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Comptes Rendus. MathématiqueIn this paper, we apply Tsuzuki’s main theorem in [12] to establish a criterion for when two abelian varieties over a function field $K$ of characteristic $p$ are isogenous. Specifically, assuming that their endomorphism algebras tensored with $\mathbb{Q}
Chiarellotto, Bruno, Trihan, Fabien
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Review of Chosen Isogeny-Based Cryptographic Schemes
Cryptography, 2022 Public-key cryptography provides security for digital systems and communication. Traditional cryptographic solutions are constantly improved, e.g., to suppress brute-force attacks.
Bartosz Drzazga, Łukasz Krzywiecki
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Failing to hash into supersingular isogeny graphs [PDF]
IACR Cryptology ePrint Archive, 2022 An important open problem in supersingular isogeny-based cryptography is to produce, without a trusted authority, concrete examples of ‘hard supersingular curves’ that is equations for supersingular curves for which computing the endomorphism ring is ...
J. Booher +14 more
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Derived isogenies and isogenies for abelian surfaces
, 2021 In this paper, we study the twisted Fourier-Mukai partners of abelian surfaces. Following the work of Huybrechts [doi:10.4171/CMH/465], we introduce the twisted derived equivalence between abelian surfaces. We show that there is a twisted derived Torelli theorem for abelian surfaces over algebraically closed fields with characteristic $\neq 2,3$.
Li, Zhiyuan, Zou, Haitao
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IACR Cryptology ePrint Archive, 2023 We propose a novel approach that generalizes interleaved modular multiplication algorithms for the computation of sums of products over large prime fields. This operation has widespread use and is at the core of many cryptographic applications.
P. Longa
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Algebraic approaches for solving isogeny problems of prime power degrees
Journal of Mathematical Cryptology, 2020 Recently, supersingular isogeny cryptosystems have received attention as a candidate of post-quantum cryptography (PQC). Their security relies on the hardness of solving isogeny problems over supersingular elliptic curves. The meet-in-the-middle approach
Takahashi Yasushi +5 more
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Towards High-Performance Supersingular Isogeny Cryptographic Hardware Accelerator Design
Electronics, 2023 Cryptosystems based on supersingular isogeny are a novel tool in post-quantum cryptography. One compelling characteristic is their concise keys and ciphertexts. However, the performance of supersingular isogeny computation is currently worse than that of
Guantong Su, Guoqiang Bai
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Karpatsʹkì Matematičnì Publìkacìï, 2013 A proof of nondegeneracy of the Tate pairing and Kolyvagin's formula for elliptic curves with good reductions over an $n$-dimensional $(n\leq 3)$ pseudolocal field, the Tate pairing associated to an isogeny between abelian varieties over pseudolocal ...
V.I. Nesteruk
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Modular isogeny complexes [PDF]
Algebraic & Geometric Topology, 2012 Minor revisions for ...
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Optimized CSIDH Implementation Using a 2-Torsion Point
Cryptography, 2020 The implementation of isogeny-based cryptography mainly use Montgomery curves, as they offer fast elliptic curve arithmetic and isogeny computation. However, although Montgomery curves have efficient 3- and 4-isogeny formula, it becomes inefficient when ...
Donghoe Heo +4 more
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