Fast algorithms for computing isogenies between ordinary elliptic curves in small characteristic

DOI10.1016/j.jnt.2010.07.003zbMath1223.14049arXiv1002.2597OpenAlexW2002479170MaRDI QIDQ2430987

Luca De Feo

Publication date: 8 April 2011

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.2597

zbMATH Keywords

algorithmselliptic curvessmall characteristicisogenies

Mathematics Subject Classification ID

Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16) Elliptic curves (14H52) Curves over finite and local fields (11G20) Isogeny (14K02)

Related Items (5)

Fast computation of elliptic curve isogenies in characteristic two ⋮ Genus 2 point counting over prime fields ⋮ Fast arithmetics in Artin-Schreier towers over finite fields ⋮ Explicit isogenies in quadratic time in any characteristic ⋮ Curves, Jacobians, and cryptography

Uses Software

• Magma
• NTL

Cites Work

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• On Elkies subgroups of \(\ell\)-torsion points in elliptic curves defined over a finite field
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• Computing Frobenius maps and factoring polynomials
• An elliptic curve trapdoor system
• Change of order for bivariate triangular sets
• Fast algorithms for computing isogenies between elliptic curves
• Speeding the Pollard and Elliptic Curve Methods of Factorization
• Fast Algorithms for Manipulating Formal Power Series
• Subquadratic-time factoring of polynomials over finite fields
• Fast Decomposition of Polynomials with Known Galois Group
• Isomorphisms between Artin-Schreier towers
• Faster Multiplication in GF(2)[x]

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