Construction of Large Families of Pseudorandom Subsets of the Set {1, 2, ..., N} Using Elliptic Curves

Pseudo-random subsets of the set {1, 2, . . . , N} have many applications in the fields of network security, cryptography and other security issues. Recently, Dartyge and Sárközy investigated the measures–the well distribution measure and the correlation measure of order k–of pseudorandomness of subsets of the set {1, 2, . . . , N}, and they presented several constructive examples for subsets with strong pseudorandom properties when N is a prime number. In this article, we present a construction of pseudorandom subsets by using elliptic curves over finite fields and estimate their pseudorandom measures. Exponential sums play an important role in the proofs.