The Math That Saved the World<br />Brad Young<br />brad@clearpoint.co.il<br />A Mathematical and Historical Analysis of th...
Agenda<br />Development of Enigma Machine – Why/How/What<br />The Rejewski Crack<br />The Turing Crack<br />Historical Imp...
WWI Cryptology<br />First major war with radio + telegraph <br />Very large volume of communications <br />Hand-ciphers<br...
Zimmermann Telegram<br />
Invention of Enigma Machine<br />Arthur Scherbius<br />Efficient!<br />(oh, and also Secure, by the way)<br />Business, Mi...
Oops<br />Publishes history book<br />Reveals the impact of crypto on WWI<br />Now, the Germans want Enigma!<br />
A<br />B<br />C<br />D<br />E<br />F<br />G<br />H<br />Reflector<br />3rd Rotor<br />2nd Rotor<br />1st Rotor<br />Lightb...
A<br />B<br />C<br />D<br />E<br />F<br />G<br />H<br />Reflector<br />Lightbulbs<br />3rd Rotor<br />2nd Rotor<br />1st R...
A<br />B<br />Pressing ‘A’ on the keyboard…<br />C<br />D<br />E<br />F<br />… lights the ‘B’ lightbulb<br />G<br />H<br /...
A<br />B<br />C<br />D<br />E<br />After each letter, the first rotor shifts one step.<br />So now, pressing ‘A’ lights a ...
A<br />B<br />C<br />D<br />E<br />F<br />Sits between keyboard and rotors.<br />Each plug cable swaps signal between two ...
Plugboard<br />
Keysize<br />A<br />B<br />Rotor Order<br />Rotor Setting<br />Plugboard<br />Wiring<br />I – III - II<br />VYJ<br />A/G, ...
German Use of Enigma<br />
German Use of Enigma<br />Day Keys (RO, RS, PB) distributed monthly in key books<br /><ul><li>For each message, sender cho...
Agenda<br />Development of Enigma Machine – Why/How/What<br />The Rejewski Crack<br />The Turing Crack<br />Historical Imp...
Biuro Szyfrów<br />1918 – Polish Independence<br />1919 – Creation (and success) of Cipher Bureau <br />1926 – Germany goe...
The Rejewski Crack<br />Intuition,Espionage,Engineering <br />Understand how Enigma works<br />Reverse-engineer the wiring...
The Math of Permutation Cycles<br /> P = <br /> P-1 = <br />
Cycle Notation<br /> P = <br /> P  =  (AECH)(BFD)(G) <br />  =    (BFD)(G) (AECH)<br />  =     (FDB)(G)(CHAE)<br /> P-1  =...
Cycle Structure<br />  =  (AECH)(BFD)(G) <br /> P = <br />     4          3      1<br />  =  (AFC)(BG)(D)(EH) <br /> Q = <...
Composition<br /> P = <br />  =  (AECH)(BFD)(G) <br /> Q = <br />  =  (AFC)(BG)(D)(EH) <br /> Q ◦ P =  Q(P()) =  (AHFDGBCE...
Identity<br />  =  (A)(B)(C)(D)(E)(F)(G)(H)<br />I = <br />P ◦ I  =  I ◦ P  =  P<br />P ◦ P -1  = I<br />I ◦ I  =  I     i...
Conjugation<br /> Conjugation of Q by P is defined as  P ◦ Q ◦ P-1<br />  P = (AECH)(BFD)(G) <br />  P-1 = (HCEA)(DFB)(G) ...
Theorem: Cycle structure is invariant under conjugation<br />Proof:<br />Suppose Q: ij, that is Q(i) = j.<br />Consider P...
Using Permuation Cycles on Enigma<br />A<br />B<br />Suppose we intercept a message: BOLJRVSQIGPQTMNWJRAKOBYTKMTTGBBRQUPWL...
Using Permuation Cycles on Enigma<br />If we have many intercepts from the same day, then they were produced with the same...
Explore the nature of En<br />A<br />B<br />En = P ◦  Rn ◦ P        where P is the plugboard permutation and Rn is rotor p...
Now, where are we?<br />Figuring out En is problem of size 1016  <br />Now, we have Rn, a smaller problem: 105<br />Just b...
Building the Rejewski Dictionary<br /> RO	RS	 E4 ◦ E1 	 E5 ◦ E2 	 E6 ◦ E3<br /> 1 2 3	AAA 	13-13	1-1-12-12	1-1-12-12<br />...
Recovering the Plugboard<br />Plugboard is the biggest problem combinatorically<br />But… It is trivial to solve<br />E4 ◦...
Paradox of Decreasing Benefit<br />Keysize<br /># Cables<br />
Agenda<br />Development of Enigma Machine – Why/How/What<br />The Rejewski Crack<br />The Turing Crack<br />Historical Imp...
1939 – Brink of War<br />Polish deliver Enigma replica and training to England and France <br />Biuro Szyfrów is dismantle...
Bletchley Park<br />HQ of British Government Code and Cypher School (GCCS) <br />
New Challenges<br />Combinatoric<br />More rotors to choose from<br />Increase # of plugs<br />Ring settings<br />Procedur...
Turing’s Solution<br />Known-Plaintext attack<br />Heil Hitler<br />Wetterbericht<br />Seeding values<br />Plaintext Crib:...
Finding Cycles<br />WETTERBERICHT<br />EXLMBTWZXBITW<br />E1:  WE<br />E5:  EB<br />E7:  BW<br />
J<br />Q<br />F<br />b<br />E<br />E1<br />E1:  WE<br />E5:  EB<br />E7:  BW<br />a<br />W<br />J<br />Q<br />J<br />B<...
J<br />Q<br />F<br />b<br />E1<br />a<br />J<br />Q<br />J<br />b<br />E5<br />c<br />J<br />Q<br />L<br />E7<br />c<br />...
M<br />V<br />C<br />b<br />E1<br />a<br />M<br />Z<br />C<br />b<br />E5<br />c<br />M<br />B<br />D<br />E7<br />c<br />...
M<br />V<br />C<br />b<br />a<br />E1<br />M<br />Z<br />C<br />b<br />E5<br />c<br />M<br />B<br />D<br />E7<br />P(false...
Turing’s Bombe<br />NOT a computer<br />Multi-Enigma Wiring<br />120 rpm  max 6 hrs to solve<br />~70% of days cracked<br...
Agenda<br />Development of Enigma Machine – Why/How/What<br />The Rejewski Crack<br />The Turing Crack<br />Historical Imp...
6 : 60,000,000 <br />   ::      <br />8 : ?<br />
Secrecy<br />Bletchley Park is gutted<br />Enigma machines captured (and distributed!)<br />Top Secret status until 1973!<...
Marian Rejewski – During and After the War<br /><ul><li>1939 – Romania
1939 – France
French cipher bureau
1940 – Algeria
1940 – Back to France
Rozycki dies in transit
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Cracking the Enigma Machine - Rejewski, Turing and the Math that saved the world

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This presentation demonstrates the historical and mathematical background to the brilliant work done by Polish and British cryptology experts before and during World War II.
The solutions provided by Marian Rejewski, Alan Turing and their co-workers had a major impact on the outcome of the war.

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Cracking the Enigma Machine - Rejewski, Turing and the Math that saved the world

  1. 1. The Math That Saved the World<br />Brad Young<br />brad@clearpoint.co.il<br />A Mathematical and Historical Analysis of the Cryptographic Attacks on the Nazi Enigma Machine<br /> Marian Rejewski<br />Alan Turing<br />
  2. 2. Agenda<br />Development of Enigma Machine – Why/How/What<br />The Rejewski Crack<br />The Turing Crack<br />Historical Impact<br />
  3. 3. WWI Cryptology<br />First major war with radio + telegraph <br />Very large volume of communications <br />Hand-ciphers<br />Playfair, ADFGVX etc.<br />Bigraph substitution + transformation<br />Encryption/Decryption<br />Inefficient …Became bottleneck<br />Cryptanalysis<br />Difficult, time-consuming…<br />But successful (mainly)<br />
  4. 4. Zimmermann Telegram<br />
  5. 5. Invention of Enigma Machine<br />Arthur Scherbius<br />Efficient!<br />(oh, and also Secure, by the way)<br />Business, Military versions<br />Early 1920’s – very poor sales<br />German economy in trouble<br />
  6. 6. Oops<br />Publishes history book<br />Reveals the impact of crypto on WWI<br />Now, the Germans want Enigma!<br />
  7. 7. A<br />B<br />C<br />D<br />E<br />F<br />G<br />H<br />Reflector<br />3rd Rotor<br />2nd Rotor<br />1st Rotor<br />Lightbulbs<br />Keyboard<br />Enigma Schematic<br />
  8. 8. A<br />B<br />C<br />D<br />E<br />F<br />G<br />H<br />Reflector<br />Lightbulbs<br />3rd Rotor<br />2nd Rotor<br />1st Rotor<br />Keyboard<br />Electric Circuit<br />
  9. 9. A<br />B<br />Pressing ‘A’ on the keyboard…<br />C<br />D<br />E<br />F<br />… lights the ‘B’ lightbulb<br />G<br />H<br />NOTE: Because it is a electric circuit, no letter can map to itself. Minor detail combinatorically speaking, but very important for the Turing crack.<br />Reflector<br />Lightbulbs<br />3rd Rotor<br />2nd Rotor<br />1st Rotor<br />Keyboard<br />Electric Circuit<br />
  10. 10. A<br />B<br />C<br />D<br />E<br />After each letter, the first rotor shifts one step.<br />So now, pressing ‘A’ lights a different lightbulb….’F’<br />F<br />G<br />H<br />Reflector<br />Lightbulbs<br />3rd Rotor<br />2nd Rotor<br />1st Rotor<br />Keyboard<br />Rotor Shift<br />
  11. 11. A<br />B<br />C<br />D<br />E<br />F<br />Sits between keyboard and rotors.<br />Each plug cable swaps signal between two letters.<br />6 cables connect 12 letters. 14 other letters are not plugged at all.<br />G<br />H<br />Reflector<br />Lightbulbs<br />Plugboard<br />3rd Rotor<br />2nd Rotor<br />1st Rotor<br />Keyboard<br />Plugboard<br />
  12. 12. Plugboard<br />
  13. 13. Keysize<br />A<br />B<br />Rotor Order<br />Rotor Setting<br />Plugboard<br />Wiring<br />I – III - II<br />VYJ<br />A/G, D/Q, J/Z,L/S, M/V, N/T<br />3! = 6<br />263 =17,576<br />C(26,2) x C(24,2) x<br />C(22,2) x C(20,2) x<br />C(18,2) x C(16,2) x 1/6!<br />(26!)3 x C(26,2)…C(2,2)x1/13!<br />C<br />≈ 105<br />D<br />E<br />F<br />≈ 1011<br />≈ 1092<br />G<br />H<br />Total Key Size ≈ 10108<br />Variable Key Size ≈ 1016<br />
  14. 14. German Use of Enigma<br />
  15. 15. German Use of Enigma<br />Day Keys (RO, RS, PB) distributed monthly in key books<br /><ul><li>For each message, sender chooses Message Key (Rotor Setting only)</li></ul>Encode Message Key using Day Key, twice<br />Move rotor to Message Key setting <br />Encode actual message<br />Set to Day Key(VYJ)<br />Change to Message Key<br />(CIL)<br />CILCILATTACKFROMNORTHATNINETHIRTYBOKJRVSQIGPQTMNWJRAKOBYTKMTKGBBRQ<br />
  16. 16. Agenda<br />Development of Enigma Machine – Why/How/What<br />The Rejewski Crack<br />The Turing Crack<br />Historical Impact<br />
  17. 17. Biuro Szyfrów<br />1918 – Polish Independence<br />1919 – Creation (and success) of Cipher Bureau <br />1926 – Germany goes dark as Enigma is adopted<br />1930 – Bring in the mathematicians (?!?)<br />Marian Rejewski<br />Jerzy Różycki<br />Henryk Zygalski<br />
  18. 18. The Rejewski Crack<br />Intuition,Espionage,Engineering <br />Understand how Enigma works<br />Reverse-engineer the wiring<br />Be able to crack the key each day<br />Permutational Mathematics<br />
  19. 19. The Math of Permutation Cycles<br /> P = <br /> P-1 = <br />
  20. 20. Cycle Notation<br /> P = <br /> P = (AECH)(BFD)(G) <br /> = (BFD)(G) (AECH)<br /> = (FDB)(G)(CHAE)<br /> P-1 = (HCEA)(DFB)(G) <br />Benefits of cycle notation:<br />Concise<br />Easier to take inverse<br />(These are benefits of efficiency)<br />
  21. 21. Cycle Structure<br /> = (AECH)(BFD)(G) <br /> P = <br /> 4 3 1<br /> = (AFC)(BG)(D)(EH) <br /> Q = <br /> 3 2 1 2<br />Benefits of cycle notation:<br />Concise<br />Easier to take inverse<br />Gives more info – Cycle Structure<br /> (This is a benefit of value-add information)<br />
  22. 22. Composition<br /> P = <br /> = (AECH)(BFD)(G) <br /> Q = <br /> = (AFC)(BG)(D)(EH) <br /> Q ◦ P = Q(P()) = (AHFDGBCE)<br /> Q ◦ P ≠ P ◦ Q - NOT Commutative<br /> Q ◦ ( P ◦ R ) = ( Q ◦ P ) ◦ R - Associative<br />
  23. 23. Identity<br /> = (A)(B)(C)(D)(E)(F)(G)(H)<br />I = <br />P ◦ I = I ◦ P = P<br />P ◦ P -1 = I<br />I ◦ I = I i.e. I = I -1<br />(ab) ≠ I , but (ab) ◦ (ab) = (a)(b)<br />i.e. (ab) = (ab)-1<br />
  24. 24. Conjugation<br /> Conjugation of Q by P is defined as P ◦ Q ◦ P-1<br /> P = (AECH)(BFD)(G) <br /> P-1 = (HCEA)(DFB)(G) <br /> Q = (AFC)(BG)(D)(EH) <br />1-2-2-3<br />1-2-2-3<br />This is not a coincidence!<br />This is not a coincidence!<br />P ◦ Q ◦ P-1 = (AC)(B)(DHE)(FG)<br />
  25. 25. Theorem: Cycle structure is invariant under conjugation<br />Proof:<br />Suppose Q: ij, that is Q(i) = j.<br />Consider P ◦ Q ◦ P-1 (P(i)).<br />P ◦ Q ◦ P-1 (P(i)) = P ◦ Q ◦ (P-1 ◦ P)(i)<br /> = P ◦ Q(i)<br /> = P(j)<br />i.e. P ◦ Q ◦ P-1: P(i)P(j)<br />Therefore…<br />If Q has k-cycle (i1, i2 … ik) then P ◦ Q ◦ P-1 has k-cycle (P(i1), P(i2)…P(ik))<br /> QED<br />
  26. 26. Using Permuation Cycles on Enigma<br />A<br />B<br />Suppose we intercept a message: BOLJRVSQIGPQTMNWJRAKOBYTKMTTGBBRQUPWLHSOLNFEQTHJOVX<br />Plaintext: abcabcCiphertext: BOLJRV<br />Define En as the permutation that occurs when Enigma machine is in state n.<br />So, in the first state, aB. In the fourth state, aJ<br />E1 = (aB …E4 = (aJ …<br />Now…Recall the effect of the Reflector, which creates 2-letter circuits<br />So, if aB, then Ba. So the cycle is closed.<br />E1 = (aB) …E4 = (aJ) …<br />So, we can now compute E4 ◦ E1 = (BJ …<br />C<br />These are the variablesa,b,c, not the actual letters<br />D<br />E<br />F<br />G<br />H<br />
  27. 27. Using Permuation Cycles on Enigma<br />If we have many intercepts from the same day, then they were produced with the same day settings. <br />So we can calculate the entire compositions…<br />E4 ◦ E1 = (BJUMPWTCFE)(ARDNHSLYZK)(G)(I)(O)(Q)(X)(V)E5 ◦ E2 = (ORJCLVHGXKF)(AUYMPZQNDWB)(ES)(IT)E6 ◦ E3 = (BWOIKTZHXB)(EPQJYLVGN)(ARCU)(DSMF)<br />Good news: <br />abc variables have been eliminated! <br />We’ve found a unique identifier!<br />Bad news:<br />It is one of 10,000,000,000,000,000 possibilities<br />
  28. 28. Explore the nature of En<br />A<br />B<br />En = P ◦ Rn ◦ P where P is the plugboard permutation and Rn is rotor permutation when in state n<br />E4 ◦ E1 = P ◦ R4 ◦ P ◦ P ◦ R1 ◦ P<br />Now, recall the plugboard…<br />P = (ab)(cd)(ef)(gh)(ij)(kl)(m)(n)(o)(p)(q)(r)(s)(t)(u)(v)(w)(x)(y)(z)<br />All 2-cycles and 1-cycles, therefore P = P-1 !<br />E4 ◦ E1 = P ◦ R4 ◦ P ◦ P ◦ R1 ◦ P<br /> = P ◦ R4 ◦ P ◦ P-1 ◦ R1 ◦ P<br /> = P ◦ R4 ◦ (P ◦ P-1 ) ◦ R1 ◦ P <br /> = P ◦ R4 ◦ R1 ◦ P <br /> = P ◦ (R4 ◦ R1 ) ◦ P <br /> = P ◦ (R4 ◦ R1 ) ◦ P-1<br />C<br />P<br />R<br />D<br />E<br />F<br />G<br />H<br />Conjugation:Cycle structure of E4 ◦ E1 is same as cycle structure of R4 ◦ R1 and is not affected at all by the plugboard!<br />E4 ◦ E1 = (BJUMPWTCFE)(ARDNHSLYZK)(G)(I)(O)(Q)(X)(V)E5 ◦ E2 = (AUYMPZQNDWB)(CLVHGXKFORJ)(ES)(IT)E6 ◦ E3 = (BWOIKTZHXB)(EPQJYLVGN)(ARCU)(DSMF)<br />1-1-1-1-1-1-10-10 ; 2-2-11-11 ; 4-4-9-9<br />Remember:<br />Keysize(R) ≈ 105<br />Keysize(P) ≈ 1011<br />
  29. 29. Now, where are we?<br />Figuring out En is problem of size 1016 <br />Now, we have Rn, a smaller problem: 105<br />Just barely small enough to attack brute force<br />
  30. 30. Building the Rejewski Dictionary<br /> RO RS E4 ◦ E1 E5 ◦ E2 E6 ◦ E3<br /> 1 2 3 AAA 13-13 1-1-12-12 1-1-12-12<br /> 1 2 3 BAA 1-1-12-12 1-1-12-12 2-2-11-11<br /> 1 2 3 CAA 1-1-12-12; 2-2-11-11 1-1-12-12<br /> 1 2 3 DAA 2-2-11-11 1-1-12-12 13-13<br /> 1 2 3 EAA 1-1-12-12 13-13 13-13<br /> 1 2 3 FAA 13-13 13-13 1-1-2-2-3-3-3-3-4-4<br /> 1 2 3 GAA 13-13 1-1-2-2-3-3-3-3-4-4 2-2-5-5-6-6<br /> 1 2 3 HAA 1-1-2-2-3-3-3-3-4-4 2-2-5-5-6-6 13-13<br /> 1 2 3 IAA 2-2-5-5-6-6 13-13 4-4-9-9<br /> 1 2 3 JAA 13-13 4-4-9-9 1-1-5-5-7-7<br /> 1 2 3 KAA 4-4-9-9 1-1-5-5-7-7 13-13<br /> 1 2 3 LAA 1-1-5-5-7-7 13-13 1-1-2-2-10-10<br /> 1 2 3 MAA 13-13 1-1-2-2-10-10 1-1-1-1-11-11<br />. . . . .<br />. . . . .<br />. . . . .<br />…<br />2-2-11-11; 1-1-1-1-1-1-1-1-4-4-5-5; 1-1-12-12 KFE 213<br />2-2-11-11; 1-1-1-1-1-1-1-1-4-4-5-5; 2-2-5-5-6-6 ZTF 132<br />2-2-11-11; 1-1-1-1-1-1-1-1-4-4-5-5; 5-5-8-8 GIC 312<br />2-2-11-11; 1-1-1-1-1-1-1-1-9-9; 1-1-12-12 AHH 132<br />2-2-11-11; 1-1-1-1-1-1-1-1-9-9; 1-1-12-12 WLA 312<br />2-2-11-11; 1-1-1-1-1-1-1-1-9-9; 1-1-5-5-7-7 YKG 132<br />2-2-11-11; 1-1-1-1-1-1-1-1-9-9; 13-13 DXI 213<br />2-2-11-11; 1-1-1-1-1-1-1-1-9-9; 13-13 ESY 321<br />2-2-11-11; 1-1-1-1-1-1-1-1-9-9; 13-13 VHX 213<br />2-2-11-11; 1-1-1-1-1-1-1-1-9-9; 2-2-11-11 UNV 231<br />…<br />1 setting every 4 minutes, x 20 hours/day = 300 / day<br />105 / 300 ≈ 1 year to complete<br />Good news; Solved the RO, RS!<br />Bad news: 105 solved, 1011 not solved<br />Cycle structure is not unique<br />…even though 105 &lt;&lt; (1012)3 ≈ 1012<br />But most have &lt; 10<br />
  31. 31. Recovering the Plugboard<br />Plugboard is the biggest problem combinatorically<br />But… It is trivial to solve<br />E4 ◦ E1 = (BJUMPWTCFE)(ARDNHSLYZK)(G)(I)(O)(Q)(X)(V)<br />R4 ◦ R1 = (MGWTREFBJU)(AKZCINLSHY)(P)(D)(O)(Q)(V)(X)<br />(BJUMPWTCFE)<br />(BJUMGWTREF)<br />Plugboard settings: P/G , C/R , E/F , etc.<br />
  32. 32. Paradox of Decreasing Benefit<br />Keysize<br /># Cables<br />
  33. 33. Agenda<br />Development of Enigma Machine – Why/How/What<br />The Rejewski Crack<br />The Turing Crack<br />Historical Impact<br />
  34. 34. 1939 – Brink of War<br />Polish deliver Enigma replica and training to England and France <br />Biuro Szyfrów is dismantled<br />
  35. 35. Bletchley Park<br />HQ of British Government Code and Cypher School (GCCS) <br />
  36. 36. New Challenges<br />Combinatoric<br />More rotors to choose from<br />Increase # of plugs<br />Ring settings<br />Procedural<br />Eliminate Message Key repetition<br />Navy / Air Force / Army mods<br />Keysize now 1023<br />
  37. 37. Turing’s Solution<br />Known-Plaintext attack<br />Heil Hitler<br />Wetterbericht<br />Seeding values<br />Plaintext Crib:Ciphertext: <br />Try to place the crib without letter any letter mapping to itself<br />WETTERBERICHT<br />WETTERBERICHT<br />WETTERBERICHT<br />WETTERBERICHT<br />WETTERBERICHT<br />EXLMBTWZXBITWZCIQ<br />P(false hit) = (25/26)length of crib<br />
  38. 38. Finding Cycles<br />WETTERBERICHT<br />EXLMBTWZXBITW<br />E1: WE<br />E5: EB<br />E7: BW<br />
  39. 39. J<br />Q<br />F<br />b<br />E<br />E1<br />E1: WE<br />E5: EB<br />E7: BW<br />a<br />W<br />J<br />Q<br />J<br />B<br />b<br />E<br />E5<br />c<br />J<br />Q<br />L<br />B<br />E7<br />c<br />a<br />W<br />
  40. 40. J<br />Q<br />F<br />b<br />E1<br />a<br />J<br />Q<br />J<br />b<br />E5<br />c<br />J<br />Q<br />L<br />E7<br />c<br />a<br />
  41. 41. M<br />V<br />C<br />b<br />E1<br />a<br />M<br />Z<br />C<br />b<br />E5<br />c<br />M<br />B<br />D<br />E7<br />c<br />a<br />
  42. 42. M<br />V<br />C<br />b<br />a<br />E1<br />M<br />Z<br />C<br />b<br />E5<br />c<br />M<br />B<br />D<br />E7<br />P(false hit) = (1/26)length of cycle-1<br />a<br />c<br />
  43. 43. Turing’s Bombe<br />NOT a computer<br />Multi-Enigma Wiring<br />120 rpm  max 6 hrs to solve<br />~70% of days cracked<br />Accurate crib?<br />Location of crib in message?<br />Find cycle in message?<br />Not too many false hits?<br />Crib seeding<br />Fake missions – Get spotted<br />18’26”N, 72’49”E = einachtzweisechsnordensiebenzweivierneunosten <br />Reimann zeta zeros<br />
  44. 44. Agenda<br />Development of Enigma Machine – Why/How/What<br />The Rejewski Crack<br />The Turing Crack<br />Historical Impact<br />
  45. 45. 6 : 60,000,000 <br /> :: <br />8 : ?<br />
  46. 46. Secrecy<br />Bletchley Park is gutted<br />Enigma machines captured (and distributed!)<br />Top Secret status until 1973!<br />
  47. 47. Marian Rejewski – During and After the War<br /><ul><li>1939 – Romania
  48. 48. 1939 – France
  49. 49. French cipher bureau
  50. 50. 1940 – Algeria
  51. 51. 1940 – Back to France
  52. 52. Rozycki dies in transit
  53. 53. Underground cryptography
  54. 54. 1942 – Spain
  55. 55. Betrayed mid-crossing
  56. 56. Arrested + Jailed
  57. 57. 1942 – Portugal, Gibraltar
  58. 58. 1942 – England
  59. 59. No security clearance (Vichy France)
  60. 60. Polish Army – hand ciphers
  61. 61. 1945 – Poland
  62. 62. 1950 – Cable salesman
  63. 63. Secret Service meddling
  64. 64. 1955 – Bookkeeper
  65. 65. Until retirement
  66. 66. 1973 – Finally learns about ULTRA
  67. 67. 1980 – Dies at age 73</li></li></ul><li>Alan Turing –Timeline<br />1936-8 – Computability, Turing Machine, Decidability, Riemann<br />1939-45 – Bletchley Park<br />1946 – Automatic Computing Engine<br />1947-48 – Algorithms, Neural Nets, AI<br />1948 – Almost an Olympian<br />1948-50 – Manchester Mark I Mersenne + ??? (Was he on a secret nuclear program?? Might explain the gov’t paranoia)<br />1950 – Turing Test<br />1951 – Mathematical Biology<br />1952 – Arrest<br />1954 – Death at age 41<br />
  68. 68. Colossus Computer <br />Cracks Lorenz cipher<br />High-level German communications<br />History of Computers<br />Z3<br />Colossus<br />ENIAC<br />Mark I<br />
  69. 69. NSA<br />
  70. 70. Addenda, Errata, Anecdotes<br />Wiring analysis<br />Hans Thilo-Schmidt<br />TTTTTTTTTTTT<br />Entry wheel order<br />Why E1-E6, instead of E0-E5 ?<br />Ring Settings and Rotor Stepping<br />“Turing. Alan Turing.”<br />Other WWII Cryptanalysis<br />Disguising ULTRA intelligence<br />Suggested Reading<br />David Kahn – The Codebreakers<br />Simon Singh – The Code Book<br />

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