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Unformatted text preview: message to bob will be numbers mod N. Any message is ultimately a binary number. Divide into O(n)bit chunks and send each in succession. a.ii. He picks e which is relatively prime to (p1)(q1) a.iii. Here’s the scheme: encrypt x > x e mod N (public key: (N,e)) decrypt: y > y d mod N (secret key: d) b. RSA: rob picks: 2 large primes p,q N=pq E is rel prime to (p1)(q1) D = e1 mod (p1)(q1) X > encrypt > y = x e mod N > decrypt > y d mod N. c. Example: Bob picks primes p = 17, q = 11. N = pq = 187. All messages are numbers in range 0 to 186. Bob picks e relatively to 16*10 = 160. E = 3 9rel prime to 160) D = 31 mod 160 = 107. Public information : (N = 187, e = 3) Secret: (d = 107) Alice wants to send him a secret Message x = 6. She sends y = x e mod N = 6 3 mod 187 = 216 mod 187 = 29. Bob computes y d mod N = 29 107 mod 187 = 6. d....
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 Spring '08
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 Algorithms, Cryptography, yd mod, xe mod, yd mod N.

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