Public key cryptography based on skew dihedral group rings

TL;DR

This paper introduces a novel public-key cryptography scheme based on skew dihedral group rings, including a key exchange protocol, a probabilistic scheme, and a key encapsulation mechanism, with a proof-of-concept implementation.

Contribution

It is the first to propose using skew dihedral group rings for public-key cryptography, developing new protocols and mechanisms based on their algebraic properties.

Findings

Developed a new key exchange protocol using skew dihedral group rings.

Created a probabilistic public-key scheme and a KEM from the protocol.

Provided a proof-of-concept implementation demonstrating feasibility.

Abstract

In this paper, we propose to use a skew dihedral group ring given by the group $D_{2n}$ and the finite field $\mathbb{F}_{q^2}$ for public-key cryptography. Using the ambient space $\mathbb{F}_{q^{2}}^{\theta} D_{2n}$ and a group homomorphism $\theta: D_{2n} \rightarrow \mathrm{Aut}(\mathbb{F}_{q^2})$, we introduce a key exchange protocol and present an analysis of its security. Moreover, we explore the properties of the resulting skew group ring $\mathbb{F}_{q^{2}}^{\theta} D_{2n}$, exploiting them to enhance our key exchange protocol. We also introduce a probabilistic public-key scheme derived from our key exchange protocol and obtain a key encapsulation mechanism (KEM) by applying a well-known generic transformation to our public-key scheme. Finally, we present a proof-of-concept implementation of our cryptographic constructions. To the best of our knowledge, this is the first paper that proposes a skew dihedral group ring for public-key cryptography.