Alan Turing's Treatise on the Enigma

117 Pages·2015·48.16 MB·English

TOP 'ECR~T
TURIUG 'S TREATI E 0 ~ THE E ITG1.A.
Photo raphic Copy of a per epared in GCCS,
ritten ca.
1Y3~-1942
TOP ECRET
OP CRE
.B.
Pag a ~ in fil of Turing' • ~r ati
38-40, 47-59
68 (but ther ar two "67" 's)
74, 81-83, 90
100? (but th r is pty 26 x 26 equare inlt d)
113-114
119? (But th r ia an unnumbered p ge iDatead)
124-128 (but tb r r two 129"' )
131
TOP SECRET
0
w (t nr 1 h In~ Ll1 1 I IHl ,r t1 n t1rrn ' 'l'h m o h 1 n
··r.
( f , h 'X · Uli I<• v ht 11 vrt t.h th' I 1111. I. r f thtt
ll' 1. TH 1 u l •Jll ll" II : !lin t.hr ll h f l,1 II 11 ( rl thioh
1 Ll r· r m t•k d. 11. In o~n Ln 111 1 ··h •1•1 • ho•1 funoti n ill
c.1.e or 1b 1,, t• r a. Wllf 11 , k• .Y 1 (l th wh 1 ~
~ ,
"~~'""' mtde t Tni•V 1 " 0 rt ln v. ':1 "nn ourr' n1. r low. thro .h th
r"r'JJ""JJ' whe•l to on of the bu b '1'11 XIIOXS"D::Jrltxn. 'l'h 1 tt,er wh1oh
7.
~
u~ 2 r ov r 'th bun 1. ••lld th re ul or no1 h 't'1rur th
~ 0
Q ·c on th --prel!l ~ k It th th 111 th po"'itlon th y
...c0..=.
~
To und r . nO tl'f orktin or th rhln,., It ~ to s ~Till
1tn
rt olro•l1 f tl m h l 1 • 1 hout th 1 •
The oirou l t t ou •l t,h '"h 1.,.
Tlie m oh 1 J'Q t.h ·h 1 nd tor ~. nr1b1
'Jih Mil\ 0 lt I l l r r, ] d h r.in r1t1., lz
(E.W)c hJoh c '~ .•• , ct.4r. 'l'h rr ot or th
wh 1 n t. I ' ' 1 r ' 1
1r1n or cour t.h r th whe 111.
n th ott r 1rtf u l n t c, ,c..., •I ~~~ ' oon ot d
oh to t y • • r h 1 t th
ord r 1. n:z•iluct-.
wUl y t.h t 1 v th t a1 t
ith c'l to. r t t c.1. 1 h c, c,., ... ,c,.,,
1 0 1 th r r on th r in C
• It l rt toHl• r L' 1I I' \I II VI r:l 'II I 1. I ) I I) ~ !<'J'/,1J f) rt1' r .
'l'h I l ~1'' 111 •1htl I 1.1 ( 011 II o L 1 liH ' r)J 11 h v y I is
in , t l1et c, 1 A r. u1 r ot rl to ca tllrou~h t
c
r
~
-
~
-~ '-
~ 'c.u,
r:JJ
r:JJ
< 7 ~~2 l
u~ 7. L. •
~ 0
Q ·c
0
'§
~
'l'h onlv outl t for th ..... 0 1.t1v. of .h Pt ery 1 thro~h th
c, .
k yt 0 hence to CJ ,. d th n t hrOUP;h th r~ ulb The result 1~
t hf't th E bulb lt hts. ,ore fl. ner l lv '/ c~n ~ y
c. I
If t· ·o oont ct C of t he Etntr1t S" lz _,r connected
t hro hthe heel th en the re. u] t f nci'l')h rin . the letter
c
c '.
oci t d "11th i!l tb let r oo i" ted ·ith
t otic th 1. if 1~ the r ult of enciph r i ~ then G is the
t of no 1 h r lnFo; P t t..h ~ l c l qo th~t the result
f enc 1h r in G o n D' v r b 1;.
11 noef r- ' rd m · n 1 ot l f he mAohine exo nt ~
f ' t th con ottons t·· n th cont~ot of the
1~. v. nd th turno .-r 1.nm · ·hich f ot he ~ositiofi or t
'Jh l. .
Co
Th ''thf , l I no lur "hi I 1~ ld "1 r ov from ,be
m hi I d 'lh io h Tn' r •t b r t. l I .. 1 1 o-.1 d t
. . .
:r1.,
mk h 17. lll. ; ) hil ••rh 1 h nt ot htoh
cl t..o .. th r lr l .. r ot r
r• n v
Ctll c ' r t.l < n
.,
ri ·ht , • 1 1 , 1' l 1 n t th l' ln h
I·•.•'PIIJitl•• l0 1111 '11'1 tJ•r l" lllll '•1 1.t f"'qflfr • t 'n I.
,,, ,,., ,, rl nt~·· nt·t.• ·t ·• •r· y1n,·• I••J.t•l , n, r tr t.• h lr •I .l1
I'" I" t t. l.n l.lu ,., • I o f' t.lrt• ''' I ; '"" 1 '' ' htttt 1.1 .., 'If' ' t, u u t)V r • ' ,
. )\I
.
.
tr1L JI ll 1.11 11.1: •• , md r, ,, Ill 'I , Ill p ,., ( ,. ~ t r er • 'l't
. l.hnl. t.ll• ( \JI'I' Ill. 11111•,111. r'l nw rr()n t.llr t:. '· 1.' 'lll;h t.h w 1
1\tld lJ. t k ~~ , h• II J,,,l
"4M.W ""'·"' M.W ..... w f.W
pu 11. lc n r t,h on h t
t.. ar HtJ:h th" t.hre· (or 4 1t
I'Ot t.• r t\wl )W! !11 thr n• , ~ r t 11 , ~'~ o tli , • 'l'h 1
w n 11 Ll1 'w 11 () 10 t t l••H' • ,",'} 11 • . t
Jlll.llt.tttn hr II,' '• u I 0 'I ttnt. oh n ·. r rt.h y 1
w1ll v th t. in t
1.t) ,. '
' r 1 1o w tn . ' P•' 1 t. HI. 'L'h ) :a! t t n th lo h
>'f l J t vl 1 • n<1 on lh r1 1nc\o
1tl•'"l l. 'l'hlt ,, \) 0 u . oh n t ' ror h 1 th 1t1
I ·1 1 ,. 1( 't on h t. • r• 1 •
•l•
'l'h• t..11r1 lu ~ IJll II• 111· 1 nc b t ' o
'I'll I I) I r l.t I ) " h , nn ln .1 a 1. to
11,
r-t ,l i b ., r 1, 1a r l :It II' •I • l, ll t.h
,, l •II• th , L.ll ••
;·(', I , I~( h
< w ( c ,. 1 n t • •t h 11 l
I 'I 1111 l t. 111] y Ofl )r ( I I Jll r h t.
'l'h•· r r t. , , t 11 ,. 1 . 11 h'. , 11 l H. • •
v• rv t. tr y t ed. 'I'J m1 , L 1
n rr l ly oon1c!1 into oontnct ·1ith the smooth aurfnce of the tyre
1
which prevents
R.n.w.,
of the li%0Xax::t:Lix it from TIDirtw,p: en·~~ging "lith the
catches of the M.w. If however it is ~hle to Rliu in to the
catch on the :byre of the H.H.w. it vfill re~r.h the C'3tch on the
u.vv.
~nd ~··ill push both R.ll. ~. ~ad M.VI. fo~·erd: of cour~e the
R.l!. ·• is llein,g pushed for!P~d by the right hP~nd pAwl in any
o~"'se. The ooourenoe of such e novement or the M.w. is c~l,ed a
'turnover'. Owing to the feet thet the r,atch is on the tyre the
position et which the turnover occ'dlrs depends onl:r on what
wheel is in the right hand position, and on the window nosition
of that wheel. For instJ:lnoe vJith German service wheels , wheel I
turns over betwe~n Q and R , i.e. if I is in the R.H. position
then th e • 'I. will move :forward vrhenever the windmv no.s i tionof
the R.H.w. changes from Q. to R. The left hP~nd pA···l oner~teCJ
s i""lilArly to the middle Dw::l, but in th1is cA.<:Je it is es'3entiel .. o
I
remember thP1t both r,~.·~· .• ond L.H • .'J. mov I fer wArd.
ilypic~ 1 ex,::;mole-:; of oonnecutive ·.·:indO"' --ositions •qith middle
··1heel :tKll turnover E-F, D R.H.W. T.O. Q. -R
AWO u ,,..J!.,J .l:..l,t
AwP BD 1 lt'.A: ~·1
JA :. { B .ru~ NJ.~F.L'Y·L. .~.)'oT::i
A.Jili CF.:>
•L\T Gl''l'
The effect of encipherin let er denends only on the
•1heel order ('. lzenl e) ad the · sition ( i.e~ Amount rot9ted) j
of the whe 1 ro er I l .e . ,!!E.1 the · r.,) •. To describe. this ,.,osit~n
.,. . re could im· g..:.ne thAt there · a t set of letters ~tt~ohed to
th•- busin~s e rt of "' c h ·1he. 1 , , n d · t h t the letters
Kbm, be seen through the · indm· 11 ~R the lett rs on t
tyr.- s. ·.he lette-rs sen would give th ·'~b olute' or 'rod'uositlon
or the ···1heel (the point of th e ei'p" ..o n • rod nositlon' will
be seen· in Chap ) •. ~·he pos,ition ·or the tyre r let1ve to th e
busin s ... Art is fixed· by me -n.9.ot ~ o·llo on the bua.inesCJ .part
which oen dro into_ boles neer the lett.ers. When· tke oll ikeln thw
!
h " 1, 11 ,. t. u' I I. I o r • c · • " v t. hn '"' ttv 1e 1 n , t v J 1 11 Til~ 1. ' ' • 1 o r 5
Lit•• t. Itt 1 1. It~ t n I '' t' l.h• I. •toto '111' t I n of th form
WltHliiW 1 tt.\on =Hod :I(, tt.ion 1- ltin~nt llun~ .,a- n oon.,t rnt
1111 , n t h o 1 ~ ( \ t b \ n 1~ u n <1' r. L n (1 d t h 1. 1\ , H , c: , , • • r111 1"" r ~
tn "' r·ohnng"' ble v t th 1, '· '~~ •••. ) • b::x::a:Ull llorm l l y a~tma
:ta c.me nrnn11~ ~ t l'' t thin nonnt~nt. 1 7.' ro (,e _..lao
'l'he
In :1 or 1 ni 11 ·1 1.11 ,... ' ool• 1.1on of th"' oon t111ot~ of thfll
Jo:1nt.rit1 ~w· l ·: .,lt.hLh k y'l nrl. hulbn o n he v_,ried. ''her re 2
p lr~l r ~ l< ·tn lrh llet with the let . ra of th "'lph.eb t
on of ,.oh pnir le&d ln t.o n Clllt t of the •:intritt w lz ~nd
tlw oth r tu one of th k y!l. tlo:rtllAllv the two ooket!I:J Are
oonn cttld to·· th 'r lJ " IJidd n 1ri ·, if howev ,. "' teoker'
i:J luR . rl into t v n lr of , ooket~, W fllnll H ory, the springs
re foro• tl A y nd n o on neo t ionr1 r 1WI' de through tta Steoker,
tl1e ~ key he in~o~, oon r r l• d to the oont rot which YIOUld othent1ae
.
he connected to til H k y n vioe-v 'l'het W nd R are
r~fll.
oon1. ct d hy :lUO h ,. lu l. Tnr n ( ( In th form 'W/R' or 'R/W• ..
'I'll e ff nt.. nf th .:t., ok r on th eno1nh r nt i~ 1'1\lit ~1mnls.
11' nt 0 L-'111 . 1 t. t n of the IZII whe 1"' 1\ et1o iph red l'veA N,
.,
(nbt r vi too t AN) ll n 't t.he n"r s1t1on 1th Jt6oker ..
A/V ,N/0, II pr r lv pn oth rto:~ , "6 ve VO; if in t .h ve the
. ..
.it ck r· 1\(V but n r • I· v lvlng t• nhould. vo VN (or "' we
nom( tl1 :1 nn y th '0 n!1 t,• t1< n' v q. ,, lll 11: f o. 1 le enoj. l)erm nt
., t h ut I ll :;t ok T V' J'f)
t.h n o· 1 1• t. rt 1l1 r lffi t h •m 0 it to·n"
r th • lr 1, (~ r .. r f r t.. It 1 r r 1llD1I 1 .t.he
't ok r .I /.K,
D/: ' V/Y. · u •lei
,,
' '1 )IJ~]" •
lV II ;V,l ·
......
~~· ,.~ ~
c;[
;~7 ~ .t... ... J..L 4.~~
s~~WA.
I Ill I IIH r•lll'l" ' • •d' drr ,c llrlrw t lr tl J' lllt, " ' 11 1 •,rJ
l 111 '" I' ' 1111 • " ''' 1 l'r''"•l , ''" t.' .,,, l,lu r1 ,It. l• 11 ( prj
I
, ''~'" ··1. h• • l'lllt'. l tid 11r' L,ll wl111• 1, r tr th r it w pot ,:r
t.lt(t 1•1\l l I \'l1lnl1 I UPI rru > 11 lilt II ''II,V '''r11,1nt~ 11 t h t i
1Wt' I 'l, till 1
'l'lte o ont r t ::h lo 1 l:l up I"l t or n· r I to the- pot is o lled 1
A Ild then the numll rin ·. 1~ o ontinu in nlook\'liee di t·eotion.
On th n JMke ou aoheme 1 tk thi
' : ) 1" IT I (J" 0 () t 0 t, l ~ 2 7 8 r-."l
~
•· Lx 11 ,. ) 11 t 01. 3 l r) 14
.,
I rom th ln t of v t• .. r th crynto r nh r the mo~t n~tu~l
., y th e 0 tnot 1 I' ill h r different. One would 'OUt
th Hin t ro, h n p in the window, .. n4
rte-r
n m t 10 th ri~o'ht ot the • I •. • 117 the lett.r
.
0 o. 00 1 .. 1 th t he o ont t f t h ' • hioh it touo!)efll, there
be ln.-; · w d to 110 r. 'l'o oon ot th e two not t10M
lt 1 old b n o ry to k tnt eon 1 r tion th rel tin
.
!103 t t 1 ot the ~ont. ot c'"' ot the E. nd tl 1ndcnn.. ~n4 1 0
the 10 it ion of th olip "Od ot n the 7h 1. Here is rul
ot tlnun tor t h in II, 1 otrloi n d t,LI'I fro· t orynto r-- h1o
•
I t• ' illu r· by I l I 1 I.
'I rlt u lrt. ht ot the 1nYer e Ulll tor the
od "bOY it "on 1• t.l 0 t. 0 1 t.n •'th
,,
,,
,.,. /'
16 ,, ,. .... .. '7 ,, '1
9 '
'' ,_ "'" ''" I
?
'.I I HI I I I I ' 1 I I I I .t If I' I I .. I I ,. I. I' I. I. I It I , (. I )j j r " n f) 1', I 1 r rj ] in
\. I• l) I I I I' 1 i ltr }) c ~ (]f '106 ibl ....
· r "' 0 ' I r 1.ll1Il '111r U" <l 1 t 1 ~ b ' 't to reo1 0'3 the PChine
\' 1' I 0 p 1. 'J. r l-1 [ 1 r (' • F c h 'llleel by r. Jml~RXXX:trt:xcp::XJJ:l'n•
strt of u• r ct 11per .-1 f!n r R y "" sauc. ee3. The aquP re in the
ri ht h nd cul1unn f the strip repr~9ent t he g'1rin.g oontPcts of the
·heel in nPturPl orde (to 1 lee the sourre of t~e striu -9gree
,·ith the contActs of the .1U,eel one must VJrqp th e strip round the
\''he· 1 with th e writing on the stri,.., inwards:). The sfluares on the
left repre'lent the plate contqcts. In the right hand column is writter
the diaKonal t wice over, these being the 'oryptogi"?.phers names' o-r tru
contPct8 as exp1PinP.d in the lest section; in the left hand column
letters ere elso written, qnd in such A' the ' squAres containing
p
represent cont~ct3 ~hich ~ re
the s me letter 1r:r. connected together. Do.'m th e centre column
~
'll y be ·:.rri t en th"'. numbers 1, ••• , 2G, 1, ••• , 2tj. These numbers serve
t o de·;cribe the osition or the ·he 1, either the rod nosition or
the ··,indo· osition Acrordt ~·to ho·: they A.e used. ':'he U"1.kehnnrlz
is re!"resented b·· ~=~ ~tri!"'' three sqUAr s ···ide, ~ontfl ining i one
colwnn t he diP ·on~l re e tPd(t h.\s is not entirely e senti"il) in
Another the num e. s l, ••• ,ZG re e~tesd, he third column repres nts
the contacts~ nd s1unres representing cont ots · hich ~re connected
cont in the s~me number 1 ich does nor eKoeed 13). The machine itsel
is renresemted b !:' she t or p per "lith slots to hold the 'wb ls' •
. I **''*
In a colu.rrm n the right is writ en the unsteokered diegone.l
~ to reuresent the Eintrit s Alz. It is convenient to repe~t
t'II•••K• this ~'~lnh~bet betv•enn ench l .ir or whe~ls. The sure
be ring the letter be·tw n the : • • ·:·. Ann the ...• ·;.·. '''ill bw
c~lled R.H. '1.' rod point ' or • '• 'output oint 1 • B t een th
wheels ... "lso ··:rite 1,. ~., 26 ·epented. The~ ataD:xK:xt-x:tti
t:iia:xj:j:q ere used f Jr d . cribin the osition o-r the wh el hen
the 1ngstel1u i~ iven. To tmder t nd haw this o,n be done
~ ne d only notice th t the s e"!fect e moveble type
,,
', . ,._ J• ... ,,
..,; ' I I J
.... ,
1. · -
I "' • .J
• c • I I
,,. A ,1. II '"
'' · ~ ·I t lf •• . • ,, . I " I I'
I J' ~ 1.. ~ ... 1.. h/ ,, ' '1 w \
. • (- 1) 3 I[ l "t.f ~·
I. ,. .{,. + " ''v J
'· -~ ~
... V\ If I
'j"t Hi
j"' I '·~ I 1.J
~ ,j ,1. " z '1·· w 'Z. I. ,, z..
.. ,. . 7 ., v 7 v r 7 V t ,, LJ
J' "' .L,. r ,., I J L.
•C 'f 3 ~ 0 I~ '1 J
'"' )( 1l ,. A " /(J
I ,,
C. j /, J -II --'-h~ -- (I It J l I '1.1 /I
'l"
L 1- " 1. ,..., D I I '"' 'D II t'\.
, 1 3 3 ,, 1\ .\ l'j r: 6)
I\
I¥- c, ' ,,_,
J..,. N ~ It,., "'
I,·
h' /"1 ~,. joj 1 ... If I 2.t" 7 I ~·
:.f ,
H 1... " /~ T r t• T i ,,
(.R 7 '/ II.. I (,5, ) ,lc.. /I '
,r
"' .\..I ~ If 'j' 11 "'' tl ',",
y
J 10 a '' Y ,I.~.. I' J j I~
~.,- f2.. ' 'I .,., ~ )( ,.. l4 )t I' l"l
... r ,., 1.1 c... l· \. '- 1,.1 '- II
I" (I 1\,... v .. ~"' vI (jl \V
,,
7 ..) '" '\.J jl I 'll .-..; \ 7 l' \.J ~ I
,.., N
$' 9 ,.., rt/ 1... .... '
w
r I) 1. ~\ M 1·' ' I (I
1
.~ ~ t1.·~ L.../
,, .r:
1~ Vo II
-I
,,
,( H 'I I' '¥' II
'If : ,,. \I
7 I( ;
I
Ir.S, 'P ~ .I ·" L
I \\
r
.r...,. ""r tQ. ~A,., '-'1 ~. ,_ ,ht u ~ ~ .J1u ., ~ ,T; 11. Wt- u. fl.(' IJ.
1-W • 7 I" I J ,. - '-"-' u ...r fill• 1·f1ih I " ... 1 " ,... 0 f.1.s ,_ I._~ .....; ;.. ' ·. .. ~- w
~~ 14,;."""V"-.Wtt_ll. ,'It t. .t 1.. 'f/..N, :~" 1t~ a.l'l.i ~ •• '" 11..
(~ t1w ~'"'1't.........."'J. ~ t1..a ~k. t1- ,. ~·· ~ w • ' • ,.
,,. ~ w-t..... ~-u.. ~I <r v~ I L...J ~ .. ' ' . ·~ • '_.r.