·' 

l· '-

Op-20--G/rvb 

Serial 0843120 

From: 

To. : 

Subject: 

Reference: 

Enclosure~ 

'VPJi:A41466ss 

~~:..~ 

NAVY DEPARTMENT 

Office of the Chief of Naval Opeaations Washington 

May 15, 1943 ~·MEMORANDUM 

· The Assistant Director of Naval Communications. _ (Op-20-G). . · Colonel W. P. Corderman. 

Suggested Solution of Commercial En#;,gmB. 

(a) Memo of Apr. 5, 1943 on the above subject.: -

·(A) Reference (a). 

l. The subject method of solution was discussed-at• 

conference at the Naval Communications Annex on May 4, 19430 

The Atrtlra" representatives present·were Major Bosen, Captain Seaman, Captain Dunvell, Mr.' Ferner, ·and Mr. Small. The Navy repre- sentatives vere Lieutenant Commander H. T. Engstrom and Lieutenant 

Commander Ro Bo Ely. 

2o Research on a machine which will carry out the suggested operation as well as other more general processes was initiated , by the Navy 1n September, 1942. General designs vere completed in January, 1943, and a model or the equipment is· now under . construction. Delive17 is expected in about one month. - · 

3. Discussions at the conference showed complete· agreement 

on the general design or the equipment. 

4. The proposal of the reference in handling turn-over 

points is sound. It is intended. however. to check the operation of a single unit before considering tandem operations. 

5. Your cooperation in submitting the reference is ·- appreciated. 

E. E. STONE 

Captain. U. S. NS.Vy-

. 

G: . 00 

-~"'a 

- 0 .c;><t,a 

. . . . .. 

- . . . ~ < ~ ,-', 

Declassified and approved for release by NSA on 10-21-2014 pursuantto E.O. 1352_6 · j ~ 
I 

I 

I 

; 

~ _ ID:.A414665B 

SUGGESTED GENERAL SOLUTION:FOR THE , COMMERCIAL ENIGMA,, WHERE ONLY THE END PLATE AND 

WHEEL WIRINGS ARE KNOWN 

*** 

By the.method to be described~ we should be able to nbreak" . . 

any average message enciphered ~ the commercial enigma, in an 

hour's testing· time, even though the indicators a.re not known. 

Thia method uses high. speed analytic machinery already 

developed. 

No plain text assumptions are neee~~ary. 

1. Ba.sic principles underlying solutiong 

~uppose a development sheet is made up by enciphering 

only the letter "E" a~ every possible setting ot the commercial 

enigma.. Tbe other 25 letters are lef't undeveloped. 

Th~n by superimposing an unknown message aga.;tnst this . ' 

development a.nd noting "bits;" the· setting where most "E•.s" are 

possible can readily be determined. 

Such a setting is not necessarily ~he proper one however, 

unles$ many hundred letters of message text were used in the 

test. 

Nov suppose that a development sheet has been ma.de bJ· 

enciphering ·tho nine highest frequenc1 letters at each setting~­

so that when any given letter -of the message to be tested is 

-1-
_slid againattbis development,, a "hit" at any position of this 

development means that e!ther an_ 0E" or a "T" or an "O" etc., 

could have been_enciphered at this position. _A no-hit means 

that a medium or low frequency letter would have been enciphered 

at this point .. 

If th1rty~s1x consecutive letters of the message are slid 

s1multaneouslr, and the~r hits· totaled, the proper setting 

should give an_estimB:>ted total of 26 hJJts (on average). Only 

seven improper'cases (out of 2,400,000 tests needed in~the· 

commercial .enigma) will equal or exceed ~his average value. 

(See paragraph ; below~) . Such a test is theretore practical 

if the tests can be ma.de speed;1l7. 

2. Equipment to be used:~~A high speed index of coincidence 

analyzer is need,ed. ··This. machine sho~d glve the total number 

ot coincidences for a superimpo~ltion 36 let~ers wide, at each 

setting. · Furthermore, at each setting, eaeh of the 36 letters 

should be tested.in its OWn eo1umn against a 26 letter alphabet 

whose 1na.ividUa.l hoequenc1es sr~ either uln or rt~n. This can 

be accomplished b7·a tape vith" 26 l~ve_ls or.more~ in which the 

frequency of "1." _is ind.ice. ted by 11punch n, and or "¢'' is 1:nd1ca ted 

by "no-punch" •. Speed ·is assumed to1 be 120,000 positions per. 

minu~e._ We understand this equipment is forthcoming soon. 

3. Mathematics irivolved:.--Given -N identical variates. 

(in this case N .= 36, since.our test is-38 letters wide) with 

-2-
,. 

' I 

.. ' 

\ 

REF ID:A414665B 

·~!E~lm~i 

any one of the varia tea to be- incliea ted by "x" and' to. take. 

on the following va.lues with ~he :probabll1t1es a.s~ocia.ted 

thereto: 

.. Random case: Causal case: 

-

x p x p ' 

1 9/26* 1 71/lOO* 

¢ ·17/26 91 29/160 ..; 

*For Ehgl.ish. if it is one of the letters 

E, T, -0, A, N6 I, R, s~ H 

Expected value x (random) = . D . 

-Variance·x (random) 

.Expected value x (causal) = 

--

9/26 or 0346 

0475 -

.710 

Question: 'What is the probability tliat the random value· 

will be greater· than the·average c~usal value, given a total 

test N variates wi~e? · 

The inverse of t~s probability was looked up 1n the 

standard normal .. ourve charts,, wherein Xt (the va.lue·foia x as 

it appears iD. the tables) was: 

r Xt· = 0710 ·- 0346. m--

.47_5 /J.l 

We found that for -Xt : 4.Ss the probability that it would equal 

OI' exceed ls only 3/1,000,000; and f.Ol' Xt to equal .4.5:r N must . ' . - . . . . 

be exactly 36 ·.letters. (AssumJ,ng- io% inaccuracy however this 

would require 54 letters.) 

.,.· 

4o .Effect of the ri.ngstellung:--The above calculations 

were ma.de considering the second-wheel titrnover point, or 

-' 

- . 
f • 'r 

"ringatellung"., to' occur at the end of the first 26 l.etters 1D · 

~~h message, ·~ arter. each set of ?6 th~earter. 

DJ:f'~eHnt ringetell\lilgs can.be proV1ded tar_; however• . ' ' b7 several ·methods• all praet1ca1· •. 

Perhaps the simplest is. to use two h1Sb speea. ana17t1c 

machirtGe., wired Ui·iiarallel·to the same counting mechanism. 

The· "mas~r" "de.velopment" t~pe is .. theJ1· Pl'~P'red in · 

duplicate, as follows: 

Ee.ch e7cle ot ~ B;lphab"ts generated ' b7 the fir-st wheel 

between motions. of :the second .'dwel, is repeated immediately 

after itself b,e~ore the kick. over. takes. place. 

Eigh~een.conseeut,.ve.letters of',the meas$ge text a.re then \I I ' • ' ' 

set up on one C?f the analytic ma.chines; the 27th t.o 44th letters 

are set up on. the. second ma.chine.· The tape on the se.cond · machin8 

is advanced 52 positions with reference to the tape on the first . . . ' . . . . 

tnachine. The two machine~ . a.re then. run 1D. sJ'llchronism. th.eir . . ./ 

outputs be+rlg Wired in ps:ra.11~1. The result is a test of 2 x 18 

or 36 letters, as required. The proper setting can be found 1r 

the breakover ·occurs somewhere be~~een the 18th and 27th letters . . . 

or the message~ these not having.been sat up on t~e test board. . . . 

Supposing the breakover to have occured however between the 27th 

and the 34th letters·, then we should have J3tarted with the 9th 

letter to set up, our test~ A second :r'lin is therefore made, , 

setting up the mach!n~s beginning a..t the 9th and 35th letters. 
'· , ,,,- "·'' R:lt"H" r==ID : A414 6 65 B ~!~H, , . · 

A third run is made at the 17th and 43rd letters •. This covers 

pract1cally_every possibility 1D just three runs. 

Since we expected,7 bad settings per run, the total 

nll!Dber of bad settings equalling or exceeding the average 

good value is therefore onl7 2'1. 

If it is desired to μse. just one ma.chine, we will 

require a tape of ten million positions, run _through thr.ee 

times. The tape is made up as follows: the basic tape is 

spread out to every other position, and its duplicate advanced 

52 positions and printed 1n between. ·The ccimbined tape is I 

then· put 1n the ana~yzer. The first 18 l_etters are then set up 

across the test strip at ever7 other position, -and the 27th to 

44th letters set up 1n between. Five million interspersed 

settings of the master tape willnof' course ~e impossible . - . . 

settings, and the effective length of the·tape as far as number 

of comparisions goes will therefore be onl7 the remaining 51 000,0001 

and half of these are duplicates •. So for three, runs ve inust still 

deal with only 21 bad settiD,gs above the average good value. 

Another method of-using a single 1m1.eh1ne consists of making 

e. tape onlJ' 5.000,,000 long, and making three Jl'UJlS with the two 

18 letter groups starting in ea.ch o~ ·three positions for ea.ch run. 

(Not to be described here.) 

-5-
'' . , •• '·"· .,,>. REF ID:A414665B 

$~$1ffi!EI 

Less letters would have to be taken, into the test of 

course, if all 26 could be. used 1D each alphabet and accurate 

' . 

frequency values 'Punched" into the tape b:r varying the sizes 

of the holes "punched"o• This·is not considered necessary, 

since the }6~v1de test should be possible with atand&rdized 

machinery. 

It should be noted that l"apid analytic apparatus is used 

.thl'oughoutJ. the times ot testing aiae exceptionally shor~J bad . ' ~ . . . 

ca$es as high as the average good ·are not to~ numerous, and ' ' ' 

can be lessenEld with~ges other than English; and best of all, 

no plain text guesses are required •. 

The bottl~neck,, it ~ny .. is in .. pl'eparation 'of the development ' . I 

tapes. · ~e have not been informed as to the exact nature _of the ·. 

machines aeeompllshing t~pe manufacture, and cannot estimate 

:times here. 

Possibilitie~ for solving Orange an~ Yellow traffic ma:y 

develop out of tbie proposed Indigo met~od. '\ 

*For German,, approximately 25 letters. 

Section B III F 
REF ID:A414665B 

lst Memo Ind. 

Director ot Commmicat~ons P.es.ea.reh, ' July 194:5. · 

To: Oommancling Otf1cer,, ArlJ.ngtOD •11 Station 

1. In e. paper C&ted 5-Apr4 19,.3. the SSS deeor1bed a. 

ttsugge-sted General Solution JoJt nte Comme1"'1ca.l Enigma v.iiere 

Only 'fhe End Plate:s And Wheel Wil'inge An lfllown•. The ba.s1c 

ide& va.~ entil'•lJ conceived and elaboratea bt SSS p~aonnel, 

independentl.J'ot any eo~taet vith the ?fa.v,. 'l'he title of the 

pa.pal' vaa unne~ee&a'.iJ1l.J' 11m1 ted.~· \'.)4'anuse the l)l'1nc1pleo llFS 

applicable to the steckered Enigma .tlao, It presented poas1bil14\"' ties for a purel1 stat1st1ca.1 method o,f solut1o~. not requir1Dg &D¥ cr1~a. 

2. In view or OUX' prenouu relations with the E&VJ' in 

;-egard to technical reaearch o.nd·det.elopment,, as tSoon as the p~oposed new solution appeared to. orre~ possib1l.1.t1es, a oonfe1•ence 1\l&a arre.nged with the .Na V'r tor ·the pt.'ll'pose of d1eclosing the idea to them a.n.d possibly in1.t1attnc e. jolnt project to~ 

1noorporat1Dg modU'1eat1one in an ez13t~ !la.VJ M.M known aa 

"Tetra-Teeeie" vith a View to tx-ying out the nev ctat1st1csl 

method conceived bz SSS peroonnel~ Tb.is conterenee vaa held 

on lia7 4. e.nd !s the one referred to 1n the 1'a.vy ;iemorandwa 

dated Ma7 15. lnaemuoh as 1 was aw7 on a missicn, I was not 

present at tbat conference~ 

3. It was only at the end ot the conrorence, after our 

repreeent&t1vee h&.d d1scloised the bil.aic pr1tle1ples of our 

proposed method of &t&tiatical solut1.on~ that the li&V7 re;pre- se~tativ'a aaw f~t to disclose to our rep»esentat1ves at the 

contei-en.ee the .tact that they had under development a nev p1eco 

or equipment kr:.C>J.Tl.\ ae "~ott, which vae· intended to opfl:rate along e011evhat new lines 1n connection with E aolut1on activities but still requi.red the use of "c~ibs~. ~e1 indicated 

hovever that the7 were aware of statistical poas1b111t1ee along lines sim1lar to · ouxae. · 

4. Attet- eoae d1seuas1on, dur1ng whicl;l our r4&presentativea pointed out'hov the "Tetra-Tessie" machine might be :modified, 

the RaYJ' repreaentat1ves thought that the. '".&Jpo11 nachine might be used.for the tJ'P9 ot stat1at1eal solution })ropoaed bJ"SSS. 
{ ·- -S"BEtF::3f.ED:A414665B 

..._;_ ,. ... 

-2- 1st memo .Ind. 

!hereupon eur repreaatat1 ves left t11th the hYJ' ·the .-orandum. 

dated April 5. to which reterenee vaa •de in the fir.st Pa.ragraph above, tor th' p1l?'pose ot aloser ntu~ bJ the Jl&VJ' to detel'lline 

the tea.s1b1l1tl' ot the solut.1on "bJ U8e or a &u1tablJ' aod1t1•d "ltJPO" •ch1Jle. 1·t ws jo1:ntl.J' agreed 110t to initiate u. 

additional deTelopMat project to-, '94u1~t. apeoit1call7 designed to opel'&t• aooOrcll.1\8 -o the J)l'illciplea d1aoloae4 in the &bove-

-.t1onad memorandum. · 

5. At no time during this eonfe:renee did the ·Be.VJ mention 

the tact that although theJ had disclosed "Tetra~TeDs1o~ to 

tha Br~tieh they had v1tl:Jheld thi.3 technical development rel.a ting to the cHn>o u :ma.chir,.e from the Bri ti eh. Thia ta.ct 

developed onl;r during a eonvei-l.la.t:ton between Com::ander Uell.ger e,nd nqselt en the evenlng ot June 17._ I must admit tbat I vas 

cone1derabl7 astonished to le$rn this raot, and it ~hould also . be stated tbat our repreaontstives ai that cont&rence vere also . taken aback when th(ry learned that the unypo" developl!lent; although dating trom September 1942. hnd not been preV1ousl1 disclosed tp ess. 

6~ Onl.f general teatuises Vere diacuseed and tew details 

ot the nHJPO equipment vere made available at the oon.f'erence. 

After more mature thought and d&liberation, keeping 1n m1nd 

the tact -~Mt the propoted ."HJPOn machine io intended tor •cr1b8 

operation, it was not and is still not clearly apparent to ua 

how the "HT.Po" machine.can be d1rect1J' appUed to the statistical 

methOd proposed b7 us; however we are at111 not cogD1.aant ot all 

eonstruetiona.l and operating det&11a or the "HJPO .. machine and 

no et.tort baa.been made b7 ua to eiecur• theBe details. It va:s 

t!ecided to vait until the :proposed eQ.l11taent ha• been reduced 

to praetiee before going turthor into the matter. 'l'hie did not 

seem to be long ert 6 ror del1 '1e"£7 ot the· ~o • machine vas 

indicated aa be1ng OD.17 about a Donth ort. 

7. In v1ev ot the toregoi.ng• it is clear that the ass is 

not unde:- &.D.J obl1g&t1on to tbe !l&VJ' tor &D1' ot the ideas 

involved 1n the SSS proposed atat1et1ca.l method or solution as. 

disclosed in the above•mentioned memorandum ot 5 April 19,J. 

8. Tbel'e 1• now cona1derable doubt in our a1nds as to vheth~ the propoa•d "BJPo• apparatus ca.n be readilJ' lllOdit1ed 

• to aceom.pliah the type or atat1st1cal .solution proposed bf us, 

SEGRE) 
... _ : ... i. . ~ 

. ( . 

REF ID:A414665B 

~lE®fiT 

Bf$lS-3 ls~ Memo Ind •. 

. .~ ' I 

and we are un.dertaJWlg stu.dies indepe.nd.entlJ' of the 1'aVJ' • .with . a view to initiating a·project·for the conetruction ot a •®"Jne 

tbat will aecorapli.sh .:t t. ' .~, . .• f • 

· .. · . · 9• · Although it is renltzed that· -tb1s. question J.nvolvee 

matters· ot po.liq• .I tee1\ Mtte:rtheleas . warr~ted 111 · Mld ng · · ·the recommendat1o~· ·that, we· Gbit\e. etrlctb" -b~ the tenm ct· our 

recent agreement vi.th the· B»it1Dh in respect to a complete 1aterchange of tecbn1cal 1.ntormation ... : aspec;tall.7 1n 1'~g$.rd to 

the "Elf. :problem. This ·may not be the til'Ae to rmke a disc;:losure 

·to the r;r1tl&h but ·I: f'eel · th$t ve maJ' want. to be- free to mke 

a disclosure Sheuld o~ prel1m1p.a.ey-. 1nve·3t1gations. prove· the 

tea.s:l.bili t7 >ot. our p1,oposa1.. . . · · · · · · · . ; : . . . 

10 •. In viaw of the fa.et that Captain Sea.man·and llr. Perner 

are utiavare ot .the situation raised by 7oui-·Umol'B.!ldum of June 

281 and ~much a~ the1 are at1ll av&1t1As trensportat~on 

it way be desirable to communicate vi.th them Vi.th a ·view to 

giving them p~oper 1n$~~uetions 1n the premis~s. · 

. ,• . . 

William P. Pr1e&aan 

Pireotor o~ ·Comnnm1 eat1ona · . Research · 

• 
r 

~ ,;; ~ - ' --

I 

REF ID:A.4146658 

'• 

.Si?SIS ,115 ~-Oen. SPSIS-' 

1st Memo In.Cl. 

. : . : ' ~ . . . 

D1r~ctor _ot Co~ce.t~ons Rf)_seareh, ' July 1943. 

To: - Co~ding Officer. Arltngton !!&11!8tat1on 

-1•' Ill a pa.per dated$ April 194:;, the SSS_ described a. 

•suggested Gener&1·so1u~1on For The COlJL111er1ca.1 En1sma Where 

Only !be· End P.late·s And ~eel Wiring~ Are- Known•. The bas1e 

·idea. was entirely·. conceived ~nd ·elaborated by SSS personnel, independently of any eon~ct with- the Navy~ The title of the 

·paper vss unnecesse.r1b'-11t.11ted) because the principles a.re 

appliceble ·to the stee~r-ecl. Enigma Also. It presented poas1b1;t1 ... ties tor.• a· purel7 statistical method o.f i:iolution~ not requiring 

any cr1bs. -· · 

_ 2. In vtev or our previous relations -w1 th _the Ne.VJ in _ regard to t.,chn!cal reseBtrch. and development, as soon as the 

proposed new solution appeared to offer poss1b111ties. a conference vas arranged with- the Navy for the purpose of disclosing the idea to them and possibly 1n1t1at1ng a joint project for 

incorporating mod.1ficat1ons 1n &n existing.Ba,,,- RAii known as 

0Tetre.-Tess1eu v1th a viev to trying out the nev statistical 

method eonce1ved by SSS pePsonn~l. This conference vas held 

on Xs.7 4,. and is the one pe.ferred to in the Navy memorandum 

dated Msy 15. Inasmuch as l was avay on a mission, I Vll.e not 

present at tha.t conf'erenoe • 

. 3. It was only-at the end of _the conference, af~er our 

l'"epresent&tives hB.d disclosed the ba:sic Pt'tineiples- of our ~reposed method of statistical. solution~ that the NaVJ" representatives se.v fit to d1sclo.~~ to our representatives at the 

conrerence the. tact that they had under development a new piece of equipment krmH;ll as lfJJypott ,. which was il'ltended to ope:Pate along somewhat nev lines in connection with E solution aQtiv1- ties but still :required the U'3e Qf "cribs"~ Thef indicated 

however that the7 we:re avazae of' ste.tistlcal poss1b1l.1t1es along lines s1mllai- to.olWs • 

. 4. Atter some discussion, -during which our representatives pointed out bov the 0Tetr&•TeBs1e" machin.e might. be modified, the Ha.VJ' :representatives thought that the "Hn>o.,_ machine might be used to11 the tJPe C?f staUsti.,cal· sol~tion proposed b7.SSS~ 

-. 
It 

REF ID:A414665B 

5PSI5-.3 -2- let memo Ind. 

Thereupon our repreeentativea lett vitb. the !f&VJ' the memorandum 

de.ted April 5, to wbich reference was •de 1n the ti.rat paragraph aboYe, for the p111'.'po~e ot closer studJ' bJ' the I&'fT to deteraine · the tee.s1b1l1ty o.t the solution b7 use ot & su1tabl7 aodiried 

"HJ'po" machine, It was Jointlr agreed not to initiate u 

additicmal. developaent·p:roject t~ equJ.PJdD,t spec1t1callJ' des1pe~ 

to operate according to the principles disclosed in the above .. mentioned mamorandum. 

s. At no time d'"LJI>ing th1B conference die. the Na.VJ mention 

the fact that although the7 had discloeed "Tetra-Tessie" to 

the D~~t1sh they had V1thheld this technical development relating to the 11HJPo'' ma.chine from the B::,itish. This fact 

developed only durir.1.g a conversation between Commander Wenger and myself on the evening of June 17. I must admit that I •-as 

oollSiderably a11ton111hed to leai~n this tact, and it should e,leo 

be s·tatQd that our representatives at that oonterenoe vere also 

takon aback vhen they learned that the ''Hypo" development~ 

al-though dating from .September 1942, had not been previously 

disclosed to ses. 

6. Onll general feattll'es were discussed and tew details 

of the ttBn>o eq1lipinent were made available s.t the conference. 

After more mature thought and d.eliberati.on. keeping 1n mind 

the tact that.the proposed ".HJ1>o• ma.chine is intended tor •crtb• 

operation, it \."2.8 not and is still not elea:z.17 appal'ent to ua 

ho-w the nlin>Q n ma.chine ce.n b~ directly applied to the sta tistic&l 

method proposed by 1w; however ve are still not cognisant or all 

constl'llctional e.nd operating dete.1ls o~ thti "HJPo• me.chin& and 

no effort l:ls.s been ma.do by us to eecure these details. It was 

decided to vait until the p11oposed equipment ha.a been ~dueed 

to pract.1ce betore go1.ng .rm~th0r into the matter. Thie did not 

see:m. to be long off~ ro11 deli vc/r.>y o~ the "Hn>o 0 machine vae 

indicated aa being .onl7 about a month ott. 

7. In. viev ot t.he fo;t"egoing,, 1 t 1s clear tbat the SSS 1s · not under 6llJ obl1gation to the Nsvy for eny of the 1deas . involved in the SS3 proposed stat1.st1e&l method ot solution as 

disclosed in the above-mentioned memorandum of 5 April 191f.}. 

O. The:re 11! now considerable doubt in our mind• as to 

whether the proposed "Hypo• appar& tua cu be :readily modified 

to accolij)l18h -th& t7Pe ot.atat1st1cal solution proposed b7 us, 
. ,. r(~~ "' '-·· ' REF.ID:A4146658 

·~-

~f@m!Et· 

SPSIS-3 -3- 1st Memo Ind. 

and we are undertaking studies independently of the NaVJ', with · a view to initiating a project tor the construction or a mac~ne 

that will accomplish it~ 

-9· ·Although it is realized ~bat this question invplves 

matters of policy,,. I feel· nevertheless warranted in.ma.king the ~econmieilda.tion that we abide strictl~ by the terms of our · 

recent sgreeDent with the British in ~espect to a complete · 1nterc~e of technical infovmat1on~ especially.in regard.to the 0

E" problem. Th1s may not be the time to make a disclosure 

to the British but I feel that ve ·m.a7 want to be free to make 

a disclosure should Olll' prelimina:t>y investigations prove the 

feasibility of our proposal. 

' 10. In view of the fact tba.t Cap~in Seaman and Mr. Ferner 

are unaware of the sitUl.\tion raised by your. memorand~ of June 

28, and 1nasnuch as ·.they are still avaitiJJg transportation it ma7 be desirable to commun1c$te with them v1th a view to · giving thou.proper instructions 1n the premises, 

William F. Priedman 

Director of Communications· · Research · · ·