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