Wouter Castryck, Bogdan Adrian Dina, Péter Kutas, Gioella Lorenzon · 2026 · arXiv
DOI: 10.48550/arXiv.2610.27922 · open-access PDF
Kami mempelajari penggunaan kriptografis dari tindakan kelompok kelas Shimura pada varietas abelian superspesial terutama berpolarisasi yang dilengkapi dengan orientasi CM, dalam konteks kriptografi pasca-quantum. Selain memberikan pengantar yang dapat diakses ke topik, diilustrasikan dengan banyak contoh, kami menyediakan alat untuk mewakili orientasi CM melalui isogenisasi dimensi yang lebih tinggi dan untuk menghitung tindakan kelompok kelas Shimura dalam model tindakan kelompok efektif terbatas.
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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