## Cryptology ePrint Archive: Report 2009/076

Construction of large families of pseudorandom subsets using elliptic curves

Zhixiong Chen and Chenhuang Wu

Abstract: Recently, Dartyge and Sárk\"{o}zy investigated the measures, i.e., the well distribution measure and the correlation measure of order $k$, of pseudorandomness of subsets of the set $\{1, 2,\ldots, N\}$, 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 using elliptic curves over finite fields and estimate the pseudorandom measures. Character sums play an important role in the proofs.

Category / Keywords: foundations / Pseudo-random - Subsets - Elliptic curves -Character sums