Paper 2018/1000 Original: eprint.iacr.org/2018/1000 ↗

Adaptively Single-Key Secure Constrained PRFs for NC1

Abstract

We present a construction of an adaptively single-key secure constrained PRF (CPRF) for $\mathbf{NC}^1$ assuming the existence of indistinguishability obfuscation (IO) and the subgroup hiding assumption over a (pairing-free) composite order group. This is the first construction of such a CPRF in the standard model without relying on a complexity leveraging argument. To achieve this, we first introduce the notion of partitionable CPRF, which is a CPRF accommodated with partitioning techniques and combine it with shadow copy techniques often used in the dual system encryption methodology. We present a construction of partitionable CPRF for $\mathrm{NC}^1$ based on IO and the subgroup hiding assumption over a (pairing-free) group. We finally prove that an adaptively single-key secure CPRF for $\mathbf{NC}^1$ can be obtained from a partitionable CPRF for $\mathbf{NC}^1$ and IO.