Isogenies and the discrete logarithm problem in Jacobians of genus 3 hyperelliptic curves

DOI10.1007/s00145-009-9038-1zbMath1182.94047OpenAlexW2163037042MaRDI QIDQ1037232

J. Blot

Publication date: 13 November 2009

Published in: Journal of Cryptology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00145-009-9038-1

zbMATH Keywords

hyperelliptic curveJacobianisogenydiscrete logarithm problemgenus 3non-hyperelliptic curvetrigonal construction

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (13)

Group Law Computations on Jacobians of Hyperelliptic Curves ⋮ The Supersingular Isogeny Problem in Genus 2 and Beyond ⋮ Generating subgroups of ray class groups with small prime ideals ⋮ Constructing genus-3 hyperelliptic Jacobians with CM ⋮ Group arithmetic in \(C_{3,5}\) curves ⋮ Cyclic Isogenies for Abelian Varieties with Real Multiplication ⋮ Decomposed Richelot isogenies of Jacobian varieties of curves of genus 3 ⋮ A new method for decomposition in the Jacobian of small genus hyperelliptic curves ⋮ Cover attacks for elliptic curves with cofactor two ⋮ Translating the discrete logarithm problem on Jacobians of genus 3 hyperelliptic curves with \((\ell ,\ell ,\ell)\)-isogenies ⋮ Super-Isolated Elliptic Curves and Abelian Surfaces in Cryptography ⋮ Modular polynomials on Hilbert surfaces ⋮ Computing $(\ell ,\ell )$-isogenies in polynomial time on Jacobians of genus $2$ curves

Uses Software

• Magma

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