Efficient Lattice-Based Zero-Knowledge Arguments with Standard Soundness: Construction and Applications

We provide new zero-knowledge argument of knowledge systems that work directly for a wide class of language, namely, ones involving the satisfiability of matrix-vector relations and integer relations commonly found in constructions of lattice-based cryptography. Prior to this work, practical arguments for lattice-based relations either have a constant soundness error \((2/3)\), or consider a weaker form of soundness, namely, extraction only guarantees that the prover is in possession of a witness that “approximates” the actual witness. Our systems do not suffer from these limitations.