Trace representation of the binary pq2-periodic sequences derived from Euler quotients

被引：5

作者：

Zhang, Jingwei ^{[1
,2
]}

Hu, Chuangqiang ^{[3
]}

Fan, Xiang ^{[3
]}

Zhao, Chang-An ^{[3
,4
,5
]}

机构：

[1] Guangdong Univ Finance & Econ, Sch Informat Sci, Guangzhou 510320, Peoples R China

[2] Guangdong Intelligent Business Engn Technol Res C, Guangzhou, Peoples R China

[3] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Peoples R China

[4] Guangdong Key Lab Informat Secur, Guangzhou 510006, Peoples R China

[5] Chinese Acad Sci, State Key Lab Informat Secur, Inst Informat Engn, Beijing 100093, Peoples R China

来源：

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2021年 / 13卷 / 02期

基金：

国家重点研发计划;

关键词：

Cryptography; Euler quotients; Finite fields; Binary sequences; Trace representation;

D O I：

10.1007/s12095-021-00475-1

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Given a binary sequence, its trace representation allows us to reconstruct itself efficiently and to analyze its properties, such as the linear complexity. In this paper, we study a family of the binary sequences derived from Euler quotients modulo pq, where p and q are two distinct odd primes and p divides q - 1. Our main contribution is to give a trace representation of this family within these assumptions by determining the defining pairs of the corresponding subsequences. As a byproduct, we rediscover some known results of linear complexities by using trace representations of the proposed sequences.

引用

页码：343 / 359

页数：17

共 33 条

[1] Fermat quotients for composite moduli [J].

Agoh, T ;

Dilcher, K ;

Skula, L .

JOURNAL OF NUMBER THEORY, 1997, 66 (01) :29-50

[2]

[Anonymous], 2014, Sci. China Inf. Sci.

[3]

[Anonymous], 2005, SIGNAL DESIGN GOOD C, DOI DOI 10.1017/CBO9780511546907

[4] ON k-ERROR LINEAR COMPLEXITY OF PSEUDORANDOM BINARY SEQUENCES DERIVED FROM EULER QUOTIENTS [J].

Chen, Zhixiong ;

Edemskiy, Vladimir ;

Ke, Pinhui ;

Wu, Chenhuang .

ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2018, 12 (04) :805-816

[5]

Chen ZX, 2017, CRYPTOGR COMMUN, V9, P445, DOI 10.1007/s12095-016-0185-6

[6] Trace representation of pseudorandom binary sequences derived from Euler quotients [J].

Chen, Zhixiong ;

Du, Xiaoni ;

Marzouk, Radwa .

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2015, 26 (06) :555-570

[7] Additive character sums of polynomial quotients [J].

Chen, Zhixiong ;

Winterhof, Arne .

THEORY AND APPLICATIONS OF FINITE FIELDS, 2012, 579 :67-+

[8] On the linear complexity of binary threshold sequences derived from Fermat quotients [J].

Chen, Zhixiong ;

Du, Xiaoni .

DESIGNS CODES AND CRYPTOGRAPHY, 2013, 67 (03) :317-323

[9] ON THE DISTRIBUTION OF PSEUDORANDOM NUMBERS AND VECTORS DERIVED FROM EULER-FERMAT QUOTIENTS [J].

Chen, Zhixiong ;

Winterhof, Arne .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2012, 8 (03) :631-641

[10]

Cunsheng Ding, 1998, Finite Fields and their Applications, V4, P140, DOI 10.1006/ffta.1998.0207

← 1 2 3 4 →