Counting points on hyperelliptic curves of genus 2 with real models

DOI10.14495/jsiaml.11.1zbMath1458.11102OpenAlexW2915590613MaRDI QIDQ3121431

Yukihiro Uchida

Publication date: 18 March 2019

Published in: JSIAM Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.14495/jsiaml.11.1

zbMATH Keywords

hyperelliptic curvespoint countingreal models

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Special algebraic curves and curves of low genus (14H45) Curves over finite and local fields (11G20) Computational aspects of algebraic curves (14Q05)

Cites Work

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• Genus 2 point counting over prime fields
• An extension of Kedlaya's algorithm for hyperelliptic curves
• Multi-point evaluation in higher dimensions
• Modern Computer Algebra
• Canonical local heights and multiplication formulas for the Jacobians of curves of genus 2
• Cryptographic aspects of real hyperelliptic curves
• Fast Polynomial Factorization and Modular Composition
• Algebraic Function Fields and Codes
• Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p
• On the analogue of the division polynomials for hyperelliptic curves.
• Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields
• Handbook of Elliptic and Hyperelliptic Curve Cryptography

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