This might sound pointless at first, but I want to know if it's computationally feasible to generate the same resulting session key in 2 different DH key exchanges. The purpose would be for a man-in-the-middle attack where both of the unsuspecting target users check to make sure they're using the same session key.
The way I am thinking it would work is that Eve establishes a normal DH key exchange with Alice. She then does a key exchange with Bob where she uses specially-crafted responses to end up with the same session key she generated with Alice.
Is it possible, and how would this work in practice? I'm guessing it would either be impossible or extremely time-consuming with large primes, etc., but that's just a quick assessment. Thanks!