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cse101_10_5_11 - message to bob will be numbers mod N Any...

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The RSA Cryptosystem 1. Public Key Cryptography a. Send secret information over an insecure channel, to someone you’ve never met. Alice wants to sent a message to bob, X -> encode -> y = c(x) -> decode -> d(y) Eve listening in, but only bob can decode it. b. A physical locker system Bob maintains a public locker that he leaves open. Anyone with a message for him should put it in the locker and shut the locker. Only bob has the key to the door. c. A digital locker system Bob has a public encryption function e() and a secret decryption function d(). Anybody who wants to sent him a message x should send him e(x). Only bob has the ability to decrypt it. D(e(x)) = x Each user (eg. Bob) has the following information. Public e() private d() The recipient tells you how to encrypt. 2. RSA (rivest sharnir adlenum) a. Here’s how bob picks his encryption and decryption functions a.i. He picks two large primes, pa and q (say 1000 bits long) set N = pq. All
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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 (p-1)(q-1) 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 (p-1)(q-1) D = e-1 mod (p-1)(q-1) 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 = 3-1 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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cse101_10_5_11 - message to bob will be numbers mod N Any...

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