On Exponential Sums and Group Generators for Elliptic Curves over Finite Fields

Abstract

In the paper an upper bound is established for certain exponential sums, analogous to Gaussian sums, defined on the points of an elliptic curve over a prime finite field. The bound is applied to prove the existence of group generators for the set of points on an elliptic curve over Fq among certain sets of bounded size. We apply this estimate to obtain a… (More)
DOI: 10.1007/10722028_24

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