Post-Quantum Key Agreement Protocol based on Non-Square Integer Matrices

TL;DR

This paper introduces a post-quantum key exchange protocol using products of rectangular matrices over Zp, claiming high security against classical and quantum attacks based on NP-complete factorization problems.

Contribution

The paper proposes a novel key agreement scheme based on non-square integer matrices and demonstrates its potential resistance to quantum and classical attacks.

Findings

Security levels exceed NIST post-quantum standards with appropriate parameters.

Matrix factorization problem is NP-complete, providing computational hardness.

No known polynomial-time classical or quantum attacks currently exist.

Abstract

We present in this paper an algorithm for exchanging session keys, coupled with a hashing encryption module. We show schemes designed for their potential invulnerability to classical and quantum attacks. In turn, if the parameters included were appropriate, brute-force attacks exceed the (five) security levels used in the NIST competition of new post-quantum standards. The original idea consists of products of rectangular matrices in Zp as public values and whose factorization is proved to be an NP-complete problem. We present running times as a function of the explored parameters and their link with operational safety. To our knowledge there are no classical and quantum attacks of polynomial complexity available at hand, remaining only the systematic exploration of the private-key space.