Given a Diffie-Helman type identification scheme, can Verifier compute secret key a of prover if the protocol works this way: Alice has a public key v = g^a and a private key a. Say g is a primitive element in a Zp* where p is prime. Bob chooses a random b, computes w = g^b, and sends w to Alice. Alice computes K = w^a and sends it to Bob. Bob accepts if and only if K = v^b. Can Bob compute a, private key of Alice just by receiving v^b. I know the answer is NO. But I am not able to convince myself as it is neither a DDH problem of CDH problem.
