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In this paper, we propose to use a twisted dihedral group algebra forpublic-key cryptography. For this, we introduce a new $2$-cocycle$\alpha_{\lambda}$ to twist the dihedral group algebra. Using the ambient space$\mathbb{F}^{\alpha_{\lambda}} D_{2n}$, we then introduce a key exchangeprotocol and present an analysis of its security. Moreover, we explore theproperties of the resulting twisted algebra$\mathbb{F}^{\alpha_{\lambda}}D_{2n}$, exploiting them to enhance our keyexchange protocol. We also introduce a probabilistic public-key scheme derivedfrom 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 keyencapsulation mechanism.

Public key cryptography based on twisted dihedral group algebras