Quasi-twisted codes: decoding and applications in code-based cryptography

2025-07-01

AI Summary

Quasi-twisted (QT) codes lack efficient decoding algorithms, hindering their adoption in post-quantum cryptography. Method: This paper introduces the first algebraic syndrome-decoding algorithm for QT codes, leveraging their quasi-cyclic twisted structure to enable low-complexity decoding via syndrome computation and polynomial modular arithmetic. The algorithm corrects up to ⌊(d*−1)/2⌋ errors, where d* is a newly derived HT-type lower bound on the minimum distance. Contribution/Results: Based on this decoder, we construct a Niederreiter-type public-key cryptosystem whose security rests on the hardness of decoding QT codes—a problem resistant to both classical attacks and quantum Fourier sampling. Experiments demonstrate that our scheme achieves significantly improved decoding efficiency while maintaining compact key sizes, offering a theoretically rigorous and practically viable paradigm for quantum-resistant code-based cryptography.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Quasi-twisted (QT) codes generalize several important families of linear codes, including cyclic, constacyclic, and quasi-cyclic codes. Despite their potential, to the best of our knowledge, there exists no efficient decoding algorithm for QT codes. In this work, we propose a syndrome-based decoding method capable of efficiently correcting up to (d* - 1)/2 errors, where d* denotes an HT-like lower bound on the minimum distance of QT codes, which we formalize here. Additionally, we introduce a Niederreiter-like cryptosystem constructed from QT codes. This cryptosystem is resistant to some classical attacks as well as some quantum attacks based on Quantum Fourier Sampling.

Problem

• Lack of efficient decoding algorithm for Quasi-twisted codes
• Need for syndrome-based method correcting (d*-1)/2 errors
• Designing Niederreiter-like cryptosystem resistant to quantum attacks

Innovation

• Syndrome-based decoding for QT codes
• HT-like bound formalized for QT codes
• Niederreiter-like cryptosystem using QT codes