Results 31 to 40 of about 1,931 (172)
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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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
, 2021 This paper introduces a new approach to computing isogenies called radical isogenies and a corresponding method to compute chains of $N$-isogenies that is very efficient for small $N$. The method is fully deterministic and completely avoids generating $
Wouter Castryck +2 more
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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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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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Efficient Computation of (2^n,2^n)-Isogenies [PDF]
, 2022 Elliptic curves are abelian varieties of dimension one; the two-dimensional analogue are abelian surfaces. In this work we present an algorithm to compute $(2^n,2^n)$-isogenies of abelian surfaces defined over finite fields.
Sabrina Kunzweiler
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Hyperbolicity and fundamental groups of complex quasi‐projective varieties (III): Applications
Proceedings of the London Mathematical Society, Volume 133, Issue 5, November 2026.Abstract This paper is Part III of a series of three. We begin by introducing the notion of h$h$‐special varieties, which can be seen as varieties “chain‐connected by the Zariski closures of entire curves.” We prove that if X$X$ is either a special smooth complex quasi‐projective variety in the sense of Campana or an h$h$‐special variety, then for any ...
Benoît Cadorel +2 more
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Kuga–Satake Construction on Families of K3 Surfaces of Picard Rank 14
Mathematische Nachrichten, Volume 299, Issue 8, Page 1894-1916, August 2026.ABSTRACT The isometry between the type IV6 and the type II4 hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank 14 and of polarized abelian 8‐folds with totally definite quaternion multiplication. We show how this isometry induces a geometrically meaningful map between such moduli spaces
Flora Poon
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Optimization of isogeny computation algorithms for post-quantum cryptography
Scientific AfricanIsogeny-based cryptography has emerged as a strong candidate for post-quantum security due to the believed hardness of finding isogenies between supersingular elliptic curves.
Mohammed El Baraka, Siham Ezzouak
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Derived isogenies and isogenies for abelian surfaces
Algebra & Number TheoryIn 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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