一类椭圆曲线二元序列的伪随机性分析

On a Family of Pseudorandom Binary Sequences from Elliptic Curve

基于二进制有限域上的椭圆曲线构造了一类二元伪随机序列,利用椭圆曲线上的指数和计算了该类序列的一致分布测度和k阶相关测度,利用线性复杂度和k阶相关测度之间的关系给出了序列的线性复杂度下界。计算结果表明,类序列具有非常好的伪随机性,在密码学和通信领域具有潜在的应用价值。

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.