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

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

Large Family of Sequences from Elliptic Curves over Residue Class Rings

SUMMARY An upper bound is established for certain exponential sums on the rational points of an elliptic curve over a residue class ring Z N , N = pq for two distinct odd primes p and q. The result is a generalization of an estimate of exponential sums on rational point groups of elliptic curves over finite fields. The bound is applied to showing the pseudoran-domness of a large family of binar...

Complete characterization of the Mordell-Weil group of some families of elliptic curves

 The Mordell-Weil theorem states that the group of rational points‎ ‎on an elliptic curve over the rational numbers is a finitely‎ ‎generated abelian group‎. ‎In our previous paper, H‎. ‎Daghigh‎, ‎and S‎. ‎Didari‎, On the elliptic curves of the form $ y^2=x^3-3px$‎, ‎‎Bull‎. ‎Iranian Math‎. ‎Soc‎.‎‎ 40 (2014)‎, no‎. ‎5‎, ‎1119--1133‎.‎, ‎using Selmer groups‎, ‎we have shown that for a prime $p...

Exponential Sums over Points of Elliptic Curves

We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on elliptic curves. Subject Classification (2010) Primary 11L07, 11T23 Secondary 11G20

Lifts of Points on Curves and Exponential Sums

We give bounds for exponential sums over curves defined over Galois rings. We first define summation subsets as the images of lifts of points from affine opens of the reduced curve, and give bounds for the degrees of their coordinate functions. Then we get bounds for exponential sums, extending results of Kumar et al., Winnie Li over the projective line, and Voloch-Walker over elliptic curves a...