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Public key cryptography based on twisted dihedral group algebras

14 December 2021
J. D. L. Cruz
Ricardo Villanueva-Polanco
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Abstract

In this paper, we propose to use a twisted dihedral group algebra for public-key cryptography. For this, we introduce a new 222-cocycle αλ\alpha_{\lambda}αλ​ to twist the dihedral group algebra. Using the ambient space FαλD2n\mathbb{F}^{\alpha_{\lambda}} D_{2n}Fαλ​D2n​, we then introduce a key exchange protocol and present an analysis of its security. Moreover, we explore the properties of the resulting twisted algebra FαλD2n\mathbb{F}^{\alpha_{\lambda}}D_{2n}Fαλ​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 the resulting key encapsulation mechanism.

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