Fast, uniform scalar multiplication for genus 2 Jacobians with fast Kummers
| Autor: | Craig Costello, Ping Ngai Chung, Benjamin Smith |
|---|---|
| Přispěvatelé: | University of Chicago, Microsoft Research [Redmond], Microsoft Corporation [Redmond, Wash.], Geometry, arithmetic, algorithms, codes and encryption (GRACE), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Inria Saclay - Ile de France |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
genus 2 0102 computer and information sciences 02 engineering and technology Scalar multiplication 01 natural sciences symbols.namesake [INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR] Mathematics::Algebraic Geometry pseudomultiplication Genus (mathematics) 0202 electrical engineering electronic engineering information engineering hyperelliptic curve cryptography Mathematics Kummer surface Elliptic curve Elliptic curve point multiplication 010201 computation theory & mathematics signatures Jacobian matrix and determinant symbols Hyperelliptic curve cryptography scalar multiplication 020201 artificial intelligence & image processing constant-time uniform |
| Zdroj: | Selected Areas in Cryptography-SAC 2016 Selected Areas in Cryptography-SAC 2016, Aug 2016, St John's, Canada. pp.18, ⟨10.1007/978-3-319-69453-5_25⟩ Lecture Notes in Computer Science ISBN: 9783319694528 SAC |
| Popis: | International audience; We give one-and two-dimensional scalar multiplication algorithms for Jacobians of genus 2 curves that operate by projecting to Kummer surfaces, where we can exploit faster and more uniform pseudo-multiplication, before recovering the proper "signed" output back on the Jacobian. This extends the work of López and Dahab, Okeya and Sakurai, and Brier and Joye to genus 2, and also to two-dimensional scalar multiplication. The technique is especially interesting in genus 2, because Kummer surfaces can outperform comparable elliptic curve systems. |
| Databáze: | OpenAIRE |
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