A New Primitive for a Diffie-Hellman-like Key Exchange Protocol Based on Multivariate Ore Polynomials

TL;DR

This paper introduces a novel key exchange primitive based on multivariate Ore polynomials, extending prior work and providing resistance against known attacks, with applications to various cryptographic protocols.

Contribution

It presents a new primitive for Diffie-Hellman-like key exchange using multivariate Ore polynomials, immune to previous attacks and adaptable to many rings.

Findings

Primitive is resistant to Euclidean domain attacks

Applicable to multiple cryptographic protocols

Supports a large class of rings

Abstract

In this paper we present a new primitive for a key exchange protocol based on multivariate non-commutative polynomial rings, analogous to the classic Diffie-Hellman method. Our technique extends the proposed scheme of Boucher et al. from 2010. Their method was broken by Dubois and Kammerer in 2011, who exploited the Euclidean domain structure of the chosen ring. However, our proposal is immune against such attacks, without losing the advantages of non-commutative polynomial rings as outlined by Boucher et al. Moreover, our extension is not restricted to any particular ring, but is designed to allow users to readily choose from a large class of rings when applying the protocol. Our primitive can also be applied to other cryptographic paradigms. In particular, we develop a three-pass protocol, a public key cryptosystem, a digital signature scheme and a zero-knowledge proof protocol.