Relationship between CCA/CPA-security and PRFs

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.

Thanks!

• "when do we think of encryption and decryption as a PRF. " - We never do that. – Maeher Apr 17 '18 at 1:47
• Can a PRF be non-injective? Can an encryption scheme be non-injective? Does any pair of participants in this conversation have the same birthday? – Squeamish Ossifrage Apr 17 '18 at 1:58