Rethinking low genus hyperelliptic Jacobian arithmetic over binary fields: interplay of field arithmetic and explicit formulæ

DOI10.1515/JMC.2008.011zbMath1146.14032OpenAlexW1996714756MaRDI QIDQ3537423

Nicolas Thériault, Z. Wang, Roberto M. Avanzi

Publication date: 6 November 2008

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

Full work available at URL: https://doi.org/10.1515/jmc.2008.011

zbMATH Keywords

cryptographyefficient implementationelliptic and hyperelliptic curvesexplicit formulæ.

Mathematics Subject Classification ID

Special algebraic curves and curves of low genus (14H45) Curves over finite and local fields (11G20) Computational aspects of algebraic curves (14Q05)

Related Items (8)

Group Law Computations on Jacobians of Hyperelliptic Curves ⋮ Counting isomorphism classes of pointed hyperelliptic curves of genus 4 over finite fields with even characteristic ⋮ Redundant \(\tau \)-adic expansions. I: Non-adjacent digit sets and their applications to scalar multiplication ⋮ Group arithmetic in \(C_{3,5}\) curves ⋮ Jacobian Versus Infrastructure in Split Hyperelliptic Curves ⋮ Non-hyperelliptic modular Jacobians of dimension 3 ⋮ Another Look at Square Roots (and Other Less Common Operations) in Fields of Even Characteristic ⋮ Efficient Explicit Formulae for Genus 2 Hyperelliptic Curves over Prime Fields and Their Implementations

Uses Software

• NTL
• HECC

Cites Work

• Hyperelliptic cryptosystems
• Constructive and destructive facets of Weil descent on elliptic curves
• Formulae for arithmetic on genus 2 hyperelliptic curves
• Computing discrete logarithms in high-genus hyperelliptic Jacobians in provably subexponential time
• A double large prime variation for small genus hyperelliptic index calculus
• Computing in the Jacobian of a Hyperelliptic Curve
• Elliptic Curve Cryptosystems
• A Remark Concerning m-Divisibility and the Discrete Logarithm in the Divisor Class Group of Curves
• Another Look at Square Roots (and Other Less Common Operations) in Fields of Even Characteristic

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