Efficient doubling on genus two curves over binary fields

Tanja Lange, Marc Stevens

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

21 Citations (Scopus)

Abstract

In most algorithms involving elliptic and hyperelliptic curves, the costliest part consists in computing multiples of ideal classes. This paper investigates how to compute faster doubling over fields of characteristic two. We derive explicit doubling formulae making strong use of the defining equation of the curve. We analyze how many field operations are needed depending on the curve making clear how much generality one loses by the respective choices. Note, that none of the proposed types is known to be weak – one only could be suspicious because of the more special types. Our results allow to choose curves from a large enough variety which have extremely fast doubling needing only half the time of an addition. Combined with a sliding window method this leads to fast computation of scalar multiples. We also speed up the general case.
Original languageEnglish
Title of host publicationSelected areas in cryptography : 11th Annual Workshop, SAC 2004, Waterloo ON, Canada, August 9-10, 2004 : revised selected papers
EditorsH. Handschuh, M.A. Hasan, R.L. Wainwright, L.M. Liebrock
Place of PublicationBerlin
PublisherSpringer
Pages170-181
Number of pages12
ISBN (Print)3-540-24327-5
DOIs
Publication statusPublished - 1 Dec 2004

Publication series

NameLecture Notes in Computer Science
Volume3357
ISSN (Print)0302-9743

Keywords

  • Binary fields
  • Explicit group operations
  • Fast arithmetic
  • Hyperelliptic curves

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  • Cite this

    Lange, T., & Stevens, M. (2004). Efficient doubling on genus two curves over binary fields. In H. Handschuh, M. A. Hasan, R. L. Wainwright, & L. M. Liebrock (Eds.), Selected areas in cryptography : 11th Annual Workshop, SAC 2004, Waterloo ON, Canada, August 9-10, 2004 : revised selected papers (pp. 170-181). (Lecture Notes in Computer Science; Vol. 3357). Springer. https://doi.org/10.1007/978-3-540-30564-4_12