一类低相关序列集的线性复杂度研究  

On the linear span of a class of low correlation sequence family

作　　者：田金兵[1] 曾祥勇[2] 胡磊[3] 

机构地区：[1]海南师范大学初等教育系,海南海口571158 [2]湖北大学数学与计算机科学学院,湖北武汉430062 [3]信息安全国家重点实验室(中国科学院研究生院),北京100049

出　　处：《通信学报》2008年第7期75-80,共6页Journal on Communications

基　　金：国家自然科学基金资助项目(60603012);武汉市青年科技晨光计划基金资助项目(200850731340)~~

摘　　要：在密码系统和通信系统中使用大线性复杂度的低相关序列能有效地提高数据的安全性,设计大线性复杂度的二元低相关序列是一个重要的研究问题。使用d-齐次函数是构造低相关序列集的一种有效途径,Key方法可以确定这些序列的线性复杂度。对正偶数n和与2n/2?1互素的任意正整数r,提出了一类周期为2n-1的2n条序列组成的二元序列集S(r)。对某些适当选取的参数r,S(r)中序列的线性复杂度为n2n/2?3或n2n/2?4。参数n可以取任意正偶数,所构造的具有大线性复杂度的序列具有广泛的使用范围。In cryptography and communication systems, application of low correlation sequences with large linear span can efficiently improve security of data, and the design of sequences with these properties was an important research problem. A useful approach to construct sequence families with low correlation was based on d-form functions, and the Key＇s method can determine the linear span of these sequences. For a positive even integer n and any positive integers r relatively prime to 2^n/2-1, a class of low correlation sequence families S^（r） was proposed, and each family contained 2^n- binary sequences of period 2^n- 1. For some suitable values of the parameter r, the linear span of those sequences in S^（r） was equal to n2^n/2-3, or n2^n/2-4 The constructed sequences with large linear span have a wide range of application since the parameter n can take any even integer.

关 键 词：伪随机序列 线性复杂度 低相关 

分 类 号：TN918.1[电子电信—通信与信息系统] TN914.53[电子电信—信息与通信工程]