Results 31 to 40 of about 3,064 (192)
The isogeny conjecture for A-motives [PDF]
Inventiones mathematicae, 2011 We prove the isogeny conjecture for A-motives over finitely generated fields K of transcendence degree ≤1. This conjecture says that for any semisimple A-motive M over K, there exist only finitely many isomorphism classes of A-motives M′ over K for which there exists a separable isogeny M′→M.
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Hash functions from superspecial genus-2 curves using Richelot isogenies
Journal of Mathematical Cryptology, 2020 In 2018 Takashima proposed a version of Charles, Goren and Lauter’s hash function using Richelot isogenies, starting from a genus-2 curve that allows for all subsequent arithmetic to be performed over a quadratic finite field 𝔽p2.
Castryck Wouter +2 more
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The Open Book Series, 2013 The remarkable structure and computationally explicit form of isogeny graphs of elliptic curves over a finite field has made them an important tool for computational number theorists and practitioners of elliptic curve cryptography. This expository paper recounts the theory behind these graphs and examines several recently developed algorithms that ...
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Let us walk on the 3-isogeny graph: efficient, fast, and simple
Transactions on Cryptographic Hardware and Embedded SystemsConstructing and implementing isogeny-based cryptographic primitives is an active research. In particular, performing length-n isogenies walks over quadratic field extensions of Fp plays an exciting role in some constructions, including Hash functions ...
Jesús-Javier Chi-Domínguez +2 more
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Mathematics of ComputationWe first give a cleaner and more direct approach to the derivation of the Fast model of the Kummer surface. We show how to construct efficient ( N ,
Corte-Real Santos, M, Flynn, EV
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A Post-Quantum Zero-Knowledge Identification Scheme [PDF]
Mathematics Interdisciplinary ResearchIn this paper, we introduce a zero-knowledge identification protocol designed for authentication within the supersingular isogeny Diffie-Hellman (SIDH) key exchange framework.
Maryam Rezaei Kashi, Mojtaba Bahramian
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The effective Shafarevich conjecture for abelian varieties of ${\text {GL}_{2}}$-type
Forum of Mathematics, Sigma, 2021 In this article we establish the effective Shafarevich conjecture for abelian varieties over ${\mathbb Q}$ of ${\text {GL}_2}$-type. The proof combines Faltings’ method with Serre’s modularity conjecture, isogeny estimates and results from Arakelov ...
Rafael von Känel
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Heights on ‘hybrid orbits’ in Shimura varieties
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract We prove the ‘hybrid conjecture’ which is a common generalisation of the André–Oort conjecture and the André–Pink–Zannier conjecture, in the case of Shimura varieties of abelian type.
Rodolphe Richard, Andrei Yafaev
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Efficient Constant-Time Implementation of terSIDH
IEEE AccessSince supersingular isogeny Diffie-Hellman (SIDH) was broken by a polynomial-time attack, several countermeasures were proposed as it was regarded as the most efficient algorithm among isogeny-based cryptosystems. Among them, terSIDH has been highlighted
Taehun Kang +4 more
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On the quaternion -isogeny path problem [PDF]
LMS Journal of Computation and Mathematics, 2014 AbstractLet $\mathcal{O}$ be a maximal order in a definite quaternion algebra over $\mathbb{Q}$ of prime discriminant $p$, and $\ell $ a small prime. We describe a probabilistic algorithm which, for a given left $\mathcal{O}$-ideal, computes a representative in its left ideal class of $\ell $-power norm.
Kohel, David +3 more
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