Cryptographic Group and Semigroup Actions. (arXiv:2301.01657v1 [cs.CR])

We consider actions of a group or a semigroup on a set, which generalize the
setup of discrete logarithm based cryptosystems. Such cryptographic group
actions have gained increasing attention recently in the context of
isogeny-based cryptography. We introduce generic algorithms for the semigroup
action problem and discuss lower and upper bounds. Also, we investigate
Pohlig-Hellman type attacks in a general sense. In particular, we consider
reductions provided by non-invertible elements in a semigroup, and we deal with
subgroups in the …

action actions algorithms attacks attention context cryptography discuss general hellman non problem