International Association for Cryptologic Research (IACR)
Abstract
Cryptographic group actions are a relaxation of standard cryptographic groups that have less structure. This lack of structure allows them to be plausibly quantum resistant despite Shor\u27s algorithm, while still having a number of applications. The most famous example of group actions are built from isogenies on elliptic curves.
Our main result is that CDH for abelian group actions is quantumly *equivalent* to discrete log. Galbraith et al. (Mathematical Cryptology) previously showed *perfectly* solving CDH to be equivalent to discrete log quantumly; our result works for any non-negligible advantage. We also explore several other questions about group action and isogeny protocols
