Homomorphic encryption is a form of encryption where a specific algebraic operation performed on the plaintext is equivalent to another (possibly different) algebraic operation performed on the cipher text. A multiplicative homomorphic cryptosystem has an encryption function E that satisfies the following property:
E(M1) * E(M2) = E(M1*M2)
where M1 and M2 are messages. Prove that EIGamal cryptosystem is multiplicative homomorphic.
Hint: (a,b) * (c,d) = (a * c, b * d).