Certain exponential sums and random walks on elliptic curves

Tanja Lange, Igor Shparlinski

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    For a given elliptic curve E, we obtain an upper bound on the discrepancy of sets of multiples z_sG where z_s runs through a sequenc Z=(z_1, \ldots ,z_T) such that k= z_1,..., kz_T is a permutation of z_1,...,z_T, both sequences taken modulo t, for sufficiently many distinct modulo t values of k. We apply this result to studying an analogue of the power generator over an elliptic curve. These results are elliptic curve analogues of those obtained for multiplicative groups of finite fields and residue rings.
    Original languageEnglish
    JournalCanadian Journal of Mathematics - Journal Canadien de Mathématiques
    Volume57
    Issue number2
    Pages (from-to)338-350
    ISSN0008-414X
    Publication statusPublished - 2005

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