Abstract: One family of pseudorandom binary sequences were constructed from elliptic curves over binary finite fields.With the help of exponential sums on elliptic curves, the well-distribution measure and correlation measure of order k were computed, and the low bound of linear complexity was derived by the relation between linear complexity and correlation measure of order k. The results show that these sequences have good randomness and provide strong potential applications in communication systems and cryptography.

Key words: Pseudorandom sequence elliptic curve, Exponential sums, Well-distribution measure, Correlation measure of order k