Pretend you are Alice and have agreed with Bob to carry out Diffie-Hellman key exchange with parameters p = 23 and g = 5. You may use a calculator to answer the following, but write down and label all the quantities you use. Assume you choose the secret random value x = 19. Compute the value gx (mod p) that you will send to Bob. In the protocol, you receive the value gy = 18 from Bob. Compute your shared secret value. Now pretend you are an eavesdropping adversary. From g, p and gy, find Bob’s secret y (it’s possible!) Describe how you found the value in part (c), and comment on how this reflects the security of Diffie-Hellman key exchange.

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