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Tanja Lange, Igor E. Shparlinski

Distribution of some sequences of points on elliptic curves

Keywords: Public key cryptography,, elliptic curves,, Koblitz curves,, character sums,, pseudorandomness

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.

Mathematical Cryptology, Walter de Gruyter

Print ISSN: 1862-2976
Volume: 1, 01/2007
Pages: 1 - 11

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