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.
翻译：在本文中,我们建议使用由集团$D ⁇ 2n$和限定字段$mathbb{F ⁇ q ⁇ 2}$提供的用于公用钥匙加密的Skew dihral集团环。 使用环境空间$mathbb{F ⁇ q ⁇ 2 ⁇ 2 ⁇ theta}D ⁇ 2n}D ⁇ 2n}$, 和一组同质协议$theta: D ⁇ 2n}\rightrow\mathrm{Aut}$( mathb{F ⁇ q ⁇ 2}), 我们引入一个关键交换协议, 并对其安全做出分析。 此外, 我们探索由此形成的 skew 集团 $\mathb{F ⁇ q ⁇ 2 ⁇ 2 ⁇ theta} D ⁇ 2n}的属性, 利用这些属性来增强我们的关键交换协议。 我们还引入了一种从我们关键交换协议中衍生出来的概率性公用公用钥匙计划, 通过对公用钥匙计划应用一种广为人知的通用转换机制(KEM), 并展示了它的安全性分析。 最后, 我们展示了我们最先进的纸面构造的首项。
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