?

(2) Alice and Bob has designed a public key cryptosystem based on the ElGamal. Bob has chosen the prime p = 73 and the primitive root a = 5. Bob's private key is an integer b = 60 such that = a = 65 (mod p). Bob publishes the triple (p, a, ). (a) Alice chooses a secret number k = 30 to send the message 123456 to Bob. What pair or pairs does Bob receive? (b) Do you think that Alice should have chosen k = 30? Give an answer and justify it. (c) What should Bob do to decrypt the pair or pairs he received from Alice? During computation, make sure Bob does not compute any inverses. (d) Verify the answer of Parts (a) and (c) in sagemath.