25/Cry Semester A final assessment 2021/22 MTH6115 /MTH6115P (2022) https://qm Page 4 Question 4 [25 marks]. In parts (a) and (b) below your calculations in Q3(e) can be useful 171 14 (a) Bob's El-Gamal public key is (p.g, h) = (37,5, 12) and his secret key is a = 20. Bob receives the message (5, 17) from Alice. Decipher it, simplifying your answer as much as possible. (b) Alice and Bob are using the Diffie-Hellman key exchange protocol and they have agreed on the prime 37. Alice uses (ea, da) = (17, 17) and Bob uses (eg,dp) = (5,29). (i) What relations should ea, da, eg and dg satisfy? Verify that this is the case for the given numbers. (ii) Alice wants to share = 5 with Bob. Calculate the three values that are exchanged through the process. (iii) Assuming that Eve sees the three exchanged numbers, what equation does she have to solve in order to recover x? What hard problem is this an instance of? I (C) Let a,