Is it Possible to Generate a Duplicate DH Session Key from 2 Pairs of DH Keys? 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!
If you're doing Diffie–Hellman in a group $G$ written multiplicatively with identity element $e$, say $G = (\mathbb Z/p\mathbb Z)^\times$ for some standard large safe prime $p$ and $e = 1$, then Eve/Mallory can simply supply $e$ as their public key to both Alice and Bob.  Then the shared secret group element is $e^a = e = e^b$.

There is a way for Alice and Bob to thwart this, by simply checking whether the peer's public key is the identity element.  But it's usually pointless because Alice and Bob will normally authenticate the entire transcript of the session—this thwarts the attack anyway because they will authenticate $g^a$ and $g^b$ as their public keys, not $e$.