Large Family of Sequences from Elliptic Curves over Residue Class Rings

Abstract

An upper bound is established for certain exponential sums on the rational points of an elliptic curve over a residue class ring $\mathbb{Z}_N$, 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 pseudorandomness of a large family of binary sequences constructed by using elliptic curves over $\mathbb{Z}_N$.