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计算机工程 ›› 2012, Vol. 38 ›› Issue (18): 100-102. doi: 10.3969/j.issn.1000-3428.2012.18.027

• 安全技术 • 上一篇    下一篇

基于椭圆曲线的二元伪随机序列构造与分析

花文昭,韩文报   

  1. (郑州信息科技学院信息研究系,郑州 450002)
  • 收稿日期:2011-10-27 修回日期:2011-12-20 出版日期:2012-09-20 发布日期:2012-09-18
  • 作者简介:花文昭(1986-),男,硕士研究生,主研方向:公钥密码学;韩文报,教授、博士生导师
  • 基金资助:
    国家自然科学基金资助项目(61003291);国家“973”计划基金资助项目(2007CB807902);全国优秀博士学位论文作者专项基金资助项目(FANEDD-2007B74)

Construction and Analysis of Binary Pseudorandom Sequences Based on Elliptic Curve

HUA Wen-zhao, HAN Wen-bao   

  1. (Department of Information Research, Zhengzhou Institute of Information Technology, Zhengzhou 450002, China)
  • Received:2011-10-27 Revised:2011-12-20 Online:2012-09-20 Published:2012-09-18

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

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