Digital signature schemes based on code equivalence and syndrome decoding from restricted errors

2026-06-30

AI Summary

This work proposes a post-quantum secure digital signature framework based on code-based cryptography to address threats posed by quantum computing. The construction relies on two core hard problems: the restricted-error syndrome decoding problem and the linear code equivalence problem. By integrating Sigma protocols with the Fiat–Shamir transformation, the authors unify these challenges into a single, efficient, and provably secure signature scheme. Notably, this is the first approach to jointly address the restricted-error model and code equivalence within a cohesive framework. The methodology successfully instantiates both CROSS and LESS—two candidates from the second round of the NIST post-quantum standardization process—demonstrating strong competitiveness in terms of security, efficiency, and resilience against quantum attacks, thereby advancing the adoption of code-based signatures in post-quantum standardization efforts.

Abstract

Digital signature schemes are an important cryptographic tool to ensure data authenticity and integrity in many applications that must be resilient to attacks, including those facilitated by quantum computers. We consider the two digital signature schemes based on error-correcting codes that are second-round candidates in NIST's call for Additional Signature Schemes, which is part of the Post-Quantum Cryptography Standardization Process. Specifically, we provide an overview of the Codes and Restricted Objects Signature Scheme (CROSS) and the Linear Equivalence Signature Scheme (LESS). We describe their underlying problems of syndrome decoding from restricted errors and code equivalence. We review sigma protocols and how they can be transformed into digital signature schemes via the Fiat-Shamir transform. Finally, we explain how this procedure yields code-based digital signatures believed to be post-quantum secure.

Problem

• digital signature
• post-quantum cryptography
• syndrome decoding
• code equivalence
• error-correcting codes

Innovation

• code-based cryptography
• syndrome decoding
• code equivalence
• Fiat-Shamir transform
• post-quantum signatures