# With known ciphertext and plaintext, find other party's Three Pass Protocol Key?

If I'm the second party participating in a three pass protocol (for simplicity, let's say Shamir's Three Pass Protocol) such that:

1. Bob sends me a ciphertext
2. I encrypt it and send it back
3. He removes his encryption and sends it back to me
4. I decrypt it fully

Using the information in steps 1 (ciphertext) and 4 (plaintext), how difficult is it for me to determine the key that Bob is using?

I know that this is a somewhat esoteric use-case, but I'm curious.

This is essentially the discrete log problem; Bob's key is a value $b$, and his encryption mechanism is computing the value $P^b \bmod p$. Given $P$, $P^b \bmod p$, recover $b$ is the definition of discrete log.