“…Let E(F q ) denote the set of F q -rational points on E. We recall that the celebrated result of Bombieri [6] implies, in particular, an estimate of order q 1/2 for exponential sums with functions from the function field of E taken over all points of E(F q ). More recently, various character sums over points of elliptic curves have been considered in a number of papers, see [1,3,8,12,13,17,18,19,25,26,28,30,32] and references therein. These estimates are motivated by various applications to such areas as • pseudorandom number generators from elliptic curves, see the most recent works [4,8,20,21,22,23] and also the survey [31];…”