The arithmetic of characteristic 2 Kummer surfaces and of elliptic Kummer lines

DOI10.1016/j.ffa.2008.12.006zbMath1220.14023OpenAlexW2021358506WikidataQ56337875 ScholiaQ56337875MaRDI QIDQ1011454

Pierrick Gaudry, David Lubicz

Publication date: 8 April 2009

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2008.12.006

zbMATH Keywords

characteristic 2Kummer surfaces

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28)

Related Items (15)

Arithmetic on abelian and Kummer varieties ⋮ Kummer versus Montgomery Face-off over Prime Order Fields ⋮ The point decomposition problem over hyperelliptic curves, Toward efficient computation of discrete logarithms in even characteristic ⋮ Fast change of level and applications to isogenies ⋮ Traces of the group law on the Kummer surface of a curve of genus 2 in characteristic 2 ⋮ Extractors for Jacobians of Binary Genus-2 Hyperelliptic Curves ⋮ Montgomery Ladder for All Genus 2 Curves in Characteristic 2 ⋮ Connecting Legendre with Kummer and Edwards ⋮ Toric forms of elliptic curves and their arithmetic ⋮ Arithmetic of the level four theta model of elliptic curves ⋮ Binary Huff Curves ⋮ A generalisation of Miller's algorithm and applications to pairing computations on abelian varieties ⋮ Kummer for genus one over prime-order fields ⋮ Curves, Jacobians, and cryptography ⋮ Differential Addition on Binary Elliptic Curves

Uses Software

• mpFq
• Curve25519

Cites Work

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• The Frobenius map, rank 2 vector bundles and Kummer's quartic surface in characteristic 2 and 3
• Sequences of numbers generated by addition in formal groups and new primality and factorization tests
• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• On the equations defining Abelian varieties. I-III
• On Montgomery-Like Representations for Elliptic Curves over GF(2k)
• The action of the Frobenius map on rank 2 vector bundles in characteristic 2
• Handbook of Elliptic and Hyperelliptic Curve Cryptography
• Faster Addition and Doubling on Elliptic Curves
• Fast genus 2 arithmetic based on Theta functions
• Varieties Defined by Quadratic Equations
• Public Key Cryptography - PKC 2006

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