Question: This problem illustrates the point that the DaffierHellman protocol is not secure without the step where you take the modulus; i.e. the Indiscrete Log Problem

This problem illustrates the point that the Daffier—Hellman protocol is not secure without the step where you take the modulus; i.e. the “Indiscrete Log Problem” is not a hard 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-Hcllman protocol. it will 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 X _B and Alice’s private key X _A? What is their secret combined key?
(Don’t forget to show your work.)

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