Results 41 to 50 of about 4,641 (196)
Algebraic geometry in cryptography: Secure post-quantum schemes using isogenies and elliptic curves
International Journal of Science and Research Archive, 2023 In this article, we discuss how algebraic geometry, especially the isogenies and elliptic curves, have been used to construct secure post-quantum cryptographic systems. Since quantum computing is a very big threat to conventional cryptographic techniques,
Syed Khundmir Azmi
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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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Transactions on Cryptographic Hardware and Embedded Systems, 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.
Patrick Longa
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Kummer Surfaces, Isogenies and Theta Functions [PDF]
The paper discusses geometric and computational aspects associated with $(n,n)$-isogenies for principally polarized Abelian surfaces and related Kummer surfaces.
A. Clingher +2 more
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Isogenies between Hessian curves
, 2022 Elliptic curves are used in post-quantum cryptography, where two parties can use compositions of low-degree isogenies to establish a shared secret. There are several forms for representing elliptic curves, and different forms require different isogeny ...
Kristensen, Ella Wolff
core
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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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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Isolated elliptic curves and the MOV attack
Journal of Mathematical Cryptology, 2017 We present a variation on the CM method that produces elliptic curves over prime fields with nearly prime order that do not admit many efficiently computable isogenies. Assuming the Bateman–Horn conjecture, we prove that elliptic curves produced this way
Scholl Travis
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KLaPoTi: An asymptotically efficient isogeny group action from 2-dimensional isogenies
IACR Cryptology ePrint ArchiveWe construct and implement an efficient post-quantum commutative cryptographic group action based on combining the SCALLOP framework for group actions from isogenies of oriented elliptic curves on one hand with the recent Clapoti method for polynomial ...
Lorenz Panny +2 more
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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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