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

Huda Naeem Hleeb Al-Jabbari, Abbas Maarefparvar

TL;DR

This work targets post-quantum digital signatures by replacing Ring-LWE/Ring-SIS with Module-LWE/Module-SIS in the Sharafi-Daghigh framework. It integrates NHSEncode/NHSDecode encoding with centered-binomial noise and seed-based public-key generation to achieve a decoding failure probability of about $2^{-60}$ while maintaining compact key material. The authors provide a formal UF-CMA security proof in the Random Oracle Model, along with security estimations against BKZ-based lattice attacks for a concrete parameter set $(n,q,k,\\eta)=(256,12289,2,16)$. Compared with related lattice-based schemes, the module-based construction delivers improved security assurances and competitive key/signature sizes, highlighting the practical viability of Module-LWE/SIS for post-quantum signatures.

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.

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

TL;DR

This work targets post-quantum digital signatures by replacing Ring-LWE/Ring-SIS with Module-LWE/Module-SIS in the Sharafi-Daghigh framework. It integrates NHSEncode/NHSDecode encoding with centered-binomial noise and seed-based public-key generation to achieve a decoding failure probability of about while maintaining compact key material. The authors provide a formal UF-CMA security proof in the Random Oracle Model, along with security estimations against BKZ-based lattice attacks for a concrete parameter set . Compared with related lattice-based schemes, the module-based construction delivers improved security assurances and competitive key/signature sizes, highlighting the practical viability of Module-LWE/SIS for post-quantum signatures.

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.
Paper Structure (18 sections, 1 theorem, 18 equations, 2 tables, 3 algorithms)

This paper contains 18 sections, 1 theorem, 18 equations, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. lattice-based cryptography
  3. Computational hard problems on lattices
  4. Learning With Errors (LWE)
  5. Ring-LWE
  6. Module-LWE
  7. SIS, Ring-SIS, and Module-SIS problems
  8. Our Contribution
  9. Proposed Digital Signature
  10. Encoding and Decoding functions
  11. Key Generation
  12. Signing
  13. Verification
  14. Decoding failure probability
  15. Unforgeability in Random Oracle Model
  16. ...and 3 more sections

Key Result

Theorem 5.1

Assume that $H:\{0,1\}^* \rightarrow R_q$ is a cryptographic hash function modeled as a random oracle. If there exists an adversary $\mathcal{A}$ (who has classical access to $H$) that can break the UF-CMA security of the proposed signature, then there exist also adversaries $\mathcal{B}$ and $\math where and

Theorems & Definitions (22)

  • Definition 2.1
  • Remark 2.2
  • Remark 2.3
  • Definition 2.4
  • Definition 2.5
  • Definition 2.6
  • Remark 2.7
  • Definition 2.8
  • Definition 2.9
  • Definition 2.10
  • ...and 12 more