Distribution of some sequences of points on elliptic curves

Tanja Lange, Igor Shparlinski

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    Abstract

    We estimate character sums over points on elliptic curves over a finite field of q elements. Pseudorandom sequences can be constructed by taking linear combinations with small coefficients (for example, from the set {−1, 0, 1}) of a fixed vector of points, which forms the seed of the generator. We consider several particular cases of this general approach which are of special practical interest and have occurred in the literature. For each of them we show that the resulting sequence has good uniformity of distribution properties.
    Original languageEnglish
    JournalJournal of Mathematical Cryptology
    Volume1
    Issue number1
    Pages (from-to)1-11
    ISSN1862-2976
    DOIs
    Publication statusPublished - 2007

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