Paper 2011/507 Original: eprint.iacr.org/2011/507 ↗

Relatively-Sound NIZKs and Password-Based Key-Exchange

Abstract

We define a new notion of relatively-sound non-interactive zero-knowledge (NIZK) proofs, where a private verifier with access to a trapdoor continues to be sound even when the Adversary has access to simulated proofs and common reference strings. It is likely that this weaker notion of relative-soundness suffices in most applications which need simulation-soundness. We show that for certain languages which are diverse groups, and hence allow smooth projective hash functions, one can obtain more efficient single-theorem relatively-sound NIZKs as opposed to simulation-sound NIZKs. We also show that such relatively-sound NIZKs can be used to build rather efficient publicly-verifiable CCA2-encryption schemes. By employing this new publicly-verifiable encryption scheme along with an associated smooth projective-hash, we show that a recent PAK-model single-round password-based key exchange protocol of Katz and Vaikuntanathan, Proc. TCC 2011, can be made much more efficient. We also show a new single round UC-secure password-based key exchange protocol with only a constant number of group elements as communication cost, whereas the previous single round UC-protocol required $\Omega(k)$ group elements, where $k$ is the security parameter.