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ASSIGNMENT
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1. Alice and Bob want to establish a common key pair using the Diffie-Hellman key exchange protocol and then use it in to send each other messages using a symmetric cipher. They agree by email on a prime p=877 and a primitive root (generator) a= 453; these are public knowledge). Then Alice chooses secret x=25 while Bob chooses secret y=13.
Alice is in Australia while Bob is in Brazil. Carl, a Canadian friend of Alice, has been tracking the email received and sent by Alice and decides that he wants to listen in on conversations between Alice and Bob. Carl therefore sets up a man-in-the-middle attack as follows.
Carl sees the set-up agreed to by Alice and Bob and he chooses secret z = 17.
Using the primitive root and her secret, Alice computes 45325 (mod 877) and sends it to Bob; however, Carl intercepts this email (which Bob never receives). Similarly, Carl intercepts Bob’s e-mail containing 45313 (mod 877) (which Alice never receives).
Determine what common key Carl sets up with Bob, and his common key with Alice.