Collisions in fast generation of ideal classes and points on hyperelliptic and elliptic curves

T. Lange, I.E. Shparlinski

    Research output: Contribution to journalArticleAcademicpeer-review

    10 Citations (Scopus)

    Abstract

    Koblitz curves have been proposed to quickly generate random ideal classes and points on hyperelliptic and elliptic curves. To obtain a further speed-up a different way of generating these random elements has recently been proposed. In this paper we give an upper bound on the number of collisions for this alternative approach. For elliptic Koblitz curves we additionally use the same methods to derive a bound for a modified algorithm. These bounds are tight for cyclic subgroups of prime order, which is the case of most practical interest for cryptography.
    Original languageEnglish
    Pages (from-to)329-337
    JournalApplicable Algebra in Engineering, Communication and Computing
    Volume15
    Issue number5
    DOIs
    Publication statusPublished - 2005

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