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

TL;DR

This paper introduces an efficient syndrome-based decoding algorithm for quasi-twisted codes and proposes a quantum-resistant cryptosystem based on these codes, expanding their practical applications.

Contribution

It presents the first efficient decoding method for QT codes and develops a new cryptosystem leveraging QT codes' properties.

Findings

Decoding algorithm corrects up to (d* - 1)/2 errors.

Cryptosystem resists classical and quantum attacks.

Formalizes a lower bound on QT codes' minimum distance.

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.