Facts & Myths of Enigma

Transcription

1 Facts & Myths of Enigma Breaking Stereotypes Arkadiusz Orłowski & Kris Gaj

2 How should we begin? Begin at the beginning, and go on till you come to the end: then stop. The King to the White Rabbit Lewis Carroll, Alice s Adventures in Wonderland

3 Who invented the wheel?

4 Who reinvented the wheel? Eduard Hugh Hebern ( ) first patent from 1915 Arthur Scherbius ( ) German patent filed in Hugo Alexander Koch ( ) The Netherlandish patent for Geheimschrijftsmachine Arvid Gerhard Damm ( ) Swedish patent

5 Who reinvented the wheel? Eduard Hugh Hebern ( ) first patent from 1915 Arthur Scherbius ( ) German patent filed in Hugo Alexander Koch ( ) The Netherlandish patent for Geheimschrijftsmachine Arvid Gerhard Damm ( ) Swedish patent

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7 Life is brutal...

8 Scherbius Enigma German patent filed in ; issued as Second German patent issued as (priority from ) U.S. patent issued Koch s patent from 1919 bought in 1927

9 Drawing from Scherbius U.S. patent

10 Military Enigma

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23 Functional diagram & dataflow

24 Enigma Daily Keys

25 Four Components of the Daily Key

26 Order of rotors (Walzenlage) 6 combinations

27 Positions of rings (Ringstellung) 26 3 combinations

28 Plugboard Connections (Steckerverbindung) ~ combinations

29 Initial Positions of Rotors (Grundstellung) 26 3 combinations

30 Total Number of Keys Was Enigma more secure than DES?

31 After Jun After Feb After Oct How often did the daily keys change? Rotors Rings Plugs Every quarter Every month 24 hrs 24 hrs 24 hrs 24 hrs 24 hrs 24 hrs 24 hrs hrs 24 hrs 24 hrs

32 Message Key: Enigma s Achilles Foot

33 Message Key Three letters (or numbers) selected randomly by every operator Determines the positions of rotors where the message encryption starts

34 Message Key cont. Protects against the separate frequency analysis of all first letters, all second letters, etc abcdefghijklmnopqrstuvwxyz Could be possibly sent in clear (the same as IVs in modern ciphers)

35 Message Key cont. Encrypted TWICE using initial positions of rotors Sent in the encrypted form in the message header

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38 Polish Signal Interception Stations Starogard Poznan Krzeslawice

39 Marian Rejewski (born 1905)

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41 Jerzy Różycki (born 1909)

42 Henryk Zygalski (born 1907)

43 Headers of messages intercepted on the same day 1. c h m g r t 2. x r w r g s 3. o w o q k k 4. f k r x o a 5. o u v q a y 6. c r x g g g 7. v v b z s e 8. u u z y a u 9. n n k m l d o a k q w d 71. q o f d y q 72. k s m p c t 73. u x u y p w 74. u n k y l d 75. x c o r b k 76. r j j h i r 77. t t g b u c 78. w x g a p c

44 Encryption as a permutation Message key q w e q w e A B C D E F Encrypted message key d m q v b n

45 How the reflecting rotor helps? Message key q w e q w e A B C D E F Encrypted message key d m q v b n

46 Determining a product of permutations Message key q w e q w e A B C D E F Encrypted message key d m q v b n AD contains d v BE contains m b CF contains q n

47 Rejewski s theorem If 2 permutations of the same degree are involutions then their product contains an even number of disjoint cycles of the same length.

48 How German clerks helped Polish to find A, B, C, D, E, F? Preference for message keys of the form: 1. qqq, aaa, etc. 2. qwe, asd, etc. 3. with all letters different

49 What remains is just to solve these equations A = S H R T R -1 H -1 S -1 B = SHQ R Q -1 T Q R Q -1 H -1 S -1 C = SHQ 2 R Q -2 T Q 2 R -1 Q -2 H -1 S -1 D = SHQ 3 R Q -3 T Q 3 R -1 Q -3 H -1 S -1 E = SHQ 4 R Q -4 T Q 4 R -1 Q -4 H -1 S -1 F = SHQ 5 R Q -5 T Q 5 R -1 Q -5 H -1 S -1

50 How to reduce the number of unknowns? T R H S

51 Gustave Bertrand

52 Hans Thilo Schmidt (H vel Asche)

53 Rodolphe Lemoine (Rex)

54 Six equations, two unknowns How difficult can it be? A = S H R T R -1 H -1 S -1 B = S H Q R Q -1 T Q R Q -1 H -1 S -1 C = S H Q 2 R Q -2 T Q 2 R -1 Q -2 H -1 S -1 D = S H Q 3 R Q -3 T Q 3 R -1 Q -3 H -1 S -1 E = S H Q 4 R Q -4 T Q 4 R -1 Q -4 H -1 S -1 F = S H Q 5 R Q -5 T Q 5 R -1 Q -5 H -1 S -1

55 Theorem that won the WWII If G & P are permutations then a permutation PGP -1 has the same cycle structure as permutation G.

56 Cyclometer

57 Polish Bomba

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59 Zygalski s sheet

60 Zygalski s sheet

61 What has changed?

62 Pyry

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70 Y - station

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79 Alan Turing

80 Gordon Welchman

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91 Joseph R. Desch ( )

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98 Howdo we knowallthat?! Well... W. Kozaczuk, 1967 M. Rejewski, 1967 G. Bertrand, 1973 F. Winterbotham, 1974

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101 All s well that ends well? Well...

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110 1979,

111 Available Translations Yugoslavia 1977 Poland 1979, 1986 U.S.A East Germany 1987 West Germany 1989 Bulgaria 1990 Germany

112 Enigma Cipher Methods of Breaking, 1989

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114 1996 (2 nd ed) 1999

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116 Question: So the Polish stuff was a god send. David Kahn: The Polish stuff was essential and an absolute god send to the British, and to the French.

117 The Enigma codes would not have been broken if it were not for the knowledge of Polish mathematicians Prince Andrew, the Duke of York

118 Enigma Lessons 1. Keeping machine secret did not help 2. Large number of keys did not help 3. Known-plaintext attack was easy to mount 4. Do not let people to generate keys 5. Key management is the weakest link

119 Take-home messages 1. Never underestimate the amount of money, time, people, attention, and risk the opponent can use 2. Train and educate your people 3. Don t worry 4. Be happy

120 "I have made this letter longer than usual because I lack the time to make it shorter." - Blaise Pascal