Post-quantum group actions from oriented superspecial abelian varieties
Original title: Post-quantum commutative group actions from oriented superspecial abelian varieties
The paper gives tools for CM orientations and Shimura class group actions, including a CM form of Kani's lemma.
The paper studies Shimura class group actions on superspecial principally polarized abelian varieties with a CM orientation for post-quantum cryptography. It explains how to represent orientations through higher-dimensional isogenies and how to compute the action in the restricted effective group action model. Results include a CM version of Kani's lemma and a trick that often halves the ambient dimension. It also analyzes when the action is not transitive, relating that to CM type.
- A method finds superspecial principally polarized abelian surfaces oriented by a given CM order.
- That method uses the Ibukiyama-Katsura-Oort correspondence.
- Transitivity obstructions are tied to the characteristic-zero notion of CM type.
From the original article
1 min read at arxiv.orgWe study the cryptographic use of Shimura class group actions on superspecial principally polarized abelian varieties equipped with a CM orientation, within the context of post-quantum cryptography.
By Wouter Castryck · arxiv.org
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