.. 

~ ... -=-y 

-

SE6R:Et DEPTH STIJDY ON THE AFSAM 109 

This paper reportl!I on the search for depths in a simub~ .. "-

of one year's traffic using AFSAM 109. Because the rule of mo~i~~ 

restricts the independent motion or wheels l, 5 and 6,the 36 d1ot1n~t 

orientationsof these wheels, in accordance with the value or 

(W5 + w6 - Wl) mod 36, distribute the cycle structure into 36 Mutunlly 

distinct cl.asses. In addition the relative stArt.lng orientation of 

the first two wheels commits the structure to one of three mutuall7 

distinct classes associated with three cycles or the first two cycle 

guarantee wheels. Hence all traffic tested was restricted to lie in 

the same one or the 108 distinct classes. It was agreed thnt 50 

messages in this one cl.ass would represent a generous upper bound on 

the maximum use or the most popular or the classes used on any one da7. All 

or the messages were assumed to be or length 5000. The ASAF 30 compr'lred 

each or the 50 messages with each or the others for depth (flush and 

track-in depth). The results of this traffic search appears in 

Appendix A. 

No suitable method was devised to generate quasi-random starts 

which would satisfy conditions typical for 5 letter indicator systems 

(such as ABC DE ABC or A ABB CC D E);therefore no attempt was 

made to bave all message starts limited in this fashion. For the depth 

study the irdicator s7stemwaa assumed to•be made up or eight random 

letters. 

SECRET UKUSA 342 

Declassified and approved for release by NSA on 06-11-2014 pursuant to E .0. 1352a 
.-

Nina notch pattams were constructed (see Appendix B) • These 

each had 10 blocks (a stretch ot notches tollowed by a stretch ot 

no not.chee )' and were calculated to be or 26 per cent saturation 

leTal in respect to propensity tor producing branch points. (See 

"Prelimin&17 Report, on AFSAM 9 Depth 5t.ud/", Robert P. Murphr). 

Using these nine pllttarns 365 sets or eight were randoml.7 

selected am arranged am each set designated as the notch ring 

arrangement tor the rotors taken in the fixed order ot motion 

control and used in simulating the 50 messages involved in the depth 

search. (See list Appendix C, omitted in all but tile copy). In order 

to decrease the number of changes from one day's arran«ement to the 

next the 118' was sorted on the not.chrihgS ot the first wheels. This 

ettectively recorded adjacent to one another the de.19 with similarly 

placed notch rings. Thia order ia listed in Appendix n, omitted in all 

but the tile OOP1• Typical ot the rest of the list is the following section. 

DAY NUMBER NOTCH RING ARPANGEMENT 

334 l 2 I. 'I - ·a 3 9 5 

305 l 2 4 8 5 ., 9 6 

222 1 2 ., 6 9 5 8 3 

182 1 2 7 6 3 5 6 8 

243 1 2 9 3 Z.8'16 

Zl8 1 3 8 9 2 7 6 5 

228 I l 3 9 4 5 6 8 2 

ll? 1 4 3 7 8 2 6 5 

191 1 4 3 9 6 8 5 7 

§IE{;RET 
To aid in randomness or the generation or the staring point or 

the 50 messages the notch rings on the tive wheels w2, w3

, w5

, w6• o.nd 

w7 which co.ntrol the big cycle ot the quasi-random generation were 

changed by the same method but on a less frequent basis. Appendix E 

shows the notch patterns and assignment to selector lines o! designated 

wheels for this quasi-random aenerat1on. 

The method used in the quasi-random setting generation is described in 

general in Appendix F and in detail in the above reference. 

let Lt. William H. Cornelius, Jr .. NSA-314 

20 June 1955 
... . . 

SICREI' APPENDIX A 

LIST OF DEPTHS FOUND BE'lWEEN MESSAGES OF LENGTH 5000 

Simulated. Date Messages in Depth 

Message Nmnber In Depth Message Number 

9 Jan h2 with 43 

14 Feb 15 with 43 

25 Fab 32 with 43 

31 Mar 35 with 42 

9 Ma7 6 with 8 

14 Jun 15 "1th .30 

21 Jun 7 with 8 

9 Aug 2 with 49 

7 Oct 14 with 46 

20 with 23 * 

11 Oct 38 with ~ 

LIST OF DEPTHS FOUND .BE'IWEEN MESSAGES OF LENGTH 10,000, BUT NOT IN DEPTH DURING 

FIRST HALF OF ONE ME$SAGE 

Simulated Date Message Number In Depth Message Number 

3 Jan 31 with 48 

6 Feb 19 with 31 

7 Apr 21 with 23 

18 May 10 with 50 

6 Jun 5 with 35 

8 Jun 26 with .3.3 

23 Jul " with 18 

2) Nov )0 with 50 

*Note two depths of 2 were found in 7 Oct traffic 
l 

2 

' 4 

5 

6 

7 

8 

9 

REF ID:A56981 

APPE.-JDIX B 

NOTCH RINGS AVAILABLE FOR AFSAM 109 MOTION CONTROL 

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 

1001001001 l l 0 l l l 0 

1110100101 1 1 0 0 1 0 1 

1110110100 1 0 0 0 l 0 l 

0111000101 1 1 0 1 1 1 1 

1101101100 0 1 0 0 1 1 1 

l 1 0 1 0 0 1 l 1 1 0 1 0 0 1 1 1 

1101001110 1 0 0 1 1 0 l 

0101011110 0 0 l l 0 0 1 

1011100010 l 0 l 0 l 0 0 

0 l 1 0 l 1 0 l 0 l l 0 0 l 

0 0 l l l 0 l l l 0 1 l l l 

l l 1 1 0 0 l 1 0 l 0 l l 0 

0 1 0 1 0 l 0 0 0 0 l 0 1 1 

1 l 0 0 1 0 l 0 1 0 1 1 l 0 

0 1 1 1 0 1 0 0 0 1 1 1 0 0 

l l l 0 1 0 1 1 0 0 l 0 0 0 

l 

l 

l 0 l 1 0 l l 1 0 1 1 

l l 0 l l l 0 0 l l 0 

APPENDIX C'l Included in 

APPENDIX DJ tile cow 011l7 

l 0 

0 l 

l 1 1 1 0 

0 l 0 0 0 

l 1 0 0 1 

1 1 0 l 1 

1 1 l 0 0 

1 l 0 1 0 

1 1 0 1 l 

l 0 l 0 0 

l 1 0 l l 
REF ID:A56981 

APPEi.'IDIX E 

SELECTOR LINE FATTERi"JS FOR 11C'UASI-RAI\!DOM" MOTION CONTRCL 

fJ 1 2 .3 k 5 6 1 8 9 10 11 12 13 14 15 16 l'l 18 19 20 21 22 23 24 25 26 'Zl 28 29 30 .31 

1 1110000110 1 0 l 0 0 0 0 l 1 l 0 0 1 0 l 1 0 0 0 l l l 

2 1100101100 0 1 1 l l 0 0 1 0 1 0 0 1 1 l l 0 0 0 1 1 0 

.3 0000011011 1 0 l 0 0 0 1 0 0 0 0 1 l 1 1 1 0 0 0 0 0 1 

- 4 l 1010100-11 1 l 1 0 0 l 0 l 0 1 0 0 0 1 1 1 0 0 1 1 0 l 

5 0000111011 1 1 0 l 0 1 0 0 l 1 0 0 0 1 l l 1 0 0 1 0 0 

- 6 1101100011 0 l 0 0 0 l l l.. 0 1 1 1 0 0 0 1 1 0 l 0 0 1 ::: - -rt 
,.. 

REF ID:A56981 

.A.PPEMDII E CONTINUED -c; ;z r--=> 

ASSIGNMENT OF SELECTOR LINE PAT'l'ERNS FOR lllQUASI-HAlIDOwa MO'fl:ON CtWtllJL CCC - - UC ze -== - - SC: - - --=--..=..-..= 

W2. N3 WS ~6 W7 

5 3 2 l 6 • ., o o o o o o o o o. o Setting fol' 32 dQs 

4 

6 

2 

l 

2 

1 

4 

2 

l 

2 

2 

6 

3 

6 

6 

2 

2 

3 

' 

l 

4 

' ' 5, 

l 

3 

6 

,. 

3 0 0 • 0 Q 0 0 0 a ., o o ~t.ing for 34 daJS 

5 ••• • e o o o o o e " o Set.ting f@~ 31 dll;Js 

l e • • • 0 0 0 

4 o ct a e e o o 0 0 0 

6 Cl t> • e .. 0 0 0 0 0 0 0 S®t~in,g X'@i" '!J'71 ~ 

.5 O 8 0 G ()GOOOO 

l • • • a o o o o o .. o o $et.ting Ker 32 ...,_ 

5 ., 0 fl .. 0 0 0 0 0 .. 0 0 Setting fGI" " --

]. "' • .. .. • • 0 " 0 .., Q 0 Setting .1t'ar 52 ._. 
... 

'· • • • • • 

) 

/ : 

• 

~ \ i - a 

-· ..... 1 •• . . ft / 2 :/ -' - -· Q·· .. l -·~ 3 : 

• / .. ~· 

: .· 

,_ -- .b ,, --\ 

• .. · 5 \ 

~ 

\ ; ... --~ \ .. ~ 

• \ .. 0 

• \ l 4-

\." 

• 

FUNCTIONAL DIAGMM OF RANDOMIZER 

• 

. • 

\ 

The figure shows t.hree cycles ot the AFSAM 109. The solid lines 

and dotted sepents ehow some or the bratiches and lead-in structure 

under the standard l'Ule ot motion. The dashed lines show graphically 

the stepping under the qUAai-random motion rule trom one AFSAM 109 

message setting to another. An initial start ie selected b)' a card 

which aatiatiea the condition that the setting be in the class ot 

setting under examination. Thie setting ia taken as the indicator 

•of the tirat AFSAM 109 message see dotted line segment marked l. 

The 5oootb 1etting ot the message recorded in the memory and the 

quasi.random &tapping l'Ule operates tor 10,000 stops to produce the . 

I initial. point ot the second AFSAM 109 message see digit 2. The 

,, 
.. . • 

.... ' .. 

A.:"PSNDDC F CX>NTINUED 

connecting dashed lines aimbolizea the qclaai-rand.om. stepping and 

the tact tlat during this rule the wheels do not obey the rulea ot 

the APSAM 109 motion. There are shown 1n the Figure the first ti ve 

massages generated under thia complex rule. Note that m.eaaage 2 and 

message 5 are in depth aa ia exhibitedrin the merging (see asterisk) 

ot the segments marked 2 and 5•