Trace representation of pseudorandom binary sequences derived from Euler quotients

被引：16

作者：

Chen, Zhixiong ^{[1
,2
]}

Du, Xiaoni ^{[2
,3
]}

Marzouk, Radwa ^{[4
]}

机构：

[1] Putian Univ, Prov Key Lab Appl Math, Putian 351100, Fujian, Peoples R China

[2] Xidian Univ, State Key Lab Integrated Serv Networks, Xian 710071, Shaanxi, Peoples R China

[3] Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Gansu, Peoples R China

[4] Cairo Univ, Fac Sci, Dept Math, Giza 12613, Egypt

来源：

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING | 2015年 / 26卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Cryptography; Pseudorandom binary sequences; Euler quotients; Fermat quotients; Trace function; LINEAR COMPLEXITY; FERMAT QUOTIENTS; CHARACTER SUMS; VALUE SET; NUMBERS; DIVISIBILITY;

D O I：

10.1007/s00200-015-0265-4

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We give the trace representation of a family of binary sequences derived from Euler quotients by determining the corresponding defining polynomials. The result extends an earlier result of Z. Chen on the trace of binary sequences derived from Fermat quotients modulo a prime. However, the case of composite modulus brings some interesting twists. Trace representation can help us producing the sequences efficiently and analyzing their cryptographic properties, such as linear complexity.

引用

页码：555 / 570

页数：16

共 36 条

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

Agoh, T ;

Dilcher, K ;

Skula, L .

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

[2] Boolean functions derived from Fermat quotients [J].

Aly, Hassan ;

Winterhof, Arne .

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2011, 3 (03) :165-174

[3] TRANSFORM TECHNIQUES FOR ERROR CONTROL CODES [J].

BLAHUT, RE .

IBM JOURNAL OF RESEARCH AND DEVELOPMENT, 1979, 23 (03) :299-315

[4]

Bourgain J, 2010, MICH MATH J, V59, P313

[5] Short character sums with Fermat quotients [J].

Chang, Mei-Chu .

ACTA ARITHMETICA, 2012, 152 (01) :23-38

[6] On the k-error linear complexity of binary sequences derived from polynomial quotients [J].

Chen ZhiXiong ;

Niu ZhiHua ;

Wu ChenHuang .

SCIENCE CHINA-INFORMATION SCIENCES, 2015, 58 (09) :1-15

[7] Trace representation and linear complexity of binary sequences derived from Fermat quotients [J].

Chen ZhiXiong .

SCIENCE CHINA-INFORMATION SCIENCES, 2014, 57 (11) :1-10

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

Chen, Zhixiong ;

Winterhof, Arne .

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

[9] INTERPOLATION OF FERMAT QUOTIENTS [J].

Chen, Zhixiong ;

Winterhof, Arne .

SIAM JOURNAL ON DISCRETE MATHEMATICS, 2014, 28 (01) :1-7

[10] 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

← 1 2 3 4 →