An addition algorithm in Jacobian of \(C_{ab}\) curves.

DOI10.1016/S0166-218X(02)00586-3zbMath1037.14010OpenAlexW2061370769MaRDI QIDQ1408367

Seigo Arita

Publication date: 15 September 2003

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0166-218x(02)00586-3

zbMATH Keywords

Gröbner basisJacobian varietyaddition algorithm\(C_{ab}\) curves

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Elliptic curves (14H52) Jacobians, Prym varieties (14H40) Computational aspects of algebraic curves (14Q05) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (5)

A generalized Kiepert formula for \(C_{ab}\) curves ⋮ The arithmetic of Jacobian groups of superelliptic cubics ⋮ Constructing Picard curves with complex multiplication using the Chinese remainder theorem ⋮ Group arithmetic in \(C_{3,5}\) curves ⋮ Jacobi inversion on strata of the Jacobian of the \(C_{rs}\) curve \(y^r = f(x)\)

Cites Work

• Hyperelliptic cryptosystems
• Arithmetic on superelliptic curves
• Computing in the Jacobian of a Hyperelliptic Curve
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