基于椭圆曲线的二元伪随机序列构造与分析

Construction and Analysis of Binary Pseudorandom Sequences Based on Elliptic Curve

基于有限域p上的椭圆曲线,利用乘法逆构造一类二元伪随机序列,通过素域上椭圆曲线的指数和,计算该类伪随机序列的一致分布测度和k阶相关测度。结果表明,周期为N的二元伪随机序列一致分布测度的上界为p1/2lbplbN,k阶相关测度的上界为p1/2(lbp)klbN,2个测度的数量级都是O(N),说明该类序列具有很好的伪随机性质。

One family of pseudorandom binary sequences are constructed from elliptic curves on finite field by using the multiplicative inverse.The properties of pseudorandom binary sequences are studied including the well-distribution measure and the correlation measure of order k.Through exponential sums along elliptic curves,the well-distribution measure and the correlation measure of order k are computed.The upper bound of well-distribution measure is p1/2lbplbN.The upper bound of correlation measure of order k is p1/2（lbp）klbN.Their magnitudes are O（N）,which indicates that this family of sequences have good randomness.