10.6 In 1985, T. ElGamal announced a public-key scheme based on discrete logarithms, closely related to the Diffie-Hellman technique. As with Diffie-Hellman, the global elements of the ElGamal scheme are a prime number q and a, a primitive root of q. A user A selects a private keyX A and calculates a public keyY A as in Diffie-Hellman. User A encrypts a plaintext M < q intended for user B as follows: 1. Choose a random integerk such that 1<= k <=q 1. 2. Compute K = (YB)k mod q. 3. Encrypt M as the pair of integers (C1, C2) where C1 = ak mod q C2 = KM mod q User B recovers the plaintext as follows: Compute K = (C1) XB mod q. 1. Compute M = (C2K12. ) mod q. Show that the system works; that is, show that the decryption process does recover the plaintext. | |
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