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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 ■,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 ■ 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.
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. Such as pseudorandom measures, such as the well-distribution measure, the correlation measure of order ■, 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 ■ 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.