Circuit-private HE for NC1 ⇒ IND-CPA PKE

Fully-black-box reduction · standard model · folklore · security loss: none

Statement

Fixing the bound $L$ at key generation to any polynomial and forgetting $\mathsf{Eval}$, a circuit-private homomorphic encryption scheme for ${\mathrm{NC}}^1$ is an IND-CPA-secure public-key encryption scheme, with the same correctness and the same CPA advantage — folklore.