11.5 (Multiplicative ElGamal). Let G be a cyclic group of prime order q generated by gG. Consider a simple variant of the ElGamal encryption system EMEG=(G,E,D) that is defined over (G,G2). The key generation algorithm G is the same as in EEG, but encryption and decryption work as follows: - for a given public key pk=uG and message mG : E(pk,m):=RZq,vg,eum,output(v,e) - for a given secret key sk=Zq and a ciphertext (v,e)G2 : D(sk,(v,e)):=e/v Show that EMEG has the following property: given a public key pk, and two ciphertexts c1RE(pk,m1) and c2RE(pk,m2), it is possible to create a new ciphertext c which is an encryption of m1m2. This property is called a multiplicative homomorphism