eprint.iacr.orgpaper

Post-quantum commutative group actions from oriented superspecial abelian varieties

Castryck, Dina, Kutas and Lorenzon study the Shimura class group action on superspecial principally polarized abelian varieties with a CM orientation, as a post-quantum commutative group action for key exchange. They give tools to represent CM orientations through higher-dimensional isogenies and to compute the action in the restricted effective group action model. These rely on a CM version of Kani's lemma and a trick that often halves the ambient dimension. The paper also gives a method for finding oriented superspecial abelian surfaces and analyses obstructions to transitivity.