Britain/France/America: lean/hungry => fat/lazy
Germany|Poland|Russian => Biuro Szyfrów
Ciezki + Monsieur Rex + HT Schmidt
1939: Poles have rotor wirings
daily key info
plugboard pairings, eg. AL PR TD BW KF OY
rotor-slot placements, eg. 231
initial rotor settings, eg. QCW
message protocol: for each msg
day-key pairings
day-key placements
new rotor setting
msg prefix: rotor setting, repeated, day-key encrypted
e.g. msg-key PGH sent as prefix eQCW(PGHPGH) = KIVBJE
exploit doubling in encrypted msg-key prefix
for each possible day-key (rotors, placements, setting), construct 1->4 2->5 3->6 permutation "fingerprint"
build lookup table: fingerprint -> Enigma key (r, p, s)
for each new day
collect msg prefixes
from prefixes, find day-key fingerprint
from fingerprint, lookup day-key
from day-key, msg-keys, deduce plugboard cabling
now complete day-key (r, p, s, cabling) known
from complete day-key, read all msg-keys
from msg-keys, decrypt all msgs
L O K R G M A B C D E F G H I J K L M N O P Q R S T U V W X Y Z M V T X Z E P M R X J K T M P E D V Y P Z X . . . . . . F Q H P L W O G B M V R X U Y C Z I T N J E A S D K represent permutation (above, 1-4) as product of cycles A -> F -> W -> A B -> Q -> Z -> K -> V -> E -> L -> R -> I -> B C -> H -> G -> O -> Y -> D -> P -> C J -> M -> X -> S -> T -> N -> U -> J so 1-4 is a (3,7,7,9) permutation
V E C J I B E W O P F A K D A L Y T 1-4: L C V T E O A B C D E F G H I J K L M N O P Q R S T U V W X Y Z B A H Q D Z J J Y S I B Y T I Q W V P Q X E Y R Q P G Y F A V 2-5: F Q P A L R A B C D E F G H I J K L M N O P Q R S T U V W X Y Z C R M U Q N I D U R C J M Z Z K N U L Y O U M W K X N B S S D 3-6: I T J B T G A B C D E F G H I J K L M N O P Q R S T U V W X Y Z H J G E K H B U K L V H J W V F O O U G P X D P C R L N K M S A S D R G I S B Z G N X O H T Z Z W N F I H C F M M W X X E
3-rotor 5-slot lookup table: 1 year to build
but now Poles can crack German communications
e.g. Goering's 1934 Warsaw visit
small German modifications
Rejewswki builds bombe
6 bombes, parallel, check 17576 settings each: 2 hours
Langer had the day keys
1938 Dec: 2 new rotors (now 5)
new rotor internal wiring ?
now 60 placements instead of 6
1938 Jan: 20 cables instead of 12 :(
Schmidt gone
1939 Jul
Poles give French/Brits Enigma replicas
bombe blueprints
1939 Sep WWII
Room 40 => GCCS, Bletchley Park (2 million words/day)
Alastair Denniston
linguistics classics puzzles math science
Oxbridge
crack day key: few hours
shortcuts
try cillies
each rotor in different position from previous day
19th century math
1900 Hilbert's problems
1931 Godel undecidability
1936 Koenig graph theory text
b 1912 London (parent: India)
1926 Sherbourne by bike
met Chris Mercom d 1930
1931 King's College Cambridge
1937 On Computable Numbers TM/UTM Entscheidungsproblem
1939 Bletchley Park
exploit 6-gram msg prefix: repeated 3-gram, encrypted day-key
use e1(p) ↔ e4(p) e2(p) ↔ e5(p) e3(p) ↔ e6(p) to identify r,s,p
factors out plugboard pairings
expected repeated 3-gram to stop
exploit probable ptext/ctext crib
use ptext/ctext loops to categorize rotor settings
factors out plugboard pairings
ptext/ctext crib alignment: e(x) ≠ x (??)
1941 Sep Churchill visit
Turing wants more staff, Travis says no
1941 Oct Dear Prime Minister ...
Churchill: make sure ... all they want ... extreme priority/
1942 49 bombes
Daily Telegraph crossword, under 12 minutes ? (6 out of 25)
globeandmail cryptic 2017-02-27 hints: 1 def 9 def 10 ana 11 dbl 12 pieces 14 def def 16 ana 18 def 19 def def 22 pieces 23 pieces 24 pieces 2 def 3 def 4 ana 5 def 6 def 7 ana 8 def def 13 pieces 15 pieces 17 ana 20 pieces 21 def def
* get crib and ciphertext * find possible alignment ...wettervorhersage........ KVBVRBCPZFQFNTTQEQOGYIIOYNG * for this alignment, draw Turing graph: join two letters if they are aligned at some position G P A Z | \| | S--Q--O--E--R--F--V--W H--N | / |/ C--T--B * find cycle in graph (a.k.a. Turing bombe menu): - E->R->T->E positions 5 15 14 5 * give this info to bombe operator * operatoro will return matching Enigma key: - rotors I-II-III ZUB cycle 5-15-14-5 H-W-N-H * now you know uncabled letters ....H........NW intxt ....W........HN outtxt
* try Enigma replica key: I II III ZUB with no cables KVBVRBCPZFQFNTTQEQOGYIIOYNG ctxt XFXTVNNHQZLWJYDSGGYMUHTGEYT ptxt (no plugboard cables) ...wettervorhersage........ desired ptxt * make deductions no cables: 5-15-14-5 H->W->N->H all cables: 5-15-14-5 E->R->T->E so cable EH WR NT * make more deductions ps j ptext/ctext x:Y ok => no further cabling with x Y ps j not ok => further cabling x Y (and/or) KVBVRBCPZFQFNTTQEQOGYIIOYNG XFXNETTEQZLRHERSJGYMUENGHEN ptxt (pairs EH WR NT) ...wettervorhersage........ desired ++++ +++++ + <- ok ... so BC EFGH PQRST ok ? <- F:Z F ok, so must be pair VZ KVBVRBCPZFQFNTTQEQOGYIIOYNG ctxt XXXWETTERVLRHERSJGYMUENGHEN ptxt (pairs EH WR NT VZ) ++++++?+++++ + <- Q:L, Q ok, so pair LO ++++++ +++++?+ <- E:J, E ok, so pair AJ KVBVRBCPZFQFNTTQEQOGYIIOYNG XXXWETTERVORHERSAGEMUENCHEN cables EH WR NT VZ LO AJ
* find 1st possible alignment of crib with ciphertext * for your alignment, draw Turing diagram * find cycle, and write down info you would give to bombe operator W E T T E R V O R H E R S A G E C A L A I S L O J L A X I O O H N X P Q H C B E S H V I V R H P V Y Q E A Z E M
networks: Wehrmacht, Afrika, Luftwaffe, Kriegsmarine
KM 8 rotors, atypical msg form, diff't msg-key protocol
U-boat wolfpack
gardening: mine location crib
pinching stealing codebooks, e.g. Operation Ruthless
Gadenia/Gonzenhein report conclusion: natural disaster or spy
ULTRA: German Italian Japanese deciphering
Greece Italy Sicily Normandy landings
FW Winterbotham The Ultra Secret
Rejewski, Denniston, Turing: no credit in lifetime
Turing
1952 convicted of homosexuality
hormone treatment, security clearance withdrawn
1954 June cyanide apple
war of nerves nepotic vista even lacerate reckon resent go astern shot token profits personality apple oath nectar reviewed enslave interrogate taken to task fortunes crackle trepan hoist fool