Problem 1 (Diffie-Hellman Cryptosystem): The classic Diffie-Hellman key exchange protocol (DH protocol), which is named after its inventors, Whitfield Diffie and Martin Hellman, is based on modular exponentiation. The DH protocol assumes that the following two public parameters have been established and are known to all participants (including the attacker): A prime number p and a generator g for Zp. The DH protocol consists of the following steps: Step 1: Alice picks a random positive number x in Zp and uses it to compute X = g x mod p. She sends X to Bob. Step 2: Bob picks a random positive number y in Zp and uses it to compute Y= g y mod p. He sends Y to Alice. Step 3: Alice computes the secret key as K1 = Y x mod p. Step 4: Bob computes the secret key as K2 = X y mod p. At the end of the protocol, Alice and Bob have computed the same secret key K = g x y mod p = K1 = K2. Indeed, we have: K1 = Y x mod p = (g y) x mod p = (g x) y mod p = X y mod p = K2 Write a program that implements the DH protocol.