Construction of k-ary pseudorandom elliptic curve sequences

Abstract

We present a method for constructing k-ary sequences over elliptic curves. Using the multiplicative character of order k of finite fields, we construct a family of k-ary pseudorandom elliptic curve sequences. The pseudorandom measures, such as the well-distribution measure, the correlation measure of order l, and the linear complexity are estimated by using certain character sums. Such sequences share the same order of magnitude on the well-distribution measure, the correlation measure of order l as the ‘truly’ random sequences. The method indicates that it is possible to construct ‘good’ pseudorandom sequences over elliptic curves widely used in public key cryptography.