Let and You may assume that is prime and is a primitive root mod
Suppose Alice and Bob are carrying out the Diffie-Hellman protocol with these parameters. As a first step, Alice sends Bob and Bob sends Alice where and are secret positive integers less than known only to Alice and Bob, respectively.
An eavesdropper Eve knows the values of and , and sees the transmissions. In particular, she sees that Alice sends Bob the number and Bob sends Alice the number What can Eve deduce about and quickly? (That is, much more quickly than computing and --please don't compute and to solve the problem!)