Papers for

cryptographic implementation teams

Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.

Post-quantum cryptography from special abelian varieties with complex multiplication

Post-quantum commutative group actions from oriented superspecial abelian varieties

Abstract: We 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. Besides giving an accessible introduction to the topic, illustrated with many examples, we provide tools for representing CM orientations through higher-dimensional isogenies and for computing the Shimura class group action in the restricted effective group action model. Here, key auxiliary results are a version of Kani's lemma "with CM" and a trick that often allows to halve the ambient dimension. We also give a method for finding superspecial principally polarized abelian surfaces that are oriented by a given CM order, which is extracted from an algebraic framework for studying CM orientations using the Ibukiyama-Katsura-Oort correspondence. We also analyze obstructions to transitivity of the Shimura class group action, related to the characteristic-zero notion of CM type.

Tue 20 OctCryptography and Security
The gist
Some cryptographic methods rely on mathematical structures called abelian varieties, which are shapes defined by a lot of symmetry. This paper studies a special kind of these shapes, called superspecial abelian varieties, equipped with extra symmetry from complex multiplication (CM). By exploring how certain group actions act on these shapes, the authors develop new techniques potentially useful for making cryptography secure against quantum computers. They provide tools to represent these structures and compute the group actions efficiently, which could help build better post-quantum cryptographic systems.
Open → 2610.27922v1