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Enigma

Enigma. Chris Christensen Department of Mathematics and Statistics Northern Kentucky University. World War I. Rotor machines. Rotor Machines. Arthur Scherbius (1878 – 1929) 23 February 1918 Hugo Alexander Koch (1870 – 1928) 7 October 1919 Arvid Gerhard Damm

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Enigma

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  1. Enigma Chris Christensen Department of Mathematics and Statistics Northern Kentucky University

  2. World War I

  3. Rotor machines

  4. Rotor Machines • Arthur Scherbius (1878 – 1929) 23 February 1918 • Hugo Alexander Koch (1870 – 1928) 7 October 1919 • Arvid Gerhard Damm (d. 1927) 10 October 1919 • Edward Hebern (1869 – 1952) 1919

  5. Enigma

  6. Enigma ciphers

  7. Enigma

  8. Enigma

  9. Security Enigma has a period of about 17576.

  10. Each Enigma cipher is a simple substitution abcdefghijklmnopqrstuvwxyz OHELCPYBSURDZTAFXKINJWVQGM (ao)(bh)(ce)(dl)(fp)(gy)(is)(ju)(kr)(mz)(nt)(qx)(vw)

  11. Setting enigma

  12. Enigma Rotor

  13. The Key • At first there were 3 rotors. • 6 ways to order the rotors.

  14. Enigma Rotors

  15. Setting the Rotors

  16. The Key • 6 ways to order the rotors. • 17576 ways to select the rotor setting.

  17. The Plugboard

  18. The Key • 6 ways to order the rotors. • 17576 ways to select the rotor setting. • 100,391,791,500 ways to set the plugboard.

  19. The positions of the turnover notches was part of the key.

  20. The Key • 6 ways to order the rotors. • 17576 ways to select the rotor setting. • 100,391,791,500 ways to set the plugboard. • 676 ways to set the turnover notches.

  21. The Key • 6 ways to order the rotors. • 17576 ways to select the rotor setting. • 100,391,791,500 ways to set the plugboard. • 676 ways to set the turnover notches. • 7,156,755,732,750,624,000 ways to set the key.

  22. Enigma Cipher abcdefghijklmnopqrstuvwxyz OHELCPYBSURDZTAFXKINJWVQGM (ao)(bh)(ce)(dl)(fp)(gy)(is)(ju)(kr)(mz)(nt)(qx)(vw)

  23. The sender and receiver must set their machines in exactly the same way.

  24. Brute Force Attack Would take 22,693,900,000 years.

  25. Breaking Enigma

  26. The Polish Codebreakers • JerzyRozycki (1909 – 1942) • HenrykZygalski (1908 – 1978) • Marian Rejewski (1905 – 1980)

  27. Bomba

  28. Bletchley Park

  29. Alan Turing (1912 – 1954)

  30. Hut 8

  31. The Turing Bombe

  32. Determining Starting Position of the Rotors

  33. Cribs • CIPHERTEXT VWHCD IUGHL UVFAO BNEWN AGZWY ZUXNN PYZWN LKMUO FRIIL OJPAE • Plaintextmarkworthxattackedxbyxtwoxpursuitxplanes

  34. No Letter Encrypts as Itself! abcdefghijklmnopqrstuvwxyz OHELCPYBSURDZTAFXKINJWVQGM (ao)(bh)(ce)(dl)(fp)(gy)(is)(ju)(kr)(mz)(nt)(qx)(vw)

  35. Crib Placement VWHCDIUGHLUVFAOBNEWNAGZWYZUXNN markworthxattackedxbyxtwoxpurs VWHCDIUGHLUVFAOBNEWNAGZWYZUXNN markworthxattackedxbyxtwoxpurs VWHCDIUGHLUVFAOBNEWNAGZWYZUXNN markworthxattackedxbyxtwoxpurs

  36. Crib Placement VWHCDIUGHLUVFAOBNEWNAGZWYZUXNN markworthxattackedxbyxtwoxpur VWHCDIUGHLUVFAOBNEWNAGZWYZUXNN markworthxattackedxbyxtwoxpu VWHCDIUGHLUVFAOBNEWNAGZWYZUXNN markworthxattackedxbyxtwoxp

  37. Crib Placement

  38. Diagram

  39. Offsets

  40. Position 1: U (20) and A (0). Position 5: U (20) and O (14). Position 9: O (14) and X (23). Position 18: W (22) and X (23). Position13: W (22) and A (0).

  41. Plugging Up Position 1: U (20) and A (0). Position 5: U (20) and O (14). Position 9: O (14) and X (23). Position 18: W (22) and X (23). Position13: W (22) and A (0).

  42. Things go Bad

  43. The Four-RotorNaval Enigma

  44. February 1942

  45. US Navy 4-rotor bombe

  46. US Navy Cryptologic Bombe

  47. NCMLJoe Desch (1909 – 1987)

  48. KKVZ BHVF H?

  49. Hebern Machine

  50. Rotor Machines ECM Mark II/M-134 SIGABA TypeX

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