Jacobian coordinates on genus 2 curves

DOI10.1007/s00145-016-9227-7zbMath1377.94053OpenAlexW2330347957MaRDI QIDQ2397457

Huseyin Hisil, Craig Costello

Publication date: 22 May 2017

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

Full work available at URL: https://doi.org/10.1007/s00145-016-9227-7

zbMATH Keywords

hyperelliptic curvesexplicit formulasscalar multiplicationgenus 2Jacobian coordinates

Mathematics Subject Classification ID

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

Related Items (6)

On the statistical leak of the GGH13 multilinear map and some variants ⋮ Implementation of point-counting algorithms on genus 2 hyperelliptic curves based on the birthday paradox ⋮ Quantum circuits for hyperelliptic curve discrete logarithms over the mersenne prime fields ⋮ Computing supersingular isogenies on Kummer surfaces ⋮ Connecting Legendre with Kummer and Edwards ⋮ Fast scalar multiplication of degenerate divisors for hyperelliptic curve cryptosystems

Uses Software

• Magma
• EFD
• eBASH
• eBACS
• AVIsogenies

Cites Work

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• Genus 2 point counting over prime fields
• A generalisation of Miller's algorithm and applications to pairing computations on abelian varieties
• Hyperelliptic cryptosystems
• The Magma algebra system. I: The user language
• Formulae for arithmetic on genus 2 hyperelliptic curves
• Sequences of numbers generated by addition in formal groups and new primality and factorization tests
• Group Law Computations on Jacobians of Hyperelliptic Curves
• Kummer Strikes Back: New DH Speed Records
• Counting Points on Genus 2 Curves with Real Multiplication
• Distortion maps for supersingular genus two curves
• Speeding the Pollard and Elliptic Curve Methods of Factorization
• Elliptic Curve Cryptosystems
• Fast Cryptography in Genus 2
• Faster Addition and Doubling on Elliptic Curves
• Efficient Hyperelliptic Arithmetic Using Balanced Representation for Divisors
• Efficient and Secure Algorithms for GLV-Based Scalar Multiplication and Their Implementation on GLV-GLS Curves
• A Heuristic Quasi-Polynomial Algorithm for Discrete Logarithm in Finite Fields of Small Characteristic
• New Point Addition Formulae for ECC Applications
• Fast genus 2 arithmetic based on Theta functions
• New Composite Operations and Precomputation Scheme for Elliptic Curve Cryptosystems over Prime Fields
• Efficient Explicit Formulae for Genus 2 Hyperelliptic Curves over Prime Fields and Their Implementations
• Selected Areas in Cryptography

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