It starts with the Semidirect Product Key Exchange (SDPKE), which is an extension of the Diffie-Hellman Key Exchange, and uses the difficulty of the Semidirect Computational Diffie-Hellman Problem to analyze various cryptosystems. We also think of the semidirect discrete logarithm problem as a cryptographic group action and classify its quantum complexity as a result. This problem has been overlooked despite its relevance. In particular, our protocol may be based on any non-commutative group. There are some superficial parallels between our method and the standard Diffie-Hellman protocol, but we believe our technique is preferable due to many important changes.