  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.
