Mat 140 Cryptology Day 4

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An overview of public-key cryptography and a wrap-up of this minicourse. For MAT 140: Introduction to the Mathematical Sciences at Franklin College.

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Mat 140 Cryptology Day 4

  1. 1. Cryptology Day 4: Going public MAT 140: Introduction to the Mathematical Sciences 24 September 2008 Robert Talbert, PhD Associate Professor of Mathematics and Computing Science rtalbert@franklincollege.edu
  2. 2. Recap of Day 3 • Bits, bytes, and binary representation of text using ASCII • The XOR operation • The Simple XOR cipher • Perfect security and one-time pads
  3. 3. Alice
  4. 4. Alice Bob
  5. 5. Alice Bob
  6. 6. Plaintext Dear Bob - The meeting will be at the embassy. Alice Bob
  7. 7. Encryption function Plaintext Dear Bob - The meeting will be at the embassy. Alice Bob
  8. 8. Encryption function Plaintext Ciphertext Dear Bob - The Qrne Obo - Gur meeting will be at zrrgvat jvyy or the embassy. ng gur rzonffl. Alice Bob
  9. 9. Encryption function Plaintext Ciphertext Dear Bob - The Qrne Obo - Gur meeting will be at zrrgvat jvyy or the embassy. ng gur rzonffl. Alice Bob
  10. 10. Decryption Encryption function function Plaintext Ciphertext Dear Bob - The Qrne Obo - Gur meeting will be at zrrgvat jvyy or the embassy. ng gur rzonffl. Alice Bob
  11. 11. Decryption Encryption Original function function Plaintext Ciphertext plaintext Dear Bob - The Qrne Obo - Gur meeting will be at zrrgvat jvyy or Dear Bob - The the embassy. ng gur rzonffl. meeting will be at the embassy. Alice Bob
  12. 12. Decryption Encryption Original function function Plaintext Ciphertext plaintext Dear Bob - The Qrne Obo - Gur meeting will be at zrrgvat jvyy or Dear Bob - The the embassy. ng gur rzonffl. meeting will be at the embassy. Alice Bob How are these communicated?
  13. 13. The key distribution problem
  14. 14. The key distribution problem
  15. 15. The key distribution problem
  16. 16. The key distribution problem
  17. 17. The key distribution problem Insecure channel
  18. 18. The key distribution problem Insecure channel
  19. 19. The key distribution problem Insecure channel
  20. 20. The key distribution problem Insecure channel
  21. 21. The key distribution problem Insecure channel CENSORED
  22. 22. The key distribution problem Insecure channel CENSORED Anonymity
  23. 23. The key distribution problem Insecure channel CENSORED Anonymity
  24. 24. The key distribution problem Insecure channel CENSORED Anonymity
  25. 25. The key distribution problem Insecure channel CENSORED Anonymity
  26. 26. The key distribution problem Insecure channel CENSORED Anonymity
  27. 27. The key distribution problem Insecure channel CENSORED Anonymity
  28. 28. The key distribution problem Insecure channel CENSORED Anonymity Many-to-many communication
  29. 29. Activity: A “public-key” cipher
  30. 30. Why does Kid Crypto work? Can an adversary find the private key from the public key? How does this solve the key distribution problem?
  31. 31. Alice Bob
  32. 32. Alice Bob
  33. 33. Alice Bob
  34. 34. Alice Bob One-way trapdoor function
  35. 35. Alice Bob Public Private One-way trapdoor function (e,n) d
  36. 36. Plaintext Dear Bob - The meeting will be at the embassy. Alice Bob Public Private One-way trapdoor function (e,n) d
  37. 37. Plaintext Dear Bob - The meeting will be at the embassy. Alice Bob Public Private One-way trapdoor function (e,n) d
  38. 38. Encryption (ex) mod n function Plaintext Dear Bob - The meeting will be at the embassy. Alice Bob Public Private One-way trapdoor function (e,n) d
  39. 39. Encryption (ex) mod n function Plaintext Ciphertext Dear Bob - The Qrne Obo - Gur meeting will be at zrrgvat jvyy or the embassy. ng gur rzonffl. Alice Bob Public Private One-way trapdoor function (e,n) d
  40. 40. Encryption (ex) mod n function Plaintext Ciphertext Dear Bob - The Qrne Obo - Gur meeting will be at zrrgvat jvyy or the embassy. ng gur rzonffl. Alice Bob Public Private One-way trapdoor function (e,n) d
  41. 41. Decryption (dy) mod n Encryption (ex) mod n function function Plaintext Ciphertext Dear Bob - The Qrne Obo - Gur meeting will be at zrrgvat jvyy or the embassy. ng gur rzonffl. Alice Bob Public Private One-way trapdoor function (e,n) d
  42. 42. Decryption (dy) mod n Encryption (ex) mod n Original function function Plaintext Ciphertext plaintext Dear Bob - The Qrne Obo - Gur meeting will be at zrrgvat jvyy or Dear Bob - The the embassy. ng gur rzonffl. meeting will be at the embassy. Alice Bob Public Private One-way trapdoor function (e,n) d
  43. 43. RSA Choose two large prime numbers p, q Calculate n = pq and m = (p-1)(q-1) Choose e such that gcd(e, (p-1)(q-1)) = 1 Choose d such that ed = 1 mod (p-1)(q-1) Alice Publicize e, n. Keep d private. To encrypt x: calculate y = xe mod n To decrypt y: calculate z = yd mod n. Fermat’s Little Theorem: Bob xed = x mod n.
  44. 44. This number is a product of two primes: 74037563479561712828046796097 42957314259318888923128908493 62326389727650340282662768919 96419625117843995894330502127 58537011896809828673317327310 89309005525051168770632990723 96380786710086096962537934650 563796359
  45. 45. Modulus (1024 bits): 9d 88 94 32 62 30 a3 3b 0f 5b 30 7c d5 69 75 21 25 99 0f e1 a8 c2 7d 5b 2b e9 24 72 48 fa 13 47 7c 53 8b 6a 56 be 66 5a 93 7c 3b bb 84 d4 90 4e ab d5 aa f1 33 de 93 2a 1c 80 e3 f5 19 25 a8 69 d3 55 44 fd 7f 76 bb 28 f5 90 62 69 57 eb 82 ba dd 73 40 c0 dd fb 7e 2b ea 86 8e 83 eb e1 5f cc f4 a5 a4 be 99 4f 90 ff 66 79 b1 44 d4 13 60 96 80 00 3d f8 49 b5 e7 82 54 b3 9d 17 56 cc 90 bb Exponent (24 bits): 01 00 01
  46. 46. Cutting edge Design/analysis of Elliptic curve Quantum block ciphers cryptography cryptography
  47. 47. Cryptology at Franklin College MAT 135 CMP 141 MAT 140 Computing I MAT 142 Calculus II MAT 240 MAT 300 MAT 233 Methods of Topics in Linear Algebra Problem Solving Mathematics MAT 361 Modern Algebra Careers: NSA and other government; network security MAT 490 and CISSP license; more Individualized Study
  48. 48. For more information http://delicious.com/robert.talbert/crypto http://www.slideshare.net/rtalbert http://en.wikipedia.org/wiki/Portal:Cryptography

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