A New Approach for Non-Interactive Zero-Knowledge from Learning with Errors

Abstract

We put forward a new approach for achieving non-interactive zero-knowledge proofs (NIKZs) from the learning with errors (LWE) assumption (with subexponential modulus to noise ratio). We provide a LWE-based construction of a hidden bits generator that gives rise to a NIZK via the celebrated hidden bits paradigm. A notable feature of our construction is its simplicity. Our construction employs lattice trapdoors, but beyond that uses only simple operations. Unlike prior solutions, we do not rely on a correlation intractability argument nor do we utilize fully homomorphic encryption techniques. Our solution provides a new methodology that adds to the diversity of techniques for solving this fundamental problem.