An Undeniable Signature Scheme Utilizing Module Lattices

TL;DR

This paper introduces a post-quantum undeniable signature scheme based on module lattices, leveraging the GPV framework, with security grounded in SIS and LWE problems, and demonstrates its implementation and security proofs.

Contribution

It presents the first module lattice-based post-quantum undeniable signature scheme with comprehensive security proofs and flexible parameter selection.

Findings

Security is based on SIS and LWE hardness assumptions.

The scheme is implemented for various parameter sets.

Provides greater flexibility compared to ring lattice variants.

Abstract

An undeniable signature scheme is type of digital signature where the signer retains control over the signature's verifiability. Therefore with the approval of the signer, only an authenticated verifier can verify the signature. In this work, we develop a module lattice-based post-quantum undeniable signature system. Our method is based on the GPV framework utilizing module lattices, with the security assured by the hardness of the SIS and LWE problems. We have thoroughly proved all the desired securities for the proposed scheme. Finally, we have implemented our protocol for different sets of parameters. The purpose of opting a module variant rather than a ring variant is to provide greater flexibility in selecting parameters.