Construction of k-ary Pseudorandom Elliptic Curve Sequences  

作　　者：WU Chenhuang WENG Xin CHEN Zhixiong 

机构地区：[1]Department of Mathematics, Putian University, Putian351100, Fujian, China [2]State Key Laboratory of Information Security/Institute ofSoftware, Chinese Academy of Sciences, Beijing 100049, China [3]School of Mathematics and Statistics, Wuhan University,Wuhan 430072, Hubei, China

出　　处：《Wuhan University Journal of Natural Sciences》2011年第5期452-456,共5页武汉大学学报（自然科学英文版）

基　　金：Supported by the National Natural Science Foundation of China (61063041);the Program for New Century Excellent Talents in Fujian Province University (JK2010047);the Open Funds of State Key Laboratory of Information Security (01-01-1)

摘　　要：We present a method for constructing k-ary sequences over elliptic curves. Using the multiplicative character of order k of finite fields, we construct a family of k-ary pseudorandom elliptic curve sequences. The pseudorandom measures, such as the well-distribution measure, the correlation measure of order e, and the linear complexity are estimated by using certain character sums. Such sequences share the same order of magnitude on the well-distribution measure, the correlation measure of order e as the ＇truly＇ random sequences. The method indicates that it is possible to construct ＇good＇ pseudorandom sequences over elliptic curves widely used in public key cryptography.We present a method for constructing k-ary sequences over elliptic curves. Using the multiplicative character of order k of finite fields, we construct a family of k-ary pseudorandom elliptic curve sequences. The pseudorandom measures, such as the well-distribution measure, the correlation measure of order e, and the linear complexity are estimated by using certain character sums. Such sequences share the same order of magnitude on the well-distribution measure, the correlation measure of order e as the ＇truly＇ random sequences. The method indicates that it is possible to construct ＇good＇ pseudorandom sequences over elliptic curves widely used in public key cryptography.

关 键 词：pseudorandom sequences discrete logarithms elliptic curves character sums 

分 类 号：TN918[电子电信—通信与信息系统]