Formulae for arithmetic on genus 2 hyperelliptic curves

DOI10.1007/s00200-004-0154-8zbMath1068.14065OpenAlexW2153226320MaRDI QIDQ1772238

Tanja Lange

Publication date: 15 April 2005

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00200-004-0154-8

zbMATH Keywords

public key cryptographydiscrete logarithmexplicit formulaefast arithmetic

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 (27)

Arithmetic on abelian and Kummer varieties ⋮ Group Law Computations on Jacobians of Hyperelliptic Curves ⋮ Linear complexity of some sequences derived from hyperelliptic curves of genus 2 ⋮ Jacobian coordinates on genus 2 curves ⋮ Bäcklund transformations for the nonholonomic Veselova system ⋮ Halving for the 2-Sylow subgroup of genus 2 curves over binary fields ⋮ Genus 2 point counting over prime fields ⋮ Traces of the group law on the Kummer surface of a curve of genus 2 in characteristic 2 ⋮ Montgomery Ladder for All Genus 2 Curves in Characteristic 2 ⋮ Rethinking low genus hyperelliptic Jacobian arithmetic over binary fields: interplay of field arithmetic and explicit formulæ ⋮ Jacobian Versus Infrastructure in Split Hyperelliptic Curves ⋮ Eta pairing computation on general divisors over hyperelliptic curves \(y^2=x^p - x+d\) ⋮ Unnamed Item ⋮ Fast scalar multiplication of degenerate divisors for hyperelliptic curve cryptosystems ⋮ An optimal representation for the trace zero subgroup ⋮ Algebraic curves and cryptography ⋮ Koblitz curve cryptosystems ⋮ A generic approach to searching for Jacobians ⋮ Extractors for Jacobian of Hyperelliptic Curves of Genus 2 in Odd Characteristic ⋮ Efficient Explicit Formulae for Genus 2 Hyperelliptic Curves over Prime Fields and Their Implementations ⋮ Comparison of scalar multiplication on real hyperelliptic curves ⋮ Cryptographic aspects of real hyperelliptic curves ⋮ A generalisation of Miller's algorithm and applications to pairing computations on abelian varieties ⋮ Faster Halvings in Genus 2 ⋮ Efficient Pairing Computation on Genus 2 Curves in Projective Coordinates ⋮ HECC Goes Embedded: An Area-Efficient Implementation of HECC ⋮ Hyperelliptic curves with compact parameters

Uses Software

• HECC

Cites Work

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• Algebraic function fields and codes
• Hyperelliptic cryptosystems
• On efficient implementation of FPGA-based hyperelliptic curve cryptosystems
• Computing in the Jacobian of a Hyperelliptic Curve
• Countermeasures against Differential Power Analysis for Hyperelliptic Curve Cryptosystems
• SCA Resistant Parallel Explicit Formula for Addition and Doubling of Divisors in the Jacobian of Hyperelliptic Curves of Genus 2
• Algorithmic Number Theory
• Algorithmic Number Theory
• Selected Areas in Cryptography
• Selected Areas in Cryptography
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura
• Advances in Cryptology - ASIACRYPT 2003
• Algebraic aspects of cryptography. With an appendix on hyperelliptic curves by Alfred J. Menezes, Yi-Hong Wu, and Robert J. Zuccherato

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