Counting Points on Genus 2 Curves with Real Multiplication

DOI10.1007/978-3-642-25385-0_27zbMath1227.94045arXiv1106.0661OpenAlexW1761705715MaRDI QIDQ3102207

Pierrick Gaudry, Benjamin Andrew Smith, David R. Kohel

Publication date: 2 December 2011

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.0661

Mathematics Subject Classification ID

Cryptography (94A60) Special algebraic curves and curves of low genus (14H45) Computational aspects of algebraic curves (14Q05) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (13)

Fast cryptography in genus 2 ⋮ Jacobian coordinates on genus 2 curves ⋮ Hilbert modular polynomials ⋮ Computing the endomorphism ring of an ordinary abelian surface over a finite field ⋮ Improved complexity bounds for counting points on hyperelliptic curves ⋮ Counting points on genus-3 hyperelliptic curves with explicit real multiplication ⋮ Computing zeta functions of cyclic covers in large characteristic ⋮ Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in \(p\)-adic cohomology ⋮ The structure of the group of rational points of an abelian variety over a finite field ⋮ Counting points on hyperelliptic curves with explicit real multiplication in arbitrary genus ⋮ Curves, Jacobians, and cryptography ⋮ Computing Galois representations of modular abelian surfaces ⋮ Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time

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