared with transmitters 3,4,5, ••• and 

no coincidence is encountered in ·any case, indicator wheels 3,4, 

5, ••• advance to segment 2. But if a coincidence is encountered 

at any comparison, the indicator wheel associated with the transmitter being compared at that moment is not permitted to advance 

any further and remains in this position. The arrangement for 

this stepping may be by means of a continuously acting ratchet 

and pawl for each wheel and only when there is coincidence is 

the pawl withdrawn and locked into inactive position. For example, 

take the first 10 letters of the illustrative message: 

1 2 3 4 5 6 7 8 9 10 

A P D M M G F A. A F 

After transmitter 1 (set to A) has been tested against the rest of 

the transmitters, the indicator wheels are at the following posit~ons: 

Indicator wheel - 1 2 3 4 5 6 7 8 9 10 

Text - A P D M M G F A A. F 

Setting of wheel - 1 2 2 2 2 2 2 1 1 2 

This corresponds with the repeated letter A in positions 1, 8, and 9 

in the sequence A P D M M G F A A F·. Indicator wheels 8 and 9 will 

now stay at position 1. 

Transmitter 2 is now tested against the remaining transmitters, 

in turn. Since the letter P does not reappear in the sequence, the 

indicator wheels 3, 4, 5, 6, 7 and 10 advance one step. The formula 

is then: 

Indicator wheel - 1 2 3 4 5 6 7 8 9 10 

Text - A P D M M G F A A F 

Setting of wheel - 1 2 3 3 3 3 3 1 1 3 

Transmitter 3 is now tested against the remaining transmitters, 

in turn. Since the letter D does not recur, the indicator wheels 

4, 5, 6; 7, and 10 advance one step. The successive formulae set 

up on the indicator wheels as the successive transmitters are 

tested in turn against the remaining ones are as follows: 

-3-
REF ID:A4146524 

Indicator wheel 1 2 3 4 5 6 7 8 9 10 

Text APDMMG F A A. F 

(A) Tl against remaining T's: 1 2 2 2 2 2 2 1 1 2 

( p) T2 against remaining T's: 1 2 3 3. 3 3 3 1 1 3 

(D) T3 against remaining T's: 1 2 3 4 4 4 4 1 1 4 

(M) T4 against remaining T's: 1 2 3 4 4 5 5 1 1 5 

lG) T6 against remaining T's: 1 2 3 4 4 5 6 1 1 6 ( F) T7 against remaining T's: 1 2 3 4 4 5 6 1 1 6. 

The f ormti.la for the word BATTALIONS is BAT TALI 0 N s 

l 2 3 3 ~ 4 5 6 7 8 

while that resulting from the test is 1 2 3 4 4 5 6 1 1 6. Therefore, 

the message does not start with .this word. 

9. The tapes in all transmitters are advanced one step and the 

same procedure is followed as before, now testing the 2d, 3d, ••• 

11th letters of the message. When the test begins with the 6th·. 

letter of the message, the following sequence of movements of indicator wheels occurs: 

Indicator wheel 

Text 

(G) Tl against remaining T's: 

t F) T2 against remaining T's::• 

(A) T3 against remaining T's; 

(V) T6 against remaining T's: (~) T7 against remaining T's: 

(Z) TS against remaining T's: 

lX) T9 against remaining T's: 

1 2 3 4 5 6 7 8 9 10 

G F A A F V ~- Z X R 

1 2 2 2 2 2 2 2 z 2 

1 2 3 3 2 3 3 3 3 3 

1 2 3 3 2 4 4 4 4 4 

1 2 3 3 2 4 5 5 5 5 

1 2 3 3 2 4 5 6 6 6 

1 2 3 3 2 4 5 6 7 7 

1 2 3 3 2 4'5 6 7 8 

The final formula corresponds with that of BATTALIONS and. hence the 

word B'ATTALIONS mafV exist at this point in the message. 

10. It will be noted that the operator must stop after each 

.test to compare the final formula with that of the word being sought. 

But by going one step further, the apparatus may be constructed so 

as to eliminate this source of delay. 

11. Let the periphery of each indicator wheel be provided with 

projecting pins permuted in accordance with ten different combinations of the Baudot code and let these pins operate the series 

of contacts of a set of comparison circuits (each as in Converter 

Type M-134-Tl) for testing the·final formula against the formula 

for the word sought, as set up on a test frame, a circuit is completed which coincides with t~ '·.: ~-::--~-::-~...-........ ~~~~~~~~~~~ Then, whenever the final formula of a text ~---,,~.,.._..._,...~~-:--~~~ lighted; otherwise the tape-stepping magnets of the tape transmitters 

are actuated and all the tapes stepped forward simultaneously whenever the final formula does not coincide with that set up on the test 

frame. Thus, once started on a message, the testing would continue 

without a stop until either a coincidence between a final formula and 

a test formula is encountered or else the end of the message is reached. 

-4-
·REF ID:A4146524 

C. The isomorph locator. 

12. In operating the. idiomorph locator it is necessary to 

set up a formula on a test frame, against which successive final 

formulae are tested in turn~ If the word sought for is not in 

the message, a new test formula has to be ·set up on the test 

frame and_ this would be done by hand. But in searching for 

isomorphs we do not have any specific formula in mind; we take 

any sequence of letters in the t~xt and compare it with similarlength sequences in the same text to see if they are isomorphic. 

13. Suppose that there are two sets of tape transmitters, 

each operating a set of indicator wheels and let one set, hereinafter called the test se·t of transmitters, be used merely to 

establish test formulae on the test frame, these formulae corresponding to and being set up by actual sequences ~n the message 

itself. Let the other set of transmitters, hereinafter called 

the message set of transmitters, be used as the source of successive final formulae to be tested against the formula set up 

on the test set of transmitters. Let the tapes on the message 

set be circular, by joining first and last characters. Let the 

arrangement be such that when a test formula is set up by the 

·test set of transmitters it stays there until the entire message 

has been tested against it; if no coincidence has been encountered, 

then a new test formula is set up by the test set of transmitters 

by advancing the tapes in these transmitters, and the process 

repeated, the tapes in the message set of transmitters being 

back again at their initial positions. When a coincidence occurs 

between a formula on the test frame and a final formula set up by 

the message set of transmitters, a circuit is completed which 

lights a red lamp and stops all transmitters. 

Washington,D.C. 

April 14, 1937 •. 

WILLIAM F. FRIEDMAN, 

Principal ·Cryptanalyst, Signal Intelligence Section, 

War Plans and Training Division, 

Office of the Chief Signal Officer. 

The foregoing invention was described to us in February, 1937, 

by Mr. Friedman: 

ROWLETT ). 

) Witnesses. 

MILLER ) 
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