河北师范大学学报—

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刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
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周期pq的二阶广义分圆二元序列的自相关值分布和2-adic复杂度

荆晓燕¹

强诗瑗²

杨名慧⁴

冯克勤⁴

(1.西北大学数论及其应用研究中心，陕西西安 710127; 2.四川大学数学学院，四川成都 610064; 3.中国科学院信息工程研究所信息安全国家重点实验室，北京 100084; 4.清华大学数学系，北京 100093)
DOI： 10.13763/j.cnki.jhebnu.nse.202301010

Determination of the Autocorrelation Distribution and 2-adic Complexity of Generalized Cyclotomic Binary Sequences of Order 2 with Period pq

JING Xiaoyan¹,QIANG Shiyuan²,YANG Minghui³,FENG Keqin⁴

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摘要/Abstract

摘要：

对于2个不同的奇素数p和q,周期n=pq的二元广义分圆序列S=S(a,b,c)((a,b,c)∈{0,1}3)具有良好的自相关性质.在一些情况下，其有理想自相关或最优自相关.基于群环语言和群环R=Z \[Г\](Г是n阶循环群)上的二次高斯和版本,用一种统一的方法确定了所有(a,b,c）∈{0,1}3时的二元序列S=S(a,b,c)的自相关值分布和2-adic复杂度.

Abstract：

The generalized cyclotomic binary sequences S=S(a,b,c) with period n=pq have good autocorrelation property where (a,b,c)∈{0,1}3 and p,q are distinct odd primes.For some cases,the sequences S have ideal or optimal autocorrelation.In this paper we determine the autocorrelation distribution and 2-adic complexity of the sequences S=S(a,b,c) for all (a,b,c)∈{0,1}3 in a unified way by using group ring language and a version of quadratic Gauss sums valued in group ring R=Z\[Г\] where Г is a cyclic group of order n.

关键词

关键词： 2-adic复杂度；二元序列 ; 自相关值分布；高斯和；流密码

Key words： 2-adic complexity；binary sequences；autocorrelation distribution；Gauss sums；stream cipher

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