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Public key cryptography based on skew dihedral group rings

6 May 2022
J. D. L. Cruz
E. Martínez-Moro
Ricardo Villanueva-Polanco
ArXiv (abs)PDFHTML
Abstract

In this paper, we propose to use a skew dihedral group ring given by the group D2nD_{2n}D2n​ and the finite field Fq2\mathbb{F}_{q^2}Fq2​ for public-key cryptography. Using the ambient space Fq2θD2n\mathbb{F}_{q^{2}}^{\theta} D_{2n}Fq2θ​D2n​ and a group homomorphism θ:D2n→Aut(Fq2)\theta: D_{2n} \rightarrow \mathrm{Aut}(\mathbb{F}_{q^2})θ:D2n​→Aut(Fq2​), we introduce a key exchange protocol and present an analysis of its security. Moreover, we explore the properties of the resulting skew group ring Fq2θD2n\mathbb{F}_{q^{2}}^{\theta} D_{2n}Fq2θ​D2n​, 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.

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