Problem 2. (30 points at 15 each) The Joy of Cryptography problem 15.3, reproduced here for your convenience. Note that in this problem, ElGamal encryption should be done exactly how it is presented in book. (a) Suppose you are given an ElGamal encryption of an unknown plaintext M G. Show how to construct a different ciphertext that also decrypts to the same M. (b) Suppose you are given two ElGamal encryptions, of unknown plaintexts M, M2 G. Show how to construct a ciphertext that decrypts to their product M M2.