Wouter Castryck, Bogdan Adrian Dina, Péter Kutas, Gioella Lorenzon · 2026 · arXiv
DOI: 10.48550/arXiv.2610.27922 · open-access PDF
Estudamos o uso criptográfico de ações de grupo de classe Shimura em variedades abelianas super especiais, principalmente polarizadas, equipadas com uma orientação CM, no contexto da criptografia pós-quântica. Além de fornecer uma introdução acessível ao tópico, ilustrada com muitos exemplos, fornecemos ferramentas para representar orientações CM através de isogenias de dimensões superiores e para computar a ação de grupo de classe Shimura no modelo de ação de grupo eficaz restrito.
Machine translation (Meta M2M100); the English original follows.
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.
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