Niederreiter cryptosystems using quasi-cyclic codes that resist quantum Fourier sampling

TL;DR

This paper demonstrates that Niederreiter cryptosystems based on certain non-binary quasi-cyclic codes can resist quantum Fourier sampling attacks, enhancing their quantum security.

Contribution

It introduces conditions under which quasi-cyclic codes ensure Niederreiter cryptosystem resistance to quantum Fourier sampling attacks.

Findings

Cryptosystem resistance to weak quantum Fourier sampling

Conditions for quasi-cyclic codes to be quantum-secure

Potential applicability to strong Fourier sampling

Abstract

McEliece and Niederreiter cryptosystems are robust and versatile cryptosystems. These cryptosystems work with many linear error-correcting codes. They are popular these days because they can be quantum-secure. In this paper, we study the Niederreiter cryptosystem using non-binary quasi-cyclic codes. We prove, if these quasi-cyclic codes satisfy certain conditions, the corresponding Niederreiter cryptosystem is resistant to the hidden subgroup problem using weak quantum Fourier sampling. Though our work uses the weak Fourier sampling, we argue that its conclusions should remain valid for the strong Fourier sampling as well.