I'm a bit confused about the relationship between CCA/CPA-security and PRFs and particularly when do we think of encryption and decryption as a PRF. Assume we have an encryption scheme $\Pi = (Enc, Dec, Gen)$ to be a CPA-secure. Can we say that:
- $Enc$ must be a PRF?
- $Dec$ must be a PRF?
What about the case when $\Pi$ is CCA-Secure?
My intuition is that we can have $Dec$ to be a PRF for both cases since it's deterministic, but not sure if that is actually required?
For $Enc$, it cannot be a PRF since otherwise, $\Pi$ won't be CPA-secure.