Commitment schemes based on module-LIP

Abstract. We propose commitment schemes based on the module lattice isomorphism problem (module-LIP). Module-LIP extends the classical LIP to the module setting, offering additional algebraic structure that can be leveraged for efficient cryptographic constructions. Building on recent advances in LIP-based cryptography, we show that module-LIP provides a natural foundation for constructing both statistically hiding and computationally binding commitment schemes. Our constructions exploit the symmetry properties of module lattices to achieve efficient opening and verification. We provide security reductions from standard lattice problems and present concrete parameter recommendations. This work extends the portfolio of cryptographic primitives based on lattice isomorphism problems.