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.
Copyright 2007, Walter de Gruyter
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