Speeding up the arithmetic on hyperelliptic Koblitz curves of genus two

C. Günther, T. Lange, A. Stein

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

    19 Citations (Scopus)


    Koblitz, Solinas, and others investigated a family of elliptic curves which admit faster cryptosystem computations.In this paper, we generalize their ideas to hyperelliptic curves of genus 2.We consider the following two hyperelliptic curves C a : v 2 + uv = u 5 + au 2 + 1 defined over F2 with a = 0, 1, and show how to speed up the arithmetic in the Jacobian JCa(F2n) by making use of the Frobenius automorphism.With two precomputations, we are able to obtain a speed-up by a factor of 5.5 compared to the generic double-and-add-method in the Jacobian.If we allow 6 precomputations, we are even able to speed up by a factor of 7.
    Original languageEnglish
    Title of host publicationSelected areas in cryptography : 7th Annual International Workshop, SAC 2000 Waterloo, Ontario, Canada, August 14–15, 2000 : proceedings
    EditorsD.R. Stinson, S. Tavares
    Place of PublicationBerlin
    ISBN (Print)3-540-42069-X
    Publication statusPublished - 2001

    Publication series

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

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