Newest papers

Post-quantum commutative group actions from oriented superspecial abelian varieties

Wouter Castryck, Bogdan Adrian Dina, Péter Kutas, Gioella Lorenzon · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.27922 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

我们研究了Shimura类群体行动在超特殊的主要偏离的阿比利亚品种上进行的加密应用,在后量子加密的背景下,配备了CM定位。除了提供一个易于访问的主题的介绍,以许多示例为例,我们还提供工具来代表CM方向,通过更高维度的偏离性,并计算Shimura类群体行动在有限的有效群体行动模型中。在这里,关键辅助结果是Kani的Lema版本“与CM”和一个技巧,通常允许将环境维度减半。我们还提供了一种方法来寻找超特殊的主要偏离的阿比利亚表面,这些表面是由一个给定的CM顺序定位的,这是一种额外的算法框架来研究CM方向使用Ibiyukama-Katsura

Machine translation (Meta M2M100); the English original follows.

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.

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Topics: Abelian group, Mathematics, Group action, Group (periodic table), Context (archaeology), Lemma (botany)

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