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!
IND-CPA/CCA encryption schemes do imply PRFs: Does IND-CPA imply PRF?

But the above result does not mean Enc or Dec must be a PRF. From its definition, a PRF is indistinguishable from a random function for polynomial-time attackers. We can easily make Enc look non-random but still secure. For instance, you can append some 0 bits to the end of the ciphertexts. As for Dec, its domain is not easy to get. If the encryption scheme satisfies the integrity of ciphertext (INT-CTXT), then you cannot even find valid ciphertexts and almost always get nothing from Dec.

Btw, as you noticed, PRFs are deterministic, so you should consider the "random tape" inside Enc when comparing them.