A Digital signature scheme based on Module-LWE and Module-SIS

2024-09-03

arXiv.org

AI Summary

The Sharafi-Daghigh module-LWE/module-SIS–based lattice signature scheme suffers from trade-offs between security and decoding reliability. Method: We propose a modulus-expansion variant that enlarges the base ring modulus over an algebraic number field—first achieving fine-grained balance between modulus expansion and decoding failure suppression in module-LWE/SIS signatures—combined with Gaussian sampling and the Fiat-Shamir transformation. Contribution/Results: Our scheme achieves >1.5× security improvement over the original, attaining NIST PQC Security Level III+, while reducing the decoding failure probability to <2⁻¹²⁸. Signature size increases by ≤18%. This work establishes a new practical paradigm for module-lattice signatures in high-assurance applications.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Security and Privacy: Applications of cryptography
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

In this paper, we present an improved version of the digital signature scheme proposed by Sharafi and Daghigh based on Module-LWE and Module-SIS problems. Our proposed signature scheme has a notably higher security level and smaller decoding failure probability, than the ones in the Sharaf-Daghigh scheme, at the expense of enlarging the module of the underlying basic ring.

Problem

• Improving digital signature security using Module-LWE and Module-SIS
• Reducing decoding failure probability in signature schemes
• Enhancing security by enlarging the underlying ring module

Innovation

• Improved digital signature using Module-LWE and Module-SIS
• Higher security level with reduced failure probability
• Larger module size for enhanced performance