In this paper, we present a new diverse class of post-quantum group-based Digital Signature Schemes (DSS). The approach is significantly different from previous examples of group-based digital signatures and adopts the framework of group action-based cryptography: we show that each finite group defines a group action relative to the semidirect product of the group by its automorphism group, and give security bounds on the resulting signature scheme in terms of the group-theoretic computational problem known as the Semidirect Discrete Logarithm Problem (SDLP). Crucially, we make progress towards being able to efficiently compute the novel group action, and give an example of a parameterised family of groups for which the group action can be computed for any parameters, thereby negating the need for expensive offline computation or inclusion of redundancy required in other schemes of this type.

翻译：本文提出了一类新型多样的后量子群组数字签名方案（DSS）。该方法与先前基于群组的数字签名方案存在显著差异，并采用群作用密码学框架：我们证明每个有限群相对于该群与其自同构群的半直积定义了一个群作用，并基于被称为半直离散对数问题（SDLP）的群论计算问题给出了所提出签名方案的安全性边界。关键之处在于，我们在高效计算新型群作用方面取得了进展，并给出了一族参数化群的实例——该群作用可针对任意参数计算，从而消除了此类其他方案所需的昂贵离线计算或冗余引入需求。