摘要: 基于有限域 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。
关键词:
伪随机序列,
椭圆曲线,
指数和,
一致分布测度,
k阶相关测度
Abstract: 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.
Key words:
pseudorandom sequence,
elliptic curve,
exponential sum,
uniform distribution measure,
correlation measure of order k
中图分类号:
花文昭, 韩文报. 基于椭圆曲线的二元伪随机序列构造与分析[J]. 计算机工程, 2012, 38(18): 100-102.
HUA Wen-Zhao, HAN Wen-Bao. Construction and Analysis of Binary Pseudorandom Sequences Based on Elliptic Curve[J]. Computer Engineering, 2012, 38(18): 100-102.