... --·. 

SElGRB2 Regraded fCON~~~l?i?p· - =·= ='" "" • .,..,..._ ( classificat.ioa~, , "· 

Exempt from GOS , E. O. 11652 ( ~---1l-lt!iM:l!l!HH-Wlft---i=+!Hi~H-F-iltaiHl+i*--IHflll++ 

t>ecl1~T~(1'.Nm~le IC COINCIDENCE COUNTER 

R. Fisher, D"!ffn officer 

Initial: ~. . Date:-1 "':l-:--:J. OC-?J~ 

1. In cryptanalysis it is Often necessary to test two or 

more sequences of cipher letters to ascertain whether they are 

enciphered in the same cryptographic substitution period. One 

method of testing such sequences is to· superimpose them, ·count 

for each colwnn the nwnber of coincidences li.e., cases of 

identity) between letters, total the coincidences for the entire 

superimposition, and calculate the total number theoretically to 

be expected. If the observed nhmber falls statistically within 

the limits of the theoretical expectancy, the superimposed sequences may be regarde~ as belonging to the same cryptographic substitution period. 

2. "Hand methods" of· counting the nwnber of coincidences 

are slow, tedious, and subject to error due to eye and brain 

fatigue after a few minutes work. The present invention pri- marily provides a system and a. mechanism for automatically 

observing and totalizing coincidences·. It may be employed for 

other cryptanalytic operations, as will be·set forth subsequently. 

3. Basically, the mechanism. comprises a series of tape transmitters of the standard Baudot or 5-unit-code type, but 

wired in a special manner for series-circuit employment, preferably through the intermediary of a plug and jack switchboard 

employing flexible conductors, and one or more electrical counters 

controlled by the transmitters. The accompanying sketch, Fig. 1, 

shows three transmitters, 1, 2; 3, arranged in this manner, with · certain conductors wired permanently to switchboard, 4, which is 

shown as divided up into several panels, 5,6;7. The transmitters 

are provided with the usual tape-stepping magnets, 8,9,10, to which 

power is delivered intermittently through a cam switch, 11, driven 

by a motor or o_ther mechanism, 20, so as to cause the tapes in the 

transmitters to step forward synchronously at about 120 steps per minute. These .tapes bear sets of perforations in the Baudot code 

corresponding to ·letters of the alphabet, and the sequence of sets 

on each tape corresponds to the seQuences of letters subjected to 

the count for coincidences, the tapes being placed in the transmitters .at the proper initial points of superimposition for the 

count. For example, suppose there be a message of 2000 letters 

and it is desired to to count the number of coincidences between 

letters l to 1000 and 1001 to 2000. Duplicate tapes of the 

message are made and one of these tapes is placed in transmitter l 

with letter number l at the initial position labo~e the transmitter 

pins); the other tape is placed in transmitter 2 with letter nwnber 

1001 at the initial position. Flexible conductors are now employed 

to connect certain contacts of panels 5 an~ 6, which for the sake 

of clarity will merely be indicated by stating the contact points 

thus connected: 

eclassified and approved for release by NSA on 

0-20-2014 ursuantto E.O. 13526 

3 
REF ID:A4146526 

Left-hand 

contacts 

of .Tl 

Power 

contact 

(27 and 47) 

l28 and 48)Left-hand 

(29 and 49) contacts 

(30 and 50) of T2 

(31 and 51) 

Lever 61 Lever 62 

of Tl of Tl 

21 and 22 23 and 

Counter Lever 75 Lever 71 

magnet of T2 of T2 

37 and 46 42 and 

l 32 and 52) 

Right-hand{33 and 53)Right-hand 

contacts ( 34 a~d 54) contacts 

of Tl (35 and 55) of T2 

(36 and 56) 

Lever 63 Lever 64 Lever 65 

of Tl of Tl of Tl 

24 25 and 26 

Lever 72 Lever 73 Lever 74 

of T2 of T2 of T2 

43 44 and 45 

4. The circuit for the counter magnet 13 is a series circuit 

passing through all ten contact levers of transmitters 1 and 2. 

Therefore, in order that counter magnet 13 be actuated, all contact 

levers 61 to 65 of transmitter 1 must be in positions that are 

homologous with those of homologous contact levers 71 to 75 of 

transmitter 2; if this is not the case then no circuit is completed· 

through the counter magnet 13. This will happen only when identical letters (no matter what these letters may be) are simultaneously passing through both transmitters, in other words, only when a coincidence occurs will the counter step forward. 

5. By extension, any number of transmitters may be wired for 

such work, the number of counters being one less than the number· 

of transmitters. 

6. In the foregoing .operations the counters of the ·machine 

are actuated by coincidences of identical letters, but it is 

obvious that the machine may be arranged to count coincidences of 

specific pairs of non-identical letters •. For example, suppose it 

is desired to totalize the number of times an A mee.ts a K in two 

sequences. By appropriate wiring this can be done, so that only when a K is passing through one transmitter while an A is passing 

through the other will the counter be actuated. Thus: 

-2-
- ' REF ID:A4146526 

? 

The principle here is that a pair of homologous levers which are 

in homologous positions (for coincidence of characters desired) 

must have their associated homologous contacts connected together; 

a pair of homologous levers which are in non-homologous positions 

must have the left-hand contact of one lever wired to the right- hand. contact of the other, and. vioe versa,· as ·shown in above 

sketch. When so arranged it is immaterial which letter comes in 

which transmitter; the results are the same whether "A" is passing through transmitter 1 while "K" is passing through transmitter 

2, or vice versa. 

7. The machine may also be used to count the non-coincidences 

just as easily. 

8. By extension of the principle, it is possible to count 

the number of coincidences between 3, 4, .••• different letters. 

For example, if it is desired to count the ·number of times the· 

letters A and B, A and C, A and. D, ••• coincide, transmitters l 

and 2 are wired to count the coincidences between A and. B; transmitters l and 3 are wired to count the coincidences between A and 

C; transmitters l and 4 are wired to count the coincidences between A and D, and so on. It is for this reason that the plugs in the panels of Fig. l are shown as provided for the possibility 

of establishing multiple connections. 

9. The machine may be used for other cryptanalytic purposes, 

fof example, determining the cryptographic period of a message without finding repetitions and factoring the intervals between 

them. Suppose a message is suspected of having a cryptographic 

period between 7 and. 15. Assuming a machine comprising 10 transmitters (with 9 counters), the message is prepared in 10 tapecopies. Copy number 1 is placed in transmitter number i. with 

the first letter in the initial pesition; copy number 2, in 

transmitter 2 with its 7th letter in the initial position; copy 

number 3 in transmitter 3 with its 8th letter in the initial 

positioni and so on. The .machine is started and that counter 

-3-
REF ID:A4146526 

whidh gives the greatest total number of coincidences shows which 

tape is in the correct position as regards periodicity and this 

gives the period. For example, if the 1st counter gives the 

greatest total, the period is 7; if the 2nd oounter gives the 

greatest total, the period is 8, and so on. 

10. Suppose it is desired to find the intervals between occurrences of a specific letter in a message, for example, A. The 

pins of transmitter 1 are locked in the "A" position, opening 

switch 38 in the tape-stepping magnet 8 of transmitter 1 at the 

same time; the message tape is placed in transmitter 2, and the 

machine is started. Only when an "A" occurs on transmitter 2 

will the counter 13 be actuated. By inserting a counter in the 

circuit of magnet 9 of transmitter 2, the number of steps the 

tape makes before counter 13 is actuated will be shown. But the 

operator would have to stop the machine instantly and this would 

require sharp attention. By substituting a relay for counter 

magnet 13, and placing this relay in the circuit of the cam 

switch 11, the machine may be caused to stop automatically. The 

counter in the. circuit of the tape-stepping magnet of transmitter 

2 will then show the interval. 

11. Other uses for the machine may develop as its flexibility 

and limitations become better understood. 

Washington, D.C. 

April 15, 1937. · 

WILLI.AM F. FRIEDMAN, 

Principal ·Cryptanalyst, 

Signal Intelligence Section, 

War Plans and Training Div. 

Office of the Chief Signal Officer. 

This invention was disclosed to us in February, 1937, by 

Mr. Friedman •. 

ROWLETT 

MILLER 

( 

( Witnesses ( 

(