Public key cryptography based on skew dihedral group rings
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In this paper, we propose to use a skew dihedral group ring given by the group D_2n and the finite field 𝔽_q^2 for public-key cryptography. Using the ambient space 𝔽_q^2^θ D_2n and a group homomorphism θ: D_2n→Aut(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 𝔽_q^2^θ 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.
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