Constraint-hiding constrained PRFs for NC1 from LWE

Abstract

Constraint-hiding constrained PRFs (CHCPRFs), initially studied by Boneh, Lewi and Wu (PKC 2017), are constrained PRFs where the constrained key hides the description of the constraint. Envisioned with powerful applications such as searchable encryption, privatedetectable watermarking and symmetric deniable encryption, the only known candidates of CHCPRFs are based on indistinguishability obfuscation or multilinear maps with strong security properties. In this paper we construct CHCPRFs for all NC1 circuits from the Learning with Errors assumption. The construction draws heavily from the graph-induced multilinear maps by Gentry, Gorbunov and Halevi (TCC 2015), as well as the existing lattice-based PRFs. In fact, our construction can be viewed as an instance of the GGH15 approach where security can be reduced to LWE. We also show how to build from CHCPRFs reusable garbled circuits (RGC), or equivalently private-key function-hiding functional encryptions with 1-key security. This provides a different approach of constructing RGC from that of Goldwasser et al. (STOC 2013).