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Unformatted text preview: b generates k n-bit random numbers, B1 , B2 , ..., Bk, and tells them to Carol. Carol generates k n-bit random numbers, C1 , C2 , ..., Ck, and tells them to Bob. (3) Bob encrypts Cb (remember, Sb is the secret he wants to buy) with the public key from Alice. He computes the FBI of Cb and the result he just encrypted. He sends this FBI to Carol. Carol encrypts Bc (remember, Sc is the secret she wants to buy) with the public key from Alice. She computes the FBI of Bc and the result she just encrypted. She sends this FBI to Bob. (4) Bob takes each of the n-bit numbers B1, B2 , ..., Bk, and replaces every bit whose index is not in the FBI he received from Carol with its complement. He sends this new list of n-bit numbers, B'1, B'2, ..., B'k, to Alice. Carol takes each of the n-bit numbers C1 , C2 , ..., Ck, and replaces every bit whose index is not in the FBI she received from Bob with its complement. She sends this new list of n-bit numbers, C'1, C'2, ..., C'k, to Alice. (5) Alice decrypts all C'i with Bob’s private key, giving her k n-bit numbers: C"1, C"2, ..., C"k. She computes Si • C"i, for i = 1 to k, and sends the results to Bob. Alice decrypts all B'i with Carol’s private key, giving her k n-bit numbers: B"1, B"2, ..., B"k. She computes Si • B"i, for i = 1 to k, and sends the results to Carol. (6) Bob computes Sb by XORing Cb and the bth number he received from Alice. Carol computes Sc by XORing Bc and the cth number she received from Alice. This is complicated. An example will go a long way to help. Alice has the following eight 12-bit secrets for sale: S1 =1990, S2 =471, S3 =3860, S4 =1487, S5 =2235, S6 =3751, S7 =2546, and S8 =4043. Bob wants to buy S7. Carol wants to buy S2. (1) Alice uses the RSA algorithm. The key pair she will use with Bob is: n = 7387, e = 5145, and d = 777. The key pair she will use with Carol is: n = 2747, e = 1421, and d = 2261. She tells Bob and Carol each their public key. (2) Bob generates eight 12-bit random numbers,...
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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