Notes for January 21, 1998 1. Greetings and felicitations! a. Reading: Pfleeger, pp. 91Ç118 2. Puzzle of the day a. Fun stuff 3. DES a. Go through the algorithm 4. Public-Key Cryptography a. Basic idea: 2 keys, one private, one public b. Cryptosystem must satisfy: (a), given public key, CI to get private key; (b) cipher with- stands chosen plaintext attack; (c) encryption, decryption computationally feasible [note: commutativity NOT required] c. Benefits: can give confidentiality or authentiction or both 5. Use of PKC a. Normally used as key interchange system to exchange secret keys (cheap) b. Then use secret key system (too expensive to use PKC for this) [ ended here ] 6. RSA a. Provides both authenticity and confidentiality b. Go through algorithm: Idea: C = Me mod n, M = Cd mod n, with ed mod f(n) = 1. Proof: Mf(n) mod n = 1 [by Fermatºs theorem as generalized by Euler]; follows immedi- ately from ed mod f(n) = 1. Public key is (e, n); private key is d. Choose n = pq; then f(n) = (pÇ1)(qÇ1). c. Example: p = 5, q = 7; n = 35, f(n) = (5Ç1)(7Ç1) = 24. Pick d = 11. Then de mod f(n) = 1, so choose e = 11. To encipher 2, C = Me mod n = 211 mod 35 = 2048 mod 35 = 18, and M = Cd mod n = 1811 mod 35 = 2. d. Example: p = 53, q = 61, n = 3233, f(n) = (53Ç1)(61Ç1) = 3120. Take d = 791; then e = 71. Encipher M = RENAISSANCE: A = 00, B = 01, ”, Z = 25, blank = 26. Then: M = RE NA IS SA NC Eblank = 1704 1300 0818 1800 1302 0426 C = (1704)71 mod 3233 = 3106; etc. = 3106 0100 0931 2691 1984 2927