Alice and Bob are using the ElGamal cryptosystem with prime p and primitive root g for p. Alice's public key is A (mod p) where a is Alice's secret key. Bob has a message m he wishes to communicate to Alice. He chooses a secret key b, computes B(mod p) and cmAb (mod p) and sends B and c to Alice. Suppose a malicious eavesdropper obtains B, c and notices that B3 1 (mod p). (a) Show that the eavesdropper can produce a short list of candidates for m from the available information. (b) Now, assume that p 103,g 5, B 56 and c 2. What are the possibilities for m in this case? Alice and Bob are using the ElGamal cryptosystem with prime p and primitive root g for p. Alice's public key is A (mod p) where a is Alice's secret key. Bob has a message m he wishes to communicate to Alice. He chooses a secret key b, computes B(mod p) and cmAb (mod p) and sends B and c to Alice. Suppose a malicious eavesdropper obtains B, c and notices that B3 1 (mod p). (a) Show that the eavesdropper can produce a short list of candidates for m from the available information. (b) Now, assume that p 103,g 5, B 56 and c 2. What are the possibilities for m in this case