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Unformatted text preview: B1 = 743, B2 = 1988, B3 = 4001, B4 = 2942, B5 = 3421, B6 = 2210, B7 = 2306, and B8 = 222, and tells them to Carol. Carol generates eight 12bit random numbers, C1 = 1708, C2 = 711, C3 = 1969, C4 = 3112, C5 = 4014, C6 = 2308, C7 = 2212, and C8 = 222, and tells them to Bob. (3) Bob wants to buy S7 , so he encrypts C7 with the public key that Alice gave him. 22125145 mod 7387 = 5928 Now: 2212 = 0100010100100 5928 = 1011100101000 So, the FBI of those two numbers is {0, 1, 4, 5, 6}. He sends this to Carol. Carol wants to buy S2 , so she encrypts B2 with the public key that Alice gave her and computes the FBI of B2 with the result of her encryption. She sends {0, 1, 2, 6, 9, 10} to Bob. (4) Bob takes B1 , B2 , ..., B8 , and replaces every bit whose index is not in the set {0, 1, 2, 6, 9, 10} with its complement. For example: B2 = 111111000100 = 1988 B'2 = 011001111100 = 1660 He sends B'1, B'2, ..., B'8, to Alice. Carol takes C1 , C2 , ..., C8 , and replaces every bit whose index is not in the set {0, 1, 4, 5, 6} with its complement. For example: C7 = 0100010100100 = 2212 C'7 = 1011100101000 = 5928 She sends C'1, C'2, ..., C'8, to Alice. (5) Alice decrypts all C'i with Bob’s private key and XORs the results with Si. For example, for i = 7: 5928777 mod 7387 = 2212; 2546 • 2212 = 342 She sends the results to Bob. Alice decrypts all B'i with Carol’s private key and XORs the results with Si. For example, for i = 2: 16602261 (mod 2747) = 1988; 471 • 1988 = 1555 She sends the results to Carol. (6) Bob computes S7 by XORing C7 and the seventh number he received from Alice: 2212 • 342 = 2546 Carol computes S2 by XORing B2 and the second number she received from Alice. 1988 • 1555 = 471 The protocol works for any number of buyers. If Bob, Carol, and Dave want to buy secrets, Alice gives each buyer two public keys, one for each of the others. Each buyer gets a set of numbers from each other buyer. Then, they complete the protocol with Alice for each of their sets of numbers and XOR all of their final results from Alice to get t...
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This note was uploaded on 10/18/2010 for the course MATH CS 301 taught by Professor Aliulger during the Fall '10 term at Koç University.
 Fall '10
 ALIULGER
 Cryptography

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