Semidirect Product Key Exchange: the State of Play
This is an incremental survey for researchers in post-quantum cryptography, summarizing existing literature without new results.
The paper surveys the state of Semidirect Product Key Exchange (SDPKE), a group-based cryptographic scheme proposed as a post-quantum alternative to Diffie-Hellman, discussing its security, platforms, and cryptanalysis.
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.