Results 41 to 50 of about 8,681 (237)
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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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
core +1 more source
Modular invariants and isogenies [PDF]
International Journal of Number Theory, 2019 We provide explicit bounds on the difference of heights of the [Formula: see text]-invariants of isogenous elliptic curves defined over [Formula: see text]. The first one is reminiscent of a classical estimate for the Faltings height of isogenous abelian varieties, which is indeed used in the proof.
openaire +6 more sources
Higgs bundles and exceptional isogenies [PDF]
Research in the Mathematical Sciences, 2016 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. We focus on isogenies onto $SO(4,C)$ and $SO(6,C)$ and their split real forms. Using fiber products of spectral curves, we obtain directly the desingularizations of the (necessarily
Steven B. Bradlow, Laura P. Schaposnik
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A Subexponential Algorithm for Evaluating Large Degree Isogenies
, 2010 An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between elliptic curves efficiently. For ordinary curves of the same endomorphism ring,
Jao, David, Soukharev, Vladimir
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Orienting supersingular isogeny graphs
Journal of Mathematical Cryptology, 2020 AbstractWe introduce a category of 𝓞-oriented supersingular elliptic curves and derive properties of the associated oriented and nonoriented ℓ-isogeny supersingular isogeny graphs. As an application we introduce an oriented supersingular isogeny Diffie-Hellman protocol (OSIDH), analogous to the supersingular isogeny Diffie-Hellman (SIDH) protocol and ...
Colò, Leonardo, Kohel, David
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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
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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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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A note on local formulae for the parity of Selmer ranks
Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 3112-3132, October 2025.Abstract In this note, we provide evidence for a certain ‘twisted’ version of the parity conjecture for Jacobians, introduced in prior work of Dokchitser, Green, Konstantinou and the author. To do this, we use arithmetic duality theorems for abelian varieties to study the determinant of certain endomorphisms acting on p∞$p^\infty$‐Selmer groups.
Adam Morgan
wiley +1 more source