~ ·.s.· ~ ;'i .· ~; ,_ ~ REF ID:A99813 

New York, Sep. 18th, 1935 

Dear Friedman: 

Since I last \\'Tote you I have put in some more time on the ADFGVX 

Cipher, ,and have come upon some points in the "general Solution~ whioh seem to 

me_ to re;quire more· light before I can satisfy myself that this is incieea a 

" general solution. 

· ... 

I crrtainly have no desire to discount the pretty solution or the messages given. Ir I mention or intimate the existence or luck in the solution, 

it is no~ that I wish to dis?arage luck in connection ?rith cryptogra~hy. O!'i 

the contrary, I know from experience how to value it; and I am convincei that 

a oryptogra~her can no more '!8t along ~~thout it than a physi~ia.n. - And 

now to mil points. I 

I Any: solution or the ADFGVX System must depend on a ietermination of 

1) the nUmber or. columns in the transposition rectangle, and 2) the number 

or lette~s in each column. 

I 

The 

1

assumption that the material at hand for this purpose will include 

12 messages written in the same key is a perfectly fair one, based, no doubt, 

on actua~ war-time experience. Is it equa?ly fair to assume that G of these 

12 messages will contain the same number of letters! Even in the l' messages 

given th9i variation in the number of letters per message is considerable - the 

shortest 1has 108 letters e.nd the longest 254; still t~-o of them contain 186 

letters. 1and this fact plays a prominent part in the solution, increasing as 

it does ,he material on which the opening steps are based. 

The 'principle or "Reversals" is, of course. basic in the solution, and is 

sure to be of service when circumstances allow. I think it would. have been 

well to pbint out that these reversals will appear only (~) if the first of 

two coluinhs has an odd number of letters and the second is~or the same kind 

(i. e. + or -) as the first; or (b) if th~ first of two columns has an even 

number or: letters ana the second is of a different ldni from'the~first. To 

state the same thing negatively: if the first of two columns has an even 

number or; letters and the second is or the same kind as the first - or if 

the first; has an odd number or letters and the second is or a different kind 

f'rom the first, there will be no reversal as betv·een these columns. Roughly, 

and without actually calculating the probability, this a f'ifty-fii'ty chance. 

The test +essages begin with 3 ~ columns each containing an odd number of 

letters, l\'D-d that is a piece or good fortune which the solvers very properly used to good advantage - but it is a piece or good fortune none the less. 

and its r~currence cannot be counted on. 

' ' 

·.· ... 

su,pose col 4 had followed col r (I am using the col numbers or the transposed text , i.e. as the message was sent); the first two sets of ten letters I would the:q. show 

I lat ten ind ten 

o,dd even. odd even 

11 A 6 2 A l Ylith weights according to 1''1gs 

·. 

I 

·3 D l 7 D 2 1 and ' of the text, these figure: 

:o F. 2 0 F 2 1st ten, odd-even l~B, even-odd 10~ 

3 G 0 4: G 4: Gnd ten, oad-even 196, even-odd 176 

~ v 1 1 v 1 

~ x 0 0 x 0 Xhere is no reversal 

~pproved for Release by NSA on 07-30-2014 pursuantto E.O. 1352a 

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~ .. \,:\ ' ~ • ·t·,' ~ REF ID: A99873. · ··· Bow let col 5 fe>llow col 4., not forgetting that two 1etters 0£ col 4- remain to 

be used. ' The third set of ten will now show: 

~·~<\."t: 

..... 

··""" .. · 

3rd ten 

odd even 

3 A 2 

:- ,. 4: D 4: ~ . ' · ..... . ' -,. .. '-.." -l-·{ .... 2 F 0 od.d.-even 14:8, even-od.cl. 123. ...... '-.. f.:.. (', i.> ~., f 0 G 2 : l v 1 Again there is reversal. . t'~ • : no •' 0 .x l 

The furt~er along we go, the more the sets of ten are bastardized. Thus, 51-60 

contains :s letters from each or two columns, and any work put on such a set of 

letters ~ould, of course, yield valid results only through the arrival ot San-

• 

.. .... -:;, ..... - ... ..... 

.. .,- i 

v.: 

. ..... '. ta Glaus. · · . · ! .· 7<•.:.~:- ,;.."'T'• .. ';-.... 

,,.,; " .-, w; ~. °ij:'t: t. .. ~ . ; .;_ .. 

ilt>\'. ~ • ~i-; .... : 

,:.>-

.-~ -

" .. 

~ h -· .... . ~ 

. 

.... ': 

=:.· . "\ 

,,·"• .. "' .. 

. . 

" 

.. 

: . ,.,-~· 

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The ;opening analysis shows that th~ second set of ten letters is preponderantly of ,a different nature from the first. Why sets of just ten were chosen is 

not stated - of which more a bit later. The conclusion is drawn that there is. 

a reverssll {'nea.r the tenth letter." Then we read, "This same sort of reversal 

takes pl~ce in the-l};i.-rd ten, but this time the break is definitely indicated • 

The simu~taneous appearance of V and X in the sequent positions 2i and 23 indicates th~t 22 is the end of one column and 23 the beginning or another." It 

is true t,hat a foot-note points out that the ,Point is not absolute, and is merely 

"an indication based upon probabilities." This remark belongs not in a foot-note 

but in tbk text proper so that it may receive due consideration. As a matter of 

fact it r~ceives no consideration whatever: from this moment on the column length 

of ll le sters is assumed to have been proved. The way was paved for this conc~.usion in the italicized statement on page 3: "A reversal of this alternation indicates th·· end or~ o~e column and the begp~i~2L ~ot_1!.e_r._" I cannot convince 

Iey'self th~t the ti-letter column length has really been proved at all. 

In itself the simultaneous appearance of V and X in positions ~~ and 23 . proves little or nothing - at most it may arouse a suspicion. In the two messages und~r consideration the phenomenon appears 6 times - at 14-15, 2~-23, ~~-~5, 67i68, 120-121 and 179-160. Three of these occurrences mark column divisions and three do not - surely there is no strong indication in that • 

i 

Possibly the text means to say that vhen, for other reasons, there is a suspicion or; break, then and then only the phenomenon may indicate the point of the 

break. Even that is, I think, too strong e.n assertion; and in this connection I.. _ -~· 

point bac~ to what l said above as to the test based on two sets of ten letters 

eacb • .... ~, I 

-~;·· Why .Just te~ letters? It segr1s to me that a cryptanalyst examining ·the :two ~ :. messages, :es,>ecially one vho is ready to be im.,ressed by the VX recurrence might 

·,,. more readily have chosen 14: j;han 10 because the same phenomenon occurs there. de 

would the~ apply his odd-andeven tests to the first and second sets of l~ with the 

follov1ing result: " 

lst l.~ 

even 

6 

even 

0 ·: 

oqd 

~ 

4: 

A 

D 

F 

G 

v 

l 

odd 

1 

2 

-4, 

A 

D 

E 

G 

v 

x 

5 

these shov. by ":ighted frequencies, 

1st l~, odd-even 196, even-odd 151 

2nd 14:, odd-even 191, even-odd 197 

... .J• 

... -,,: " .. 

. .;.. . ' 

:c- : .. .. 

Ii 

- ~ 

l 

~ 

2, 

J; 'X 

I 

I 

3 

3 

l 

·o 

3 

1 

3 

3 

~ 

l 

3 

.. 

We should have a rectangle with 9 columns of l~ letters and 4 of 15. We may consider the ,second column one of 14 letters with a reversal (not v9ry strong) or 

one of 15 ,(odd-e~en 208, even-odd 197) without a reversal. In the latter case 

the secon~ column (no reversal after a colUDm with an even number of letters) 

.. 

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.. 

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' ;--...... 

.. . 

:; .. . . 

- : ! 

·-

i, .... . . 

. . -

REi- ID: A99873 . woul.d be o:f the same kind (say +) as l:.h<:' f"irst.- The would-be solver would be 

up a tree:. a·ut so I believe lYOuld th'? actual solvers or the messages except 

for a pie;ce of luck: they noted the VX repet.!. tion at 22-23 and drew conclusions 

which see~ to me not warranted, and these conclusions proved correct. Our hy- pothetic~l solver drew conclusions Little if any less warrantei and came out 

wrong: o~ man's meat and another man's poisonl 

I ri:nd myself unable to agree with the argument on !;)age 5 demonstrating tha.t 

all the ijirst f'ive collUl!Ils are longs "Employing the same reasoning as before, 

it is quite evident that there is a break bet'Y10en ;5 and ~6." The break between 

22 and 23! was assumed mainly because or the VX phenomenon there; nothinf; of that 

kind occurs here. The only other previous reasoning that can apply is that 

brought ~o bear on the first twenty letters (page 4, top). The conclus1on drawn 

there is ~hat "this reversal would indicate that column 1 or· the transposition 

rectangle'• ends so'Tlewhere near the tenth letter. 11 How can the evidence here be 

said to pbint to more than a break in the neighborhood or 55 - to a break at 

exactly 5:5? The point is important, because from this conclusion that there is 

a break at 55 is drawn the further very weighty conclusion that the first five 

columns ~re all long. Suppose we examine the matter a little further. 

Let 'us ass•Jme t:he correctness of' the conclusion that there is a break e.t 

22, and that colwnns 1 and ~ contain ea.ch 11 lett~rs and are + columns. Let 

us now arbitrarily suppose that column 3 contains 10 letters and is the short 

column o~ the message. Column 4 and all subsequent columns will then be long. 

I see not~ing at this point - nothing indeed short or the actual cor~ect arrangement; of' the columns - to contradict this asswn,tion; following the text, 

columns 5. and 6 (letters45 - 55 and 56-66) compare as f'ollowss I 

I - ! 'JOl 6 

odd even 

4: 3 I A 

4: D 

0 F 

2 G 

l v 

l x 

0 

3 

4: 

0 

0 

col 6 

odd even 

0 A 3 

5 D 3 

0 F 3 

2 G l 

5 v 0 

0 x 0 

Weighted Freq acc•g to Figs 1 and 21 

col 5, odd-even 154, even-odd 121 

col 6, odd-even 206, even-odd 139 

On the as1sumption that :.; is a short column, col 5 would contain letters 4:~54: and I • col 6 let,ters 55-65, showing 

· ool 5 

odd, 

3 

2 

3 

4. 

0 

0 I 

A 

D 

F 

G 

v 

x 

even 

4: 

4: 

0 

1 

l 

0 

col 6 

odcl even 

3 A 0 

3 D 4: 

3 F O 

2 G 1 

0 v 5 

l x 0 

Vieighted F'req as before: 

col 5, odd-even 137, even-odd 160 

col 6, odd-even 138, even-odd 189 

Both 5 aDd 6 are now minus where they were plus beforeJ but what is there at this 

I stage to show that this is wrong? I 

I 

•Ihe term: "transposition rectangle" seems to be used in two contradictory senses. 

Here, and! in the third line below figure ' (page 5) it means the rectangle after 

transposition has taken place; 6 lines above the bottom of' page 6, on the other 

hand, it ~9ans the rectangle containing the message before transposition - or I 

so unders~aud it • 

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·. 
... 

REF.ID:A99873. 

'Ihe ponclusion tha . th~ fl rst 5 columns are long is Ti tal to the reasoning 

of po.r,e 6, which !)laces column :? in the orisina.l transposition rectangle. And 

even then, the column is placed throu~h the presence in the twelve messap.;es ot 

a message: with one additional short column - a n~w piece or good fortune to 

add to thpse already mentioned. 

I ah,all be much interested to hear what the message solvers say on these 

points - and glad to be corrected where I am wrong. I 

Uordially yours 

c~ J·~ o_,j_ __ a-J'"- ~