论文标题
公共密钥密码学，基于偏斜二面体戒指
Public key cryptography based on skew dihedral group rings
论文作者
论文摘要
在本文中，我们建议使用组$ d_ {2n} $给出的偏斜二面体组环和有限字段$ \ mathbb {f} _ {q^2} $用于public-key密码学。 Using the ambient space $\mathbb{F}_{q^{2}}^θ D_{2n}$ and a group homomorphism $θ: D_{2n} \rightarrow \mathrm{Aut}(\mathbb{F}_{q^2})$, we introduce a key exchange protocol and present an analysis of its security.此外，我们探讨了生成的偏斜组环$ \ mathbb {f} _ {q^{2}}^θD_{2n} $，利用它们来增强我们的密钥交换协议。我们还引入了从我们的关键交换协议中得出的概率公钥计划，并通过将众所周知的通用转换应用于我们的公开键方案来获得关键封装机制（KEM）。最后，我们提出了我们加密结构的概念验证实现。据我们所知，这是第一篇提出偏斜二面体集团戒指的论文。
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 $\mathbb{F}_{q^{2}}^θ D_{2n}$ and a group homomorphism $θ: D_{2n} \rightarrow \mathrm{Aut}(\mathbb{F}_{q^2})$, we introduce a key exchange protocol and present an analysis of its security. Moreover, we explore the properties of the resulting skew group ring $\mathbb{F}_{q^{2}}^θ D_{2n}$, 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.
