Of the many families of cryptographic schemes proposed to be post-quantum, a relatively unexplored set of examples comes from group-based cryptography. One of the more central schemes from this area is the so-called Semidirect Product Key Exchange (SDPKE), a generalisation of Diffie-Hellman Key Exchange that is plausibly post-quantum. In this report we survey the state of the literature relating to SDPKE, providing a high-level discussion of security, as well as a comprehensive overview of the proposed platforms and the main cryptanalytic ideas relevant to each.

翻译：在众多被提出作为后量子密码方案的家族中，基于群的密码学是一个相对未被充分探索的领域。其中较具代表性的方案之一是所谓的半直积密钥交换（SDPKE），它是迪菲-赫尔曼密钥交换的一种推广，具有潜在的后量子安全性。本报告对SDPKE相关文献的研究现状进行了综述，从宏观层面探讨了其安全性，并全面概述了所提出的平台及与每种平台相关的主要密码分析思路。