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> Problem 4: The ElGamal message transmission (a) The ElGamal protocol: This encrypts a given message m in F_p using the public key (g, y, p) - requires random numbers in the range [2,..p-2]. Output: M = [M1, M2] = [g^k, m*y^k], where k is a random number. > (1) (b) A decryption program, using Maple's discrete log program: The following program computes the discrete log DL_g(y) in F_p. It can (and will) be used to find the secret key x = DL_g(y). > (2) This program will be used in the following decoding program which recovers the original message m from M:= [M1, M2]. > (3) (c) Test the above programs: Encode the message m = 20080919 twice, using the public key (g,y,p) = (2222, 35029140, 112233449) > (4) > (5) (5) Note that each call of the encryption program yields a different ciphertext. > 20080919 20080919 Thus, both encrypted messages decrypt to the same original message. > (6)