Semidirect Product Key Exchange: the State of Play

TL;DR

This paper surveys the current research on Semidirect Product Key Exchange, a promising post-quantum cryptographic scheme based on group theory, discussing security, platforms, and cryptanalysis.

Contribution

It provides a comprehensive overview of SDPKE, summarizing existing literature, security considerations, platforms, and cryptanalytic approaches in a single survey.

Findings

SDPKE is a plausible post-quantum alternative to Diffie-Hellman.

Various platforms for SDPKE have been proposed and analyzed.

Cryptanalytic techniques are actively being developed for SDPKE.

Abstract

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.