Modular equations for hyperelliptic curves

DOI10.1090/S0025-5718-04-01682-5zbMath1086.11028OpenAlexW2131033185MaRDI QIDQ4821057

Pierrick Gaudry, Éric Schost

Publication date: 7 October 2004

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-04-01682-5

zbMATH Keywords

SEAFrobenius polynomialfactorization pattern

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Curves over finite and local fields (11G20) Computational aspects of algebraic curves (14Q05)

Related Items (10)

Multiradical isogenies ⋮ Complexity results for triangular sets ⋮ Genus 2 point counting over prime fields ⋮ A concise proof of the Kronecker polynomial system solver from scratch ⋮ ON THE DISTRIBUTION OF ORDERS OF FROBENIUS ACTION ON ^-TORSION OF ABELIAN SURFACES ⋮ Trisection for genus 2 curves in odd characteristic ⋮ Trisection for non-supersingular genus 2 curves in characteristic 2 ⋮ Division polynomials for hyperelliptic curves defined by Dickson polynomials ⋮ Modular Polynomials for Genus 2 ⋮ Curves, Jacobians, and cryptography

Uses Software

• Kronecker

Cites Work

• Straight-line programs in geometric elimination theory
• Counting points on curves over finite fields
• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• Complexity results for triangular sets
• Counting points on elliptic curves over finite fields
• Computing the number of points on an elliptic curve over a finite field: algorithmic aspects
• Deformation techniques for efficient polynomial equation solving.
• Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p
• Computing in the Jacobian of a Hyperelliptic Curve
• On the analogue of the division polynomials for hyperelliptic curves.
• Subquadratic-time factoring of polynomials over finite fields
• Examples of torsion points on genus two curves
• Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields
• A Gröbner free alternative for polynomial system solving
• Counting points on curves and Abelian varieties over finite fields
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