Public key cryptography based on twisted dihedral group algebras

Abstract

<p style='text-indent:20px;'>In this paper, we propose to use a twisted dihedral group algebra for public-key cryptography. For this, we introduce a new <inline-formula><tex-math id="M1">\begin{document}$ 2 $\end{document}</tex-math></inline-formula>-cocycle <inline-formula><tex-math id="M2">\begin{document}$ \alpha_{\lambda} $\end{document}</tex-math></inline-formula> to twist the dihedral group algebra. Using the ambient space <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{F}^{\alpha_{\lambda}} D_{2n} $\end{document}</tex-math></inline-formula>, we then introduce a key exchange protocol and present an analysis of its security. Moreover, we explore the properties of the resulting twisted algebra <inline-formula><tex-math id="M4">\begin{document}$ \mathbb{F}^{\alpha_{\lambda}}D_{2n} $\end{document}</tex-math></inline-formula>, 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.</p>