Distribution of some sequences of points on elliptic curves

Tanja Lange*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


We estimate character sums over points on elliptic curves over a finite field F q 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
Pages (from-to)1-11
Number of pages11
JournalJournal of Mathematical Cryptology
Issue number1
Publication statusPublished - Jan 2007


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