{2} Alice and Bob has designed a public keyr cryptosystem based on the ElGamal. Bob has chosen the prime p = T3 and the primitive root or = 5. Bob's private key is an integer b 2 EU such that ' E och E '55 [mod p}. Bob publishes the triple (p, or, }. {a} Alice chooses a secret number k = 30 to send the message 123456 to Bob. 1What pair or pairs does Bob receive? {b} Do you think that Alice should have chosen it = 3U? lGive an answer and justify it. {c} 1What should Bob do to decrypt the pair or pairs he received from Alice? During computation, make sure Bob does not compute anyr inverses. {d} Verify the answer of Parts {a} and {c} in sagemath. 14+3+ll+=34 marks Part {a} The student receives 14 marks if all the steps of the computation are cor rect and all the relevant workings are present. This includes 3 marks for correct-11..r breaking the message into smaller messages, 5 marks for giving all the steps to encrypt the message, and 3 marks for stating the message that Bob receives. For different level of correctness the student receives between 13 and I] marks. Fart (b) The student receives 1 mark if the student gives a correct answer1 and 2 marks for a correct justication. For different level of correctness the students receives between 2 and ll marks. Fart [ch The student receives 11 marks for following all the steps to decrypt each small message. This includes 3 marks for correctly decrypting each small message1 and 2 marks for the correct procedure to avoid computing inverses. For different level of correctness the students receives between Ill and [1 marks. Fart [d] In each case, the student receives 3 marks if a correct sagemath code is provided. Fbr different levels of correctness1 the student receives between 3 and ll marks. For different level of correctness the students receives between 5 and I] marks