Results 31 to 40 of about 5,346 (174)
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
doaj +1 more source
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
doaj +1 more source
Higgs bundles and exceptional isogenies [PDF]
, 2015 We explore relations between Higgs bundles that result from isogenies between low-dimensional Lie groups, with special attention to the spectral data for the Higgs bundles.
Bradlow, Steven B., Schaposnik, Laura P.
core +2 more sources
Isogeny in superstable groups [PDF]
Archive for Mathematical Logic, 2014 We study and develop a notion of isogeny for superstable groups. We prove several fundamental properties of the notion and then use it to formulate and prove uniqueness results. Connections to existing model theoretic notions are explained.
openaire +3 more sources
Class number formulas via 2-isogenies of elliptic curves [PDF]
, 2012 A classical result of Dirichlet shows that certain elementary character sums compute class numbers of quadratic imaginary number fields. We obtain analogous relations between class numbers and a weighted character sum associated to a 2-isogeny of ...
McLeman, Cam, Rasmussen, Christopher
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Do All Elliptic Curves of the Same Order Have the Same Difficulty of Discrete Log?
, 2005 The aim of this paper is to justify the common cryptographic practice of selecting elliptic curves using their order as the primary criterion. We can formalize this issue by asking whether the discrete log problem (DLOG) has the same difficulty for all ...
Jao, David +2 more
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Rational Isogenies from Irrational Endomorphisms
, 2020 In this paper, we introduce a polynomial-time algorithm to compute a connecting \(\mathcal {O}\)-ideal between two supersingular elliptic curves over \(\mathbb {F}_p\) with common \(\mathbb {F}_p\)-endomorphism ring \(\mathcal {O}\), given a description of their full endomorphism rings.
Castryck, Wouter +2 more
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The arithmetic of genus two curves with (4,4)-split Jacobians
, 2011 In this paper we study genus 2 curves whose Jacobians admit a polarized (4,4)-isogeny to a product of elliptic curves. We consider base fields of characteristic different from 2 and 3, which we do not assume to be algebraically closed.
Bolza +21 more
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Mathematika, Volume 72, Issue 2, April 2026.Abstract In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case A=Fq[T]$A = \mathbb {F}_q[T]$. We deduce closed‐form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree.
Sjoerd de Vries
wiley +1 more source