This problem illustrates the point that the Diffie-Hellman protocol is not secure withoutthe step where you take the modulus; i.e. the "Indiscrete Log Problem" is not ahard problem!
You are Eve and have captured Alice and Bob and imprisoned them.
You overhear the following dialog.Bob: Oh, let's not bother with the prime in the Diffie-Hellman protocol, itwill make things easier.
Alice: Okay, but we still need a base a to raise things to. How about a = 3?Bob: All right, then my result is 27.Alice: And mine is 243.
What is Bob's private key XB and Alice's private key XA? What is their secret combinedkey?