Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography

TL;DR

This paper introduces a new class of twisted Reed-Solomon codes with structural properties that enhance their potential for cryptographic applications, especially in resisting certain structural attacks.

Contribution

It generalizes twisted Reed-Solomon codes, identifies a large dual-closed subfamily, and analyzes their Schur squares, advancing their use in code-based cryptography.

Findings

The new codes form a large class of MDS codes.

A subfamily resistant to structural cryptographic attacks is identified.

Schur square dimensions are often large, indicating strong structural properties.

Abstract

We present a generalisation of Twisted Reed-Solomon codes containing a new large class of MDS codes. We prove that the code class contains a large subfamily that is closed under duality. Furthermore, we study the Schur squares of the new codes and show that their dimension is often large. Using these structural properties, we single out a subfamily of the new codes which could be considered for code-based cryptography: These codes resist some existing structural attacks for Reed-Solomon-like codes, i.e. methods for retrieving the code parameters from an obfuscated generator matrix.