TY - JOUR

T1 - Distribution of some sequences of points on elliptic curves

AU - Lange, Tanja

AU - Shparlinski, Igor E.

PY - 2007/1

Y1 - 2007/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38149054261&partnerID=8YFLogxK

U2 - 10.1515/JMC.2007.001

DO - 10.1515/JMC.2007.001

M3 - Article

AN - SCOPUS:38149054261

VL - 1

SP - 1

EP - 11

JO - Journal of Mathematical Cryptology

JF - Journal of Mathematical Cryptology

SN - 1862-2976

IS - 1

ER -