) 

TOP SECRE!F=~NOE 

INTRODUCTION 

This series of' "problems" is the outgrauth of' 8. higbly informal. 

discussion of "phenm:iena" presented to a recent gathering of certain 

technical personnel. of operations, at which time passing reference 'Was 

made to historical solutions, citing certain properties which bad 

to be no·~ed before further analysis ns frui t:rul. 

• 

The idea occurred that perhaps a series of' example (in which one 

&>es not have to reconstruct entire messages of plain test, etc.) woul.4 

serve as a use:f'ul adjunct to the ordinary crY,Pt coarses. It is realized 

that the ground upon which the autbor is treading is tar from firm 

-- opinions as to what one might-be expected to observe and eon.sider 

"phenomenal" -dif'fer! A1so1 hind-sight-often blinds one to the f'act 

th&t even so-called obtt.ous properties are often obscured 1n a person's 

zeal to tackle such a problem 'from all. angles at once. With so :mm:cy" 

things to look for, "it is surprising that so often the weak link is 

spotted relatively quickly! 

It is nry- feeling, however, t1'.at as an over-all. indication of' a 

person's ability to react quickly to cryptographic stimuli, these probl.ema 

might be an ihteresting cba11enge to those wi10 are desirous of testing 

their perceptive judgement, at the same time offering a cbance for 

learning a few of the countless properties which have been encountered :ln 

the past. As experience is probably the bi~gest fo.ctor. in success v.I. th 

these (along with c~tanalyi:;ic :l:maginat:tonJ the acolyte is at a serious 

disadvantage, but on the other hand has the opport-unity for greater 

rewards as f'ar as gaining information and explanation is concenied. 

For the benefit of the aforementioned acolyte, it might be worth 

out1ining some of the possib1e approaches and "thinga to look for". 

Some properties are obvious (usually properties of ident!ft' rather 

than. relationshi_p). If' a message uses only 10 letters or the , one can h&Tdl.y help but notice the f'act on simple inspection! If' every 

fourth cligit of text is a 11 2, or 31 it might take a few more gJ.ances 

to notice. 

Many properties are latent however - in keeping with the la:wB of 

physics one DDlSt put some effort into the operation to prodl.lce a 

"phenomenal" result. This lilanipu.lat:l.on: might involve more complex 

establisbmt-""llt of iden.tif'l (unusual frequencies, heavy vowel content, eta.) 

or else an establishment of relationship between individual positions or' 

groups (by subtraction, comparison, sequential relatjonship1 positional 

;relationsh"lp, etc.). One DDlSt be familiar v!th established procedures ind technical vocabulary, such as d.if.'f'erencing (major and min.or), delta 

effects (horizontl\l. or vertical), isomorphs, sum•checldng; sliding cribs, 

and the like. No attempt "is herein made to clear up any questions Which 

.ICC'ise in regard to tecltniques, and it is assumea. that answers to such 

questions are readily available elsewhere. It is felt that in the process 

TOP SECRET CANOE 

ursu nt to E. 0. 1352 
ot doing theGe probl.ems, certedn techniques ZlOV unfamiliar to some 

individuils, 11111 becom cl.ee't" o Certain statistie&l. measurements such 

as· the IaCo (Index of Coinc!Ld:en.ce) shoul.d be~ :f'amili&r tools,· for 

eumpleo Cyclic properties "" e:Lt~ of' idml:t:Lty OT.' relationship 0 

that show up only wiien a given 1ntenal or v:f.dth is considered,, are 

obv:toulSly no·t; to be igo.oredo 

Appended to the collection of problems is a brief' discussion of 

the basic principleB involved in each,, oftc \With ref'erer.ce t.o the 

actual. system. 1.ipon 'Which the probl.em. is basedo The orig1nal. historical. 

problem. has somet:im.es been -dil!lltorted alm:>et beyond rei::ognition in an 

attempt at aimplif'ication·- the gmieral prmcip1e bas been the gos.l 

rather tbe.n specif'ic application,, aud no pr6tense is 1D2lde that one 

ooal.d. learn about the actual historical problem (Germ..\'t keyvi'ord,, for 

exmple) by reading the appended re:mm-kso It is hoped that. later a 

m>re complete, bibliography wou.1.d ~ble the reader t.o fol.lbw up on ffD.Y' 

point to get the true f'acts of the cue rather than a emattering of 

concepts,, but it is :f'elt tb.&t 8Uch au attempt is beyorul the scope of 

this preeeL.+..ationo 

One :f'urther cmti.on ...... the read.el:' aboul.d :cot spmd &'IJ. im.d:ue e:mount 

of time pcrw1ding on &rJ:9' givm problem.a If a 0 reacticm" ia ?1.0t f'orf;;h ... coming &f'ter a relatively short: t~ (~ in m.inu.tee mthftr than 

hours) we eoul.d best pr.ofit b:r aecept:f.ilS the ~.ti!~ in thr! 

appendix_, a:a.d tu.r.!J.1.ng to the !I.ext p:roblm..11 (it ie to bei hoped,, Yi th one 

more 1J1Sll!Ory cell al.erted f'or possibl.e r.eQae-ll.r1"e21ce some time soma place 

of' the llll8m! phencm:l~.na) .. 

TOP SECRET CANOE 
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PROBLEM I 

Following &'l"e common groups of a certain code: 

2912 

0741 

6635 

7175 

2462 

9313' 

It is suspected that some time off set ju.xtapostion at the f'ollow:Lng cipher 

represents an overlap. Can you eonf'irm this suspicion, af'ter an examfnation of 

the code and ciphert 

A Lo4.73 9615 2807 1131,. 2886 7130 5520 0106 7022 8349 3471,. etc. 

B L3202 7736 3988 5217 0514 8261 4917 8372 3036 8971 4592 etc. 

PROBLEM 2 

:i;s·there anything in the f'ollo1r!ng list of' cipher beginnings, sorted 

by date, which is phenomenal.? 

DATE (1) (2) (3) ( li-) (5) -

1/1 09411 02178 91380 55079 65503 .. 

3/1 77365 20li-17 89103 75319 77168 

7/1 31Jo51 61239 76219 20132 52587 

ll/l 16737 511-188 lOll.6 17083 34198 

l.3/1 41070 75034 86705 1'o930 02930 

19/1 02918 91725 59741 62622 09164 

25/1 63152 83132 30247 60030 76293 

2/2 49052 44o68 45088 98967 73108 

3/2 34701 78643 655~9 ~553 89121. 

5/2 81098 91227 70342 48138 4o333 

8/2 27763 33198 61982 93000 72847 

i'6l' S!lO!mT 

SGJRl!F! Il!ii'OHWs:'ff6If 

-1-

TOP SECRET CANOE 
{ ' ' TOP SEffifHDfAS@~NOE 

PROBLEM 3 

What do the i"oUcnr:i.ng beginnings of message suggest? 

PROBLEM 4 

ABURZ DAnB 

BSKTI IMA.CL 

IMUH DDORC 

OOSGS WZDBA 

ASEST CLGSK 

DNCUA BFRm' 

QFTAU FUQ;E'I' 

I<RJIJ BEFSE 

HSIKU IIRVF 

MAGMK OGVTJ 

BPSVV JGAED 

EDHSS MIDIU 

BGDVY ADBWC 

DHLBL T.BQJIU 

EPRNA NIO..."%J" 

EAMAC ZiPBV 

FQCTA WJNRJ 

FQCTA W~J 

INOAN AOQHS 

GOQON OOWKF 

CRSOB DUXZM 

IESPD REIST 

OIPUV XMPSH 

NHB.UR XINGZ 

ACOCO PLIQO 

DSPAO WPYUA 

.AANVX QAWCR 

OAIQE VYSTG 

CROBS YJZXH 

NDmP :EMZKY 

LNHD'I' RUVQl. 

FJMDQ CAIWF 

ONFOF BNAVM 

EBFRX SOBRX 

QKBFR UBWDN 

QKBF.R UBWDN 

P-.LAEG APCOE 

What explanations a.re possib1e f'or the manifestations of the 

following cipher: 

2193 4'709 2890 1919 2703 8193 4743 6232 7890 6623 7703 

PROBLEM 5 

Can you detest any property of' the following: 

19273 62019 09821 31988 

PROB:GEM 6 

-Country X is thought to be using a doub1e...additive system,, involving 

an 8-1etter keyword Which somehmr designates two starting points in a 

series of additive 1ines,; both additive streams are added to the pl.a.in 

code to obtain cipher. In testing possib1e cribs (with a recovered code) 

when the f'ollowing crib is ru..'l'l. against the cipher,, certain. evidence about 

the eypothesis of double additive is obtained. 

Crib: 09436 02145 00107 

To be tested all Juxtaposition.so (lsto group of plain against 

1st. group,, 2nd. group 3rd. etc of cipher). 

c 

• 

Message: AEROABRO 19274 24983 72109 01~74 88583 20363 65438 71002 . 

NSA Form 781-C13S 1 Jul 52 TOP SECRET CANOE 
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TOP SECR1E1F~2\NOE 

'What :i.s the peculi&T"ity of the fol.l.ow:l.ng portion of cipher text, and 

What might it imply? . 

PtJRFH TCFGU OLZDX CBZAR~ JOEZB NWZA.O 

PROBIEM 8 

Backgroundg 

This country's min system seemingly invol.ved one ... time usage of 

l.i teral. key (or unique settings of machine encipherment ) • In.dice.tors 

seem to be first groups, as in the pastsi these groups were patter.nized 

and progressive, e .. g .. , AABBC, AABBE, etc .. 

New series of' messages show no repeats of l.etters vithin first groups, 

and no continuity from message to message, e .. g. XRBDA, LOARQ1 etc .. 

Eventually one reusage ( 'l) of key vas noted ... two message With first 

group identical. The I .. c .. of these two messages,, when comp&T"ed ,, was 

a;pproxilllate·ly l.Ba 

In the process of an&cy11is, dif:f'erences (on a normal. alphabet) -were 

taken vertically (message B subtracted from message A) nth the i"ollov.ing 

tabulation of' occurence .. 

0 l 2 3 4 I 5 6 7 8 9 10 •11• ·12· · 13 • 14-: -::15"l 1.J.6• .17"• (181',19, ~20 21 

~ 28 13_19: 11 16 15 23 15 18 18 . 19 · 17. 16 ll 12 u 19 17 18 10 15 l.6 '-" "'u .... ' •• 

22 23 24 25 

19 J.O ___ J.? __ 1! .. ~ -- - ---- , ·--

Can you detect and explain the p~rtyvhich instilled sufficient 

confidence to emab1e the reading of the de.Pth? 

PROBIEM 9 

PJJ a separate problem to the preceding, the foll.owing key was recovered 

by reading ·the overlap mentioned,, and the property ten.tatiV'ely established 

that each line of' 25 J.etters of key consisted of' 25 unique V&lues of the 

26 possible .. 

CAPHOF"a.BKGMDQYSEJ~ITJZW 

:JKSDBHCm:rmsx:QFLZAWGMOVN 

RMCDTJOBUNFAKHZLoooetCo 

On the basis of cribs the following additional. key looked reuonabl.e. 

Can you predict any subsequent key? 

Form 781·C13S TOP SECRET CANOE 
' ) 

RBKWYEMCLZAGASJVHWQI'rP"'UOF 

HIJGT".NR 

PROBLllM 10 

t' 

What kind of system does the f'oll.o'tfJ.ng case of' two cipher beginnings 

suggest? 

L389612J.r.o15a329111125109B11-8613 

• L38961791a109091a316892974I.611 

PROBIEM 11 

Foll.Oll'ing is a list of first four and last four digraphs of' a series 

of' messagens,, sorted on f'irst dignq>ho (Evi.aence h&s been noted that the 

&Y'lltem. is probably a book-type li tereJ. key ul8ed to encipher digraphs from. 

a buic chart pageJ> and rowacolumn coordinates of' the starting and ending 

poitlts are probably indicated.) Is anything apparent which might :f.nitiate 

solution of' the indicator eystem.T 

AB KL OR AHouSS XA IX CF 

AB CR BA ZioooKE'.AB OS OI 

AB OF CL :ow;;;T.P BR VO IJ) 

AB KM HI IG:: :EX YQ DC AQ 

AB ZL BI ISoooYQ AC RZ OK 

AC PA FR OB~ o ~VP AA BF MB 

AC RL ZC AK~~ ;AB OV CJ BB 

AC TD NN ll"~o ;TJ ZX AH TV 

AC LZ TB MB~ooQV NJ MA SI 

AC CN DG CHo o oXT AB KZ RD 

AD BR RS NUeooKZ GI KV SK 

.AD NO EL VPoooOF ER DN NT 

AD OV ML EE.,, oNG AD OV LE 

PROBLEM 12 

A cer-!iain system with plenty of' traffic,, has a type of' indicator which 

is probably not guing to yie1d to ordinary ~is,, however, certain 

depths (?) sem. to :lmply Nniee of' key,, probably from a key book.. Can you 

note enything about the f'ollOWing tilO message111,, seemingcy in depth, which 

wul.d sugge11t an obvious method of' attar-h on the entire syatem? 

10913 6428 1097 6819 22S1 2908 437G etco 

za:;13 6428 0322 0731t. 7365 2908 9281 eteo 

S=mfff lid' ORMArlOi'f 

Form 711·C13S TOP SECRET CANOE 
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PROBLEM 13 

Three isologs (same plain code, diff'erent additive) are au.apected in 

the f'oll.mdng cues. Is there any property which would enable you to 

make a eonaecture about the~ of underl.J"!ng additive'! 

A 16851~ 69919 39414 7032Jt. 02849 

B 36852 48787 31638 68223 02811.8 

c 58071'- 36686 53850 89"-5 91738 

A 43351 1811.l 71353 96670 

B 4o127 o6090 69232 91'650 

c 85570 32333 58121 05761 

Count:ry X hu been using one-time additive on 5"'<11git code. 

Additive padB were serially numbered ( d.U'f'erent series on each link). 

Pads have 1&8 grou1111 o;t. each page, v:Lth pad number preceding each block 

of' 48 groups.. Thlis.11 the first group of a message might be 0001, the 

50th 0002, the 99th 0003, etc., 

A.body of traffic shoved u11 such sequence of indicators yet unrelated 

4-digi t numbers were intersperced at the proper intervals.. The following 

is a list of 'Pad ( 'l) number11 as they appeared in order of usage Vi thin 4 

separate links, gi Ying the groups immediately following each li-digi t number. 

Link A Link B Li:Q.k c L1nk D 

Enc., Cipher Enc-.. Ci;eher Enc. Ci;eher Enc. Cipher 

Pad 

~ Pad Pad 

7772 32179 4o713 5572 45945 6~ 57764 

2873 28103 5342 33101 8016 8345Jt. 3779 44851 

3331 53520 3166 75919 7957 04416 0724 811479 

3139 55684 7732 52818 0130 . 20192 8248 37657 

6849 71902 6993 98358 9804 58217 1079 75~2 

266o an29 5906 38061 38c4 1728o 8o82 39320 

31li.2 55900 3813 81282 5116 91305 2860 60553 

3878 61199 5619 30260 1759 36429. 6203 57808 

3149 55991 0503 47036 o493 27516 ~26 146lf.1 

7603 10955 6936 98938 880JI. 82270 

491'.4 98337 

758o 17o48 

c.5 ... 

~p SEleBB! 

OB7JeRH! fi&lleRMftfteff 

Form 781·C13S TOP SECRET CANOE 
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PROBLEM 15 

The ftlll.atr.f.ng key represents the first 4 groups on several one-time 

pad pageso It is SU8peeted that some simpl.e device was uaed to print 

wccessive pages.11 but the order of generation bu been shuffledo However, 

oollatera.1 inf ormettion implies the f'irat two pada listed happen. to have 

been generated eeqwmtlyo · 

0439 9305 1237 9981 

4337 7942 5896 7705 

4284 78~ 5103 7057. 

6104 2187 4643 7057 

3396 6932 am. 6742 

7761 5770 0365 5638 

5652 0163 9722. 0753 

0955 9710 1425 9674 

9971 1998 81R>1 1732 6 .. {ll 276o 4915 2690 

7l.8o 5129 0744 5559 

1076 8492 3871 8342 

1755 8664 3952 8194. • 9688 J.623 8900 lll3 

3203 6886 2llf-9 6027 

2622 4513 7628 4279 

Bl.28 3559 6680 3269 

0580 9257 16o4 9819 

3782 6653 2388 6163 

4725 7614 5322 7173 

83n 3960 6455 3770 

2416 4970 74ll 4798 

5466 0398 9061 0932 

6o97 2035 1'896 2445 

9849 1801 8539 1086 

PROBLEM 16 

The f'ollowing is su~cted to be the l!mne plain text of two messages 

enciphered by a 1dmple 5=\Theel H&gelin device ( nonco0verlapped) a Is 

anything apparent which enables the reconstruct:J,on of at l.eut one portion 

of the machine 11 s set ... up'! 

( 1) BSD.FF IMTUO RYAWQ EFJTF BdRVS OSPXQ VUGKS BPmB OQVMB 

(2) BSDFG XMTIA F"iMKC IAXAM QSV'l'.F VVFVE CEDXC JUSYE BPlIZP 

PROBLEM 17 

Thili!I is a me!SM.ge md a reflilmd liilent the next de.yo 

, 

SCDS CQPJ PXRH NHCJ llT.BD SBFM '!CBJS Wl'm' nro PKMD QRM MCDlJ' ~ID HIPP 

sens CQJ?J IXDG )1EPK LWCI SCSN' MCHQ W!CH YKUO OKNI QSDT STAJ QPAT Gl!'(J{ 

'!BRB PFLY LBPD KO'fK UWBF GFIB BROP BQKI ll'KB DDLO KNPP SDIB KBRH PESS 

YCJC MDAY K'!OD KE"fJ UWCH FJKS CSBL CQJH KQJ:C DRMP JMLQ SAAS LJSG I.NCR 

FMm 7Bl·C13S TOP SECRET CANOE 
I 

, • 

TLRL DVPB HR.CC RPSS PCJH IIWA BC~ FSi\1 KHC¥:: CLQK BIHK BFNC SQ;LI QAGY 

RR'TR AVW JSBD SMRQ LPKG EFWB SBQP RRRD IJQB DMQ;J' IJ'HL CSAP SQ!\:&' RBFY 

PQSS ABBQ BI.EX 

IRSR OHCQ C.AMX: 

PROBLEM l.8 

What ·type of system d.ceil the foll3"lng melili&ge wggest,, and how f'ar can 

you go in deciphering? 

EBKDV CGJKN OVYGC KMJVP HNKSV 

ERGKX BVDJK YVZDI KOMVP BFKXV 

BTZKM RVXKB VEGCK MIVDO HKNFV 

ZIJKX AVYTK DVBKM VOELK CNVPS 

YKElVE GRI<XB VCHMK BFVCE IKNVJ 

XKYGV QUKCW VPARK XG 

PROBIJJM l.9 

What are the .propertiersi of the folloY:ing :modified en.mpl.e of certain 

pages of' additive? (The !lize of the page hul been reduced f'or purpose 

of' 111.wBtre.tiono) 

00811.9 12593 1'.4620 35201 96070 

34165 31521 34298 58736 l.2184 

22017 23371 73817 791108 39721· 

38496 6"855 04629 87589 84165 

79774 6o8o2 59631 o6965 03452 

23015 07764. 15782 31021t. 58967 

56162 96<>48 87c65 2671.v.1 9l36o3 

83598 49978 30159 21439 J.i.2537 

PROBLEM 20 

wzno 

The folloving represen:Ls a typical page of' !my used by country 

How would you dermcribe the property- wbich appeare? 

14792 81469 57035 02479 5811r.7 

36925 1.4703 92580 57036 25703 etco 

PROBLFM 2l. 

In the f'ollcnring 11erie11 of cipher beginnings it 'Will be noted that 

there 1rs one point between mccessive col.umue through which off'c.set repeats 

do not pus u hits.. (They Dl'1' pick 'Ill' again u continuations o'f hits)., 

What rs:l.mple explanation il!il there for thir!B? 

'fOP S!'llimT 

smYRPP.l Iil?e:RMA'ftO!f 

Form 781·C135 rFOP SECRET CANOE 
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. 

PROBIEM 22 

TOP SEORBIFN@>NNOE 

P'wODGTZHQWmlJXHUU 

OAZPWODGTZVEKBNVY 

AQWTZPWODGmmm.ID 

TGHZA.QW'l'PWCRUBNIU 

KPZTGRNAZVENOEKBN 

TGRNARPIZAEKIINDKC 

PWODGTZHKXUNUYWXJ 

RQWTZVJTGGNIYNNOE 

OAZHQWTZl!JRUUNIUL 

XHQWTZVJ'l'GL."fIYNNO 

ZHQWTZHQWTlf.[YNlD: 

The following cipher count suggaat in general. what t~ of encipher ... 

amt (~aum.i.ng underlying plain ... text rather tban code)"l 

A 14 

B 2 

c 4 

D 6 

E 15 

F 3 

G 5 

H 7 

I 13 

J 1 

K 3 

L 8 

M 7 

N 6 

0 12 

p 8 

9 9 

IJ 9 

s 7 

T 7 

u 14 

v 7 

w 8 

x 8 

y 16 

z 9 

PROBLEM 23 

The beginnings of a large "body of traftia1 lih,m enmdned Showed certain 

1ettera to have a very low frequency :Ln certain columnso Thus, in the 

first col.umn, B 1 N and X were either absent or low; in tb.e 11ecorid co1umn 

A and U ; in the third K,, M, and QJ in the fourth Bend Y; in the fifth 

E; in the sixth R and s.. What type a'f system aces this sugge111t"l 

... a ... 

mp SEeRm 

mm:i:w DP9BMtd':I6lf 

Form 781-C13S TOP SECRET CANOE 
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.... 

PROB:raM 24 

In a l.Ong cipher mes1111age a signiticant rei,peat showed up1 beg:fnn:1n;t 

at the 103rd.'i' and 51'.5th1 pos1tion8!11a In addition, a eignigicmit iso:r:morph 

'WU observed beginning Yith the 16th, and lOlsto position.so · ilthough 

many explana1~ions &'re 1ooeely "posa1ble111 

6 Vh&t epeaif'ic ids might you 

be inclined to purwe? 

PROBIEM 25 

A certa:i.n country has been Im.ow. to use a 2e.part code of four digit 

groups, enciphered v:f.th book adclitiveo Indie&torl! in the put have listed: 

which book (of' 3 or 5) /1 2 ... digit page» m:ul row and column coordinatee, e.g., 

Book 11 Page 53,, Row 6, Column 4o Thill starting point might be indicated · by two la-..dig:l.t groups of various patterns.11 using the· extra dig1 ts as checks; 

by either sum-checking or by- repetition. Thus11 Book, Page units, Page Tena, 

8lld the sum of' these three digits (abbreviated u BPPS) would· be 1539 in 

the above example, and the raw ... colunm.a, checkied by repetition, voul.d be 6464 .. This plain indicator (1539 6461f.) might be enciphered in various lMYBi of'ten 

by mean.a of & 11epsrate cha.rt of' 1.00 8codigit additivesa The control for 

this additivei (ioeo11 which of the l.00 indicator additiVtJS were used) might 

be hidden in the meaaage, or actu&lly dependdJ'm:t; upon fixed positions of 

cipher; f'or eDmple6 the first 2 digit&§ of the 4th group might be used as 

such a control. Even the group count u tramrm:t.tted might ba used &!I part 

of the ~trc•lo The enciphered indicator might appf:ar in variOU.11 precs 

arranged plac:ea f'or given pj!riodo OccuiOMJ.lly a check on the ending point 

might also be. made by inserting a Moond indicator tonrd8 the end of the 

mel!!lllll&geo The: probl.em given invo1wa a conl!!lirste.n.t method of enciphering Yith ... in a homogenttOU& periodo (Sorted en firrst group a) 

0238 ~58 5312 (!Ult three) 4301 1750 1007 

o475 0953 2936 l.8ll 9317 6022 

1418 8561 0393 1799 1390 28o8 

2387 6216 2906 08ll. 121.8 2880 

• 2422 5959 7178 5338 1703 3124 

3757 3345 9021 2Ji.87 8430 7103 

3956 Jr.J.66 1268 3625 6643 Jrlt.65 

4703 9201t. 9317 5034 1709 8130 

5223 21Ki8 lll.7 l.919 IJ.731 1529 

6790 8686 0778 9478 6o23 9289 

7631 9921 Wl7 0676 7173 9877 

9217 3326 2308 1'o31 2802 5466 

9502 2235 5518 .2518. 9513 3346 

9598 8517 2417 1108 2062 7070 

.,.9 ... 

~p SEeBE! 

~P.1:¥ INFSBIWHell 

Form 781·C135 'POP SECRET CANOE 
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• 

PROBLEM 26 

This problem is related to Problem 25, with the same coliutry and 

genei'al t;ype of 1ndic&tor involvedo In logging messages, a clerk"'" .. noticed certu.in ::eec:ru.l.i&l" behavior of' cipher d!gitso What pheilomenon 

of these groups (the first 4 of each message can you detect, and bmr 

far can you go 1n recovering certain elements? 

9221.i- o66l. 91.i-99 1200 

2715 4254 1272 7184 

4134 4931 66oo 2$!77 

4139 4953 9898 5881 

0021 5156 7705 3324 

4090 71'.94 8988 9755 

1900 TI9' .1531 9835 

2901 243 UJ.6 5687 

0590 5330 6644 I 0006 

8216 6756 9490 1230 

3178 7472 928o 9667 

4920 oll-23 5659 0713 

3521 7349 4494 3205 

673)&. 32Jr.o 3209 2370 

4172 0450 99~5 4462 

2817 6173 23o6 2569 

0059 8656 5201 0202 

0769 3031 7736 1367 

J.691 9574 4411 9422 

J.800 4337 0991 0349 

3018 7972 6837 l.975 

5967 0501 0707 7979 

6172 3724 23o6 2569 

5253 7209 7194 3812 

6486 6Ji.6o 3108 3576 

3576 4336 7833 96oo ' 5343 3662 U67 l.902 

642Ji. 03Jr.o 1482 Ji.593 

3335 4572 5829 4771 

2901 2434 6837 1975 

3281 5633 5891 5285 

7102 6092 cir.Bo 6167 

7005 2922 962Ji. 6429 

9980 4242 8622 08311-

9129 Oll.O 8892 1196 

7202 3958 7408 4327 

9215 6373 3410 9813 

8833 3414 8864 8791 

8396 6044 8123 J.625 

8964 1731 2826 4315 

9907 6754 1477 4533 

la-050 0932 8811 8799 

2901 2434 2222 6655 

0053 5947 7l26 3815 

2411 411-59 94o8 1227 

45Ji.9 4llo3 7823 9625- ... io-

!LlOP SEeBB'f 

5HeeR!i¥ fHlileftMl\l!!e!f 

Form 781·C13S TOP SECRET CANOE 

* 

.I 
I 

' 

. ' 

PROBD!lM 27 

It is suspected tbat the following two messages were enciphered 

on the same page of' additive, and migb.t overlap at some point. Can 

Y?U prove the case? 

A.. 8276 6498 6629 3081 7416 8811 3905 4578 aJ83 6283 17o6 

Bo 2287 2538 9092 6255 2830 6558 5015 o685 4710 9210 8863' 

PROBLEM 28 

The f'ollow:tng ciphers were received a few days apart. 

Ao RimC IGEOE NHNSR FYGOC OPOGS llANSD NEPEA. Ml!:B!m mmK EOAIB 

COORU OEEFI EIMAL KRNXX 

Bo RUORC OPOFY GTSDT MEO.AL .ANSDN EPPCI GIMAE EFIEG SRIKR NRTSI . 

EAMEE OEHEC OOBRF EHNSR 

PROBLEM 29 

Indicator evidence not ahovn implies the f'olUnr.tng messages start 

at the same point 1mm additiVl!f booka Can you detect and u:pl&in a 

property which should yield a quick relative sol.ution? 

Ao 90219 22043 20699 1Ji.Bo2 22127 92817 etca 

Bo 67436 94200 97816 23356 9671'6 14372 etca 

Co o69l.6 50742 13709 55906 01235 83969 etc a 

D. 90216 61488 26699 J.6994. 22122 43083 etc. 

E. 29114 62823 31'679 83123 94020 43206 etc. 

PROBLEM 30 

• 

A machine cipher is being employed which necessitates lmor.f.ng the 

setting of 10 'Wheels, of 1.ength 151 1.51 15,,. 151 10, 101 171 191 21 and 23 

respectively'. The first end last few groups are likely' candia.&tea 'tor 

disguising the indicator. Can you ~ver the entire indicating system 

on the foll.awing n..ssa.ges, the first of' which baa been read and c1eflnite~ 

fixes the first f'our Wheels (each length 15) at the 3rd, 5th, 1st and 8th 

setting point, respectively? 

Form 781·C13S TOP SECRET CANOE 
. ' 

\ 

, TOP SEC~T~~A19NOE 

First 3 Groups 

DABFQ MECDQ osmru 

BroDS MNMQ;P JRIIIS 

CFAED CWFY OINHJ 

DSBXD BGGBN QQOUB 

XBBHC ERVlN ISBHC 

EOQRQ MRWIX DFJLK 

ACOBA QXQl?S PP.FV:B 

RFQn BWIL LIVRD 

QM:BJm' BACl'D XVSLL 

SDZSO QBAID!' mMlW 

FHMVQ FSUE.'Y JOSSN 

MEXQJ3 SWDSG VICOJ 

HAXCM ONTDQ TAGXB 

OODEQ AlOOBC ISHLN 

VRVAQ MBBRB KSLWW 

PROBL!M 31 

Ia.st 3 gmu.:ps 

HRBDB 00.QI .APRTI 

KYOIU LtRTL AMA.IF 

WOLKJ RQWPT RGDQJ3 

JWIIN TCKVT LBBJM 

.ALKDJ VLtJR PKGKO 

NV'l.'UC PNIKF AFOEV 

IISGE WRNKW IVlFC 

HGXVW KQIVL LOOEX 

VlREQ IAJLQ llmQT 

:rx:w.I'.r CTVCN IIMLQ 

cmoP Q.TAGI QCDPS 

T0mrJ APVIC CO'l'CB ' 

INZNY JWVRA NMBTI 

mw: BBTPI WPRJR 

mmE GKGWI .ALtKL 

Foll.oving are three messages auapected to be enciphered at some point 

on the sa.e page of additive (not necessarily l.eve1 starting). Can they 

be maae into a depth? 

8978 9813 eao2 2411 !1367 4609 709~ I.83Ji. 77'J6 47013 4o83 S1Bd ... :21!1J6 etc. 

2091 2846 3986 8019 3468 6013 TI38 4081 6613 2879 8931&. 8199 3768 etc. 

7768 0124 4879 0811 1'<>36 8739 3681 6911 7083 3681. 8224 2571 7698 etc. / 

... 12 ... 

---

Form 781·C13S TOP SECRET CANOE 
. • 

. 

> TOP SECRETA8~NOE 

PROBIJ!:M 32 

Follo'ring are several messages sent on one dq: 

1 .. YGMKX BESDF GBKOD GAWZD tJTMLK etc .. 

2o FDHCJ NEGPB NVDSZ HZJDE A'WDJL etc. 

3 .. .ARZDZ BMKw.B MEHI CJ'NDR AWrzJ!V SMKOL etc. 

4. Q,'BNVE SZilK EEBMF UDKHW DDIAL etco 

A message on a different de:y' beg8.11.: 

PXDAN RUJUV XSADV YU.AYO VWZRQ etc. 

PROBLEM 33 

FolloYing are three insomorphs in a :f'ractionat1ng system. Without 

spending &IJ.y great deal of time attempting to reconstruct the el.ements1 

can you g:t:ve a reasonabl.e eypothesis as to the manner in. 'Vhich the 

cipher differs? (The next problem otters an opportunity for more 

CC>llq)l.ete reconstruction. 

EAXGCZKIADRSMNZIES 

XYCULKBEY.BNRFPREX 

DXBAMLIWXROQPGnIDQ 

PROBu:M 34 

In a ayatem. s:tmilar to the above., it 'Will be noted that the three 

isol.ogs are not 1801D0r,phic. However., the messagea should enable you 

to recover certain of' the enciphering el.ementso 

1.. ANOEK RACSY LBCJP RUJOOQ RXMIC OVUSL IFZON 

2.. .ALQUD RZD.FY EIKBY IBRTO EJLUG BPQSE QXVOL 

3., ECJYH ZTOAK UNOP HZEPM GQQIP NQZSK TORJC 

Form 781·C13S 'l~OP SECRET CANOE 
~ 

• 

. . REF ID:A59039 

TOP SECRET CANOE 

PROBLEM 35 

~ follow:lng are known to be enci~hered indica:tora. TheoreticaJ.U:, they should show a 3.,d1g1t line number (the starting point ot additive) 

Checlted in some way. Is there miy property which .. ' vould yield to solution 

of' the indicators and possib1e overlapping? 

PROBIJ!M 36 

2037 3201 

2065 3245 

2905 4565 

Ji-746 7J.i.58 

1253 1969 

4o88 6424 

0189 0297 

3752 5896 

5Ji.7Ji. 86o2 

0791 1243 

The f'ollmr.lng isologic begimllings imp];y vbat izype of encipherment'l 

(In ybur reasondq, you will probab:cy determine the actual. plain text). 

SEOGVIQKKAOCX 

ZIMHTLVRGBRYT 

WNNHSPPGMFXAW 

TGOEZHQGLZWWV 

LTONTJRBF.ARUY 

VMGKUHNEJHQIZ 

SBMJWMtJENGQVR 

RMFJBEUCMYQAX 

Form 781·C13S TOP SECRET CANOE 

.. 
. . . 

• 

PROBIEM 37 

What can YoU say about the foll.ow1ng group•~ 

CVBNM GFDSA MZXCV ERTYU 

IASD.F XCVBN BVCXZ RTroI 

KLASD 

PROBLEM 38 

Follor.lng is the beg.lngiing of a message, &nd a resend the next aq. 

A property can be noted and W:1 th suf'ficient background on a particular · 

pbaae of conmunications an even more specific phenomena can be explained. 

A. :BQ;EU5 DEQBK 8DA5S 

8FuXY WU.Jm EFQ,'BK 

Bo OQ7LG D7POO V31JG9 

BFIMY WURHI ENPOC 

• 

FOJ"m 781·C13S TOP SECRET Ci\NOE 

> 
> 

• 

. 

' 

REF ID:A59039 

TOP SECRET CANOE 

PROBIEM I 

PROBUM 2 • 

PL 86-36/50 USC 3605 

EO 3 . 3 ( h) ( 2 ) 

One of' the more ~ mtl:wd11 of indiCll.tm' enciphexment involves 

the 1111b~tion of one gr'OUp f'rcml mother o In this cue the second group 

mbtracted from the :f rO'U.:l:'th in rnqu.ent me81Rge11S yiel.dll the interesting 

aeries .. 

At f1r111t b1ush it might appear that the last three digits of this differenc~ in them!!lel:veliil f'om the only 11tartling pbenomena.1> and perhaps 

imply the starting point or pad n.eima of s11ccesi!ive encipher.men.ts,, How .. 

ever, the progrel§lrmion of the :firBt t'\lm dig! ts when noted and aualyzed, 

shows that the two digit date lDUllt be wbtracted from the fourth group 

(With c~) before the---;ioond group :I.rs applied ('Without c~) 

to form a uz1i orm. Beriers o 

-'+th Group 

55079 

75319 

20132 

4th Group Lei!& 

date 

51to79 

72319 

13132 

2nd Group 

02178 

ooJl.17 

61239 

Indicator 

52901 

52902 

52903 etc,, 

Form 781·C13S TOP SECRET CANOE 
' , 

REF ID:A59039 

TOP SECRET G:l\NOE 

PROBIEM 3 

This is typical. of the aspeci&lized problelml vbich are obvioua to 

tbose experienced in certain pbUes of' the vork, and not necessarily' 

m,eaningf'Ul. to otheresa The limitations of the first s:llc col.tmm8 are 

such that there -:t:a a point in the alphabet beyond Vhich no cipher · l.etter appears ... .,. in the first col.umn thi11 "absence" area is R to z, 

in the second column T to z, etca From the positive viewpo:tnt, the -

higest l.E:tter used in these col.Ulllll8 ~a Q3 s,, u, w, Y, (and Z) respective• 

l.yo In terms of' numbers, the limitaticm.s 17:i 191 21.1 231 25 and 26 

would suggest Hagelin indicator& to anyone who has been exposed to the 

machine a 

PROm:;EM 1,. 

PROBUM 5 

A simple example of' a FIBONACCI series, (this t:ype of ke1.· might 

be used by an agent for enmp1e3 Who cm remember a short s~etch of 

key and generate a much longer series fTom. it), in this case, the f'irst 

and second digits are aummed to creat!.the eighth,, the secon.d and third 

to create "the ninth,, etca · 

Form 781·C13S 

PL 86-36/50 USC 3605• 

EO 3 . 3 ( h) ( 2 ) 

TOP SECRET CANOE 
. 

' 

A more complex Fibonacci series might be: 

Can you analyze it? 

' In actual cuesi such Fibonacci usage as has been determined hu 

been oftentimes :much more compl.ex; sometimes the· user 'W'ill go through" several steps of' combination of different aeriesi using a f'fn&l. version 

which exhibits no propertieai yet-is based on two or more aeries 

(unused) 'Which do have propertieso PL 86 _ 36150 use 

PROBLEM 6 EO 3.3(h) (2) 

NSA Form 7B1-C13S 1 Jul 52 TOP SECRET CANOE 

3605 
. • 

PROBLEM 7 

NSA Form 781-C13S 1 Jul 52 

TOP 8EG1¥6?r1t1.L~OE 

PL 86-36/50 USC 3605 

EO 3 . 3 ( h) ( 2 ) 

TOP SECRET CANOE 
PROBIEM 8 

PROBLEM 9 

PROBIJ!M 10 

~L 86-36/50 USC 3605 

EO 3 : 3 ( h) ( 2 ) 

The difference between the two ciphers given is: 

Those experienced 'Vlith con"Nntions of pl.a:in. numbers in lame 

monome=cl:f.Juom.e 11ystms would tl!lpOt this typical. difference ...... in 1ll&ey' 

such systems the number "l." is indicated in pl.a1n u a daa:ble digit· 111111118 

( "2w u w22" 1 etco (Some systems UBe a triple check - 1111 222, 

etco) 

NSA Form 781-C13S 1 Jul 52 TOP SECRET CANOE 
. ' 

TOP SEC1!l!f'lf= !@ll3NOE 

· · When a number in one message falls· over a number in a message in 

depth, the difference is cha:racterirstica ·or course~ by itself'; thia 

Vin nc>t· "read" the depth ...... other tools are necesisar':Ff'or ultimate. 

solution, but an unclertitand.ing of' the basic probl.em ma;y be obtainedo 

PROBIEM ll 

This is a simplified amnple of' the indicator WBage of the Japanese 

Military Attache 11yatm. uased early in the lM.ro 

(ZT)o~~ (KP) .AB CS 

(JS) o u (YQ) AC BZ 

(CH) oo o (XT) AB KZ 

(EE)ooo (NG) AD ov 

(01) 

(OK) 

~:~ Among the con11iderat"ions 1iOUl.d be the poasibili ty that a die.graphic 

page designation is made at the begUm:fng of the :message (Vi th possibly 

a different di.a.graph being Wiled u a control) and also that the encUng 

point of key is checked by an indif!!&tor s:lmilarly enciphered by a 

different control1 pl.aced at the end of the meaaagea Perhaps row and 

column. coordinates are inclu~d in the ind:.1.cator u vello 

Thus the AD OV ... AD (JI/ might imply a message ended on the same 

page as it began, and :the control happened by chance to be·· the same 

diagraph a (Which is control and which cipher remains to be seen) • The 

AB R - AB CS occurrence might J.ead to the eypothesis that here the 

ending was on a consecutive page from the beginning,, the control being 

AB and the enciphered pages CR and CS a This might iJJq>J.y normal alphabets 

were used to encipher the page designation.. If' the chain AB ZL - AC BZ, 

AC CN - AB KZ is checke9- the following -relative solution might be obtained. 

(Only "page" encipherment can be thus quick:cy confirmed. if' the indicator 

is "PP RC" the rov-column digraph will probabl.y 0 come out in the wash".) 

Control AB Control AC 

Key AA Key so 

Starting Page YK Ending Page YK 

Cipher ZL Cipher RZ 

Control AC Control AB 

Key so Key .AA 

Starting Page JY Ending Page JY 

Cipher CN Cipher KZ 

=21-

NSA Fo"rm 781-C13S 1 Jul 52 TOP SE.CRET Ci\NOE 
• • 

TOP 8ECftlt¥ = ~N.N"OE 

(!t is- of course appreciated that ZL from RZ gives the same difference 

as KZ f'rom CN) a 

In the actual system involved,, the sol.ution of' indicator enab1ed the 

c6mplete reading of the system (which involved an underlying digraphic 

code- chart) and,, more important the solution of the simple irersion using 

normal alphabets enabled the more complex solution of subsequent periods 

using mixed components which by themselves could have offered great 

obstacles. 

The importance of continuity~ and getting into the simpler versions 

before they become impossibly complex,, cannot be over-emphasized .. 

PROBLEM 12 

PROBLEM 13 

-22- // 

PL 86-36/50 USC 3605 

EO 3 . 3 ( h) ( 2 ) 

NSA Form 781-C13S 1 Jul 52 TOP SECRET CANOE 

• 

• 
J 

. 

NSA Form 781-C13S 1 Jul 52 

...23 .. 

PL 86-36/50 USC 3605 

EO 3 . 3 ( h) ( 2 ) 

TOP SECRET CANOE 
. ' 

PROBIEM l.4 

PROBLEM 15 

NSA Form 78f-C13S f Jul 5!! 

TOP 8ECMlhAA :n::r; 1 = μ.Ul ,t>~~OE i:l 

=2 -

PL 86-36/50 USC 3605 

EO 3 . 3 ( h) ( 2 ) 

TOP SECRET CANOE 
> 

. 

It will be noted that the relationl!lhip between the f'irst digits 1 

of' the'f'irl!lt two groups listed is constant ..,_ O to 9, l. to 8, 2 to 

4, etco This is a decimation of the actual lfequence used on each 

vhl!!'el.. Knowing the first two keys are in sequent order, the true 

sequence J.528043976 is obtained even more simply., The reader can 

certainl..Y work out the rules of' m6tion f'rom this pointo 

PROBUM J.6 

.. ·· 

PL 86-36/50 USC 3605 

EO 3 . 3 ( h) ( 2 ) 

This problem is not too s~le to analyzeo Possibly few readers 

w:f.11 spot the cycl.e of 5, but (discounting the f'irst few letters, 

identici.l..ly enciphered before a mistake caused the shifting of one 

message relationship) there is a completely isomorphic representation 

of' 5 alphabets hereo 

Thus, starting with the 9th letter indexing the lower message 

in terms of' the upper, on a cycle of 5 lw:tth a minimum of'" .garbles) shows: 

-25-

NSA Form 781-C13S 1 Ju/ 52 TOP SECRET CANOE 
I 

> 

Upper 

Beat ABCDEFGHIJKLMNOPQRSTUVWXYZ 

1 CDRM HF KNA LQST W Y 

2 CPIN HM LMD EQRTSBU WX 

3 BCT H JAKLR PMQDS O Y 

4 C A DFG HJL OQSR T Y 

5 OLBD S GHJKA M CQRUVW Y 

If one takes the trouble to solve these messages (as a 5 wide 

polyalf>habet;ic substitution) one will note that the same 5 alphabets 

are used in eacb,, but one of them 9 dropped a stitch' o Many tricks can 

be .vsed in recovery,, as one quicldy gets the inpression that the sequences 

are ... ·baaed.' on ~ywords (accounting for the largely undisturbed relationships 

in certain parts of the alphabet)o 

EO 3 . 3 ( h) ( 2 ) 

PROBLEM 18 PL 86-36/50 USC 3605 

This is based on a Germ.an.Jo l system,, which used a dictionary 

code, sending page and line n er ot the desired word (using a standard 

poc:Jret dictionary) o Instead of sending figures,, however,, the letters 

DURCHWALKE were substituted for l = O ,, with N used as a separator 

between page and line and between successive combinations o U:rmecessary 

digits were omitted (page l line 1 sent NDNDN, for example). 

In the problem given, instead of using a keyword (with only 11 letters appear~g in the text) the maker has used a simple substitution with variants , so that e·ach digit can be portrayed. by two or three letters at different 

times o The use or the variants is not random, however o One notes that 

every .few letters either a V or K is present -- with never more than 

three intervening letters o 

Also the order KVKVKVK is almost invariableo If these two letters 

are the separators, an eleven=wide box is suggested, and a lucky guess as 

to ·t\te· o~~t !'b~ed on the 11-22 relationship of K to V) would pay- off. 

At :worst.11 the~ limitations afforded by the fact that not all digits appear 

as :beginnmg 'page or line nullibers would lead to a partial solution. 

PROBLEM 19 

The property to be noted here is one of distribution -- within the 

first groups (the left hand column o.f 5-digit additive) there are exactly 

£our o•s,, four l's, four 21s, etco The same property holds for each of 

the other .fo1.lr columns o 

-26-

NSA Form 781-<1115 1Jul52 TOP SECRET CANOE 
' ' 

. 

I 

PROBLEM 20 

./ 

PROBLEM 21 

This illustrates an extended monoaJ.phabetic substitution., wherein 

the key is constant :for 10 letters., then changes to a different /key. 

Within these stretches everything is monoalphabetic., so off-set.hits 

occur, but disappear when the 'border' is reached and reappear only 

after both off-sets get into the same 'territory' again... The irregular 

imerval between partial hits (WTZVJTGLNllN and WTZBQWTNilN) isi an 

exmrple o.r a very simple thing Wliich can be temporarily perplerlng 

when one knows the overall messages do not involve either monoalphabetic 

or single-position cyCiic keys o 

.. 

PL 86-36/50 USC 3605 

EO 3 . 3 ( h) ( 2 ) 

PROBLEM 22 

This is based on the properties of the original Japanese machines 

(Red) which preceded Purple, wherein vowels were substituted '£or vowels., 

and consonants for consonants (through a rather complex substitution 

process)... The result at first.blush bears a resemblance to transposition, 

but the flatness of course precludes such a theory ... 

PROBIBM 23 

Those familiar with Enigma might be roq>ected to quickly spot the 

word NUMBER. as a cliche, due to the non-crashing features of such 

reeiprocal systems,, where a letter can not be enciphered as itself". 

Overall. counts of such traffic (which includes certain strip systems 

as well as machines) should show a reverse curve o:f the normal frequency ... eJCpectations o:f plain text -- E would be low in the cipher., for instance. 

PROBLEM 24 

-27-

l 

NSA Fann 781-C13S 1 Jul 52 TOP SECRET CANOE 
' ' 

\ 1 TOP SEC1R1Ezr~2tNOE 

PROBLEM 25 I ....---------------. 

-28-

Form 781·C13S TOP SECRET CANOE 

I 
' ' 

\ ' ' 

Form 78l•C13S 

I 

EO 3 . 3 ( h) ( 2 ) 

PL 86-36/50 USC 3605 

-29-

TOP SECRET CANOE 
I , 

EO 3 . 3 ( h) ( 2 ) 

P.1 86-36/50 USC 3605 

-30-

FMm 7Bl·C135 rrOP SECRET CANOE 
EO 3 . 3 ( h) ( 2 ) 

FL 86-36/50 USC 3605 

-31-

NSA Form 781-C13S 1 Jul 52 TOP SECRET C1\:NOE 
TOP SE~AGNNOE 

PROBLEM 27 

PROBLEM 28 

This will probably be quickly spotted ae: a literal. transposition,,_ 

but perha.ps not all readers v.tll aa quickly notice the prope1'1;ies 

which make solution ll!limp1eo With the e:x:ce.ption of a few letters 

(which di:f'f'er between the message21.ll and imply a different word appearing within the two "versions) the first message can be broken into 

segments of' 3 or 4 letters, each segmsnt then being matched with an 

identical segment in the second m.e!!lf!&.geo Assuming &l.m0i"t-ide.iitica1 ·-

text, but different colllDm u tr~~itior.a. keys9 the/pl.a.in is easily 

recoverable o 

PROBLEM 29 

NSA Fo"" 781-<135 1 Jul 5!! 

~L 86-36/50 USC 3605 

EO 3 . 3 ( h) ( 2 ) 

TOP SECRET CANOE 

• 
t "\ l 

' 

• • 

EO 3 . 3 ( h) ( 2 ) 

(Notice 9021 - 9220 and 671~3 - 6942) FL 86-36/50 USC 3605 

PROBLEM 31 

PROBI.l!M 32 

First of' all, this e:x.am91e must be studied on the cut of 4-let"l:;er 

groups., 

Consider: 

lo YGMK XBES DFGB KODG 

2o FDHC JNEG 

? 

3o ARZD ZHMK WBDT ERIC JrIDH 

PL 86-36/50 USC 

EO 3. 3 (h) (2) 

-33-

NSA Form 781-C13S 1 Jul 55! TOP SECRET CANOE 

• 

3605 
J 

,. -, 

Note that there is a close relationship (never more than 2 letters removed) 

between these messages at this pointo Other such relationships show no 

evidence of additive, as "hits" and "near misses" come a"!; all points (but 

stay on f:;he beat of' 4) ... It is seen that relationships fa.11 into classes 

of 2 and 3 letters at a time in alphabetical order, and the clusters are: 

A-C, G-I, J-L, M-0, P-R, ST, UV, WX, and YZ 

If' one assumes such a conversion table (with variants)as: 

The texts begin: 

012 etco 

ADG 

BEH 

CFI 

1. 9243 8o16 1120 etca 

2o 1120 3412 

3. 0591 9243 l~ 0 504 7 1692 

One can solve the next days message on the square 

which yie1ds: 

PROBLEM 33 

01.2 etc .. RUX 

SVY 

TWZ 

9243 8o16 1120 etco 

In order f'or the true isomorphs to shov through, there should be 

either a constant method of enciphering the elements of' fractionation 

(ioeo the substitution on rows and/or columns would be constant, but 

dif'f'eren-t. between messages) or~ if' constantly cba.nging (as by running 

keys, moving commutators, etcoJ the keys or motion must be the same 

(or isomorphic in the case of' keys)o In other words, different 

settings plus different motion of' at least one COJmnUtator would probably 

not cause true isomorphism, but different settings and the same motion 

might.. Disregarding plain text Bnd frequency relationships, no motion 

and the e:a.me motion are indistingushable intheir cipher isomorphic 

phenomena.. With enough data, a relative square could be obtained in 

the type of' problem given if' rows are constant and columns are 

isomorphic, or vice versa .. -

One could also build up a distorted type of square if, 'Without 

being identical, the rows and/or columns a.re slides of each other 

(12345 as coordinates of' one message going to 23451 in the other)o 

Random isomorphism on both sides simultaneously (12345 equivalent to 

15243, f'or example) wou1d be much more difficult to untangleo 

-34-

NSA Form 781-C1 35 1 Jul 52 TOP SECRET CANOE 
I ~· ' 

It is seen on the problem. given that a11 3 messages cannot be 

treated simul.taneousl.y as being constant on the same element, for the 

chains built up wou1d be too largeo (X,C,L,E,D,M1F,P etc wou1d a11 

have to l>e in the same row or col.umn!) However, indexing and chaining 

the relationships o:f' measa.gea 1 to 2, l. to 31 and 2 to 3 yie1d.s: 

l-2 1-3 2-3 

CXLIE ROED xm 

AY XAGBN RQCB 

GU PMC UA 

KZH ZL LKM 

DB KIW HI 

NPRS SQ ON 

FM EW 

FPG 

This ~l.ies that CXLIE might a11 be on the same row, or the 

l!Jame column, or perhaps diagona.l.l.y related if the coordinates are 

slide between messageso By the same token XAGBN, and independently 

RQCB are related in some fashion. A square can be made which will 

satisfy all these conditionso Hovever1 if we are fortunate enough 

to have a simpl.e slide of coordinates {or identy) in all. cases of, a 

much simpler sol.ution is possible. In such a case, going back to the 

mesaeges, E is next to X, X is next to c, C is next to L, etc. (Or 

at worst the reiat'fonships are Oii"'&n adjacent diagonal) • 

In this case, we must be careful hovwe associate the letters, 

chaining them exactly: 

IEXCL 

AY 

GU 

ZKH 

DB 

SRNP 

MF 

EDRO 

NGAXB 

CMP 

ZL 

KIW 

SQ 

The square falls into place allDost automatically now. 

PROBLEM 34 

-35-

lXD 

CBRQ 

UA 

KIM 

HI 

EW 

NO 

FPG 

PL 86-36/50 USC 3605 

EO 3 . 3 ( h) ( 2 ) 

NSA Form 781-C13S 1 Jul 5!1 TOP SECRET CANOE 

, 
PROBLEM 35 

PROBLEM 37 

• • 

// 

~L 86-36/50 USC 3605 

EO 3 . 3 ( h) ( 2 ) 

Form 781·C13S . '"FOP SECRET CAN·OE 
TOP SECRE~5el!NOE 

PROBIDI 38 

PROBLEM 36 

Readers of Jules Verne will recognize this simple polyal.phabetic . cipher, using digital. key -- onl.y 10 possibl.e ciphers :for any plain 

l.etter, of course. The lowest form (counting on a normal al.pb&bet) 

in each column should represent plain pl.us O or lusu.ally1 and the 

cliche stands out like the proverbial. sore thumb. 

Form 781·C13S 

-37-

PL 86-36/50 USC 3605 

EC? 3 . 3 ( h) ( 2 ) 

TOP SECRET CANOE 

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