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Arithmetic Crosscorrelation of pseudorandom binary sequences of Coprime Periods

IEEE TRANSACTIONS ON INFORMATION THEORY 2022年第11期68卷 7538-7544页

作者： Chen, Zhixiong Niu, Zhihua Winterhof, Arne Putian Univ Fujian Key Lab Financial Informat Proc Putian 351100 Fujian Peoples R China Putian Univ Key Lab Appl Math Fujian Prov Univ Putian 351100 Fujian Peoples R China Shanghai Univ Sch Comp Engn & Sci Shanghai 200444 Peoples R China Austrian Acad Sci Johann Radon Inst Computat & Appl Math A-4040 Linz Austria

The (classical) crosscorrelation is an important measure of pseudorandomness of two binary sequences for applications in communications. The arithmetic crosscorrelation is another figure of merit introduced by Goresky and Klapper generalizing Mandelbaum's arithmetic autocorrelation. First we observe that the arithmetic crosscorrelation is constant for two binary sequences of coprime periods, which complements the analogous result for the classical crosscorrelation. Then we prove upper bounds for the constant arithmetic crosscorrelation of two Legendre sequences of different periods and of two binary m-sequences of coprime periods, respectively.

关键词： pseudorandom binary sequences crosscorrelation arithmetic crosscorrelation Legendre sequences binary m-sequences

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NEW METHOD OF GENERATION OF SHIFTED LINEAR pseudorandom binary sequences

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PROCEEDINGS OF THE INSTITUTION OF ELECTRICAL ENGINEERS-LONDON 1974年第8期121卷 905-906页

作者： LATAWIEC, KJ POLYTECH INST OPOLE DIV AUTOMATIC CONTROLPOB 32145-951 OPOLE 1POLAND

An original, quite general and relatively simple method of generation of any advanced or delayed pseudorandom binary sequences (p. r. b. s. ) has been developed. The method is based on state-space/transition-matrix approach to the problem of generation of p. r. b. s. Any shifted sequence may be generated by a single linear-feedback shift register with extra modulo-2 adder driven from appropriately selected outputs of register stages.

关键词： Other special applications of computing pseudorandom binary sequences modulo 2 adder Switching theory generalised method linear sequences binary sequences state space/transition matrix technique sequence generation shifted sequences single linear feedback shift register random number generation

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Trace representation of pseudorandom binary sequences derived from Euler quotients

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APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 2015年第6期26卷 555-570页

作者： Chen, Zhixiong Du, Xiaoni Marzouk, Radwa Putian Univ Prov Key Lab Appl Math Putian 351100 Fujian Peoples R China Xidian Univ State Key Lab Integrated Serv Networks Xian 710071 Shaanxi Peoples R China Northwest Normal Univ Coll Math & Stat Lanzhou 730070 Gansu Peoples R China Cairo Univ Fac Sci Dept Math Giza 12613 Egypt

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.

关键词： Cryptography pseudorandom binary sequences Euler quotients Fermat quotients Trace function

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Linear Complexity of pseudorandom sequences Derived from Polynomial Quotients: General Cases

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2014年第4期E97A卷 970-974页

作者： Du, Xiaoni Zhang, Ji Wu, Chenhuang Northwest Normal Univ Coll Math & Stat Lanzhou 730070 Gansu Peoples R China Xidian Univ State Key Lab Integrated Serv Networks Xian 710071 Shaanxi Peoples R China Putian Univ Key Lab Appl Math Putian 351100 Fujian Peoples R China

We determine the linear complexity of binary sequences derived from the polynomial quotient modulo p defined by F(u) equivalent to f(u) - f(p)(u)/p (mod p), 0 = 0, where f(p)(u) equivalent to f(u) (mod p), for general... 详细信息

We determine the linear complexity of binary sequences derived from the polynomial quotient modulo p defined by F(u) equivalent to f(u) - f(p)(u)/p (mod p), 0 <= F(u) <= p -1, u >= 0, where f(p)(u) equivalent to f(u) (mod p), for general polynomials f(x) epsilon Z[x}. The linear complexity equals to one of the following values [p(2) - p, p(2) - p + 1, p(2) - 1, p(2) - 1, p(2)} if if 2 is a primitive root modulo p(2), depending on p equivalent to 1 or 3 modulo 4 and the number of solutions of f'(u) equivalent to 0 (mod p), where f'(x) is the derivative of f(x). Furthermore, we extend the constructions to d-ary sequences for prime d vertical bar(p - 1) and d being a primitive root modulo p(2).

关键词： cryptography pseudorandom binary sequences polynomial quotients finite fields linear complexity

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pseudorandom ARRAYS FOR BUILT-IN TESTS

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IEEE TRANSACTIONS ON COMPUTERS 1986年第7期35卷 653-658页

作者： BARDELL, PH MCANNEY, WH IBM

Parallel pseudorandom sequences for use in built-in test are discussed. The two-dimensional nature of these sequences-makes it natural to consider the resulting binary arrays. Some of the desired properties of such arrays are discussed, as well as some of the problems. Generators for such arrays are described. A conventional LFSR with parallel output is shown to be a poor choice for such a generator. Several compact generators are described, which are shown to be compromises between complexity and varying degrees of implementation of the desired properties in the resulting sequences. One of the compact generators produces sequences which have the desired properties for built-in tests.

关键词： Two Dimensional Window Property Built In Self Test Stimuli Linear Dependencies In M sequences Parallel LFSR sequences pseudorandom binary sequences pseudorandom sequences

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Pseudo noise sequences for engineers

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ELECTRONICS & COMMUNICATION ENGINEERING JOURNAL 1996年第2期8卷 79-87页

作者： Mutagi, RN Baseband Process. Div. Space Applications Centre Ahmedabad India

Pseudo noise (PN) sequences are widely used in digital communications and the theory involved has been treated extensively in the literature. However, a practising engineer is interested in the fundamentals and the applications of PN sequences, and the methods of generating them with hardware. This paper presents, without the mathematical rigours, some of the interesting characteristics and the use of these characteristics in the generation and acquisition of PN sequences. The series-parallel method of generating PN sequences at high speeds with low-speed devices, which is of interest to hardware designers, is discussed. Some applications of PN sequences in communications and instrumentation are discussed.

关键词： pseudorandom binary sequences digital communications binary sequences digital communication PN sequences low-speed devices Codes digital instrumentation instrumentation Telecommunication applications random noise hardware Logic circuits pseudonoise sequences generation high speeds shift registers pseudonoise codes Other topics in statistics linear feedback shift register sequences series-parallel method m-sequences maximal length binary sequences pseudonoise sequences acquisition

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Linear complexity of binary sequences derived from Euler quotients with prime-power modulus

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INFORMATION PROCESSING LETTERS 2012年第14-15期112卷 604-609页

作者： Du, Xiaoni Chen, Zhixiong Hu, Lei Putian Univ Dept Math Putian 351100 Fujian Peoples R China Chinese Acad Sci State Key Lab Informat Secur Grad Sch Beijing 100049 Peoples R China NW Normal Univ Coll Math & Informat Sci Lanzhou 730070 Gansu Peoples R China Xidian Univ State Key Lab Integrated Serv Networks Xian 710071 Shaanxi Peoples R China

We extend the definition of binary threshold sequences from Fermat quotients to Euler quotients modulo p(r) with odd prime p and r >= 1. Under the condition of 2(p-1) not equivalent to 1 (mod p(2)), we present exact values of the linear complexity by defining cyclotomic classes modulo p(n) for all 1 <= n <= r. The linear complexity is very close to the period and is of desired value for cryptographic purpose. We also present a lower bound on the linear complexity for the case of 2(p-1) equivalent to 1 (mod p(2)). (C) 2012 Elsevier B.V. All rights reserved.

关键词： Euler quotients Fermat quotients pseudorandom binary sequences Linear complexity Cryptography

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pseudorandom bit generator based on non-stationary logistic maps

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IET INFORMATION SECURITY 2016年第2期10卷 87-94页

作者： Liu, Lingfeng Miao, Suoxia Hu, Hanping Deng, Yashuang Nanchang Univ Sch Software Nanchang 330031 Peoples R China Nanchang Inst Technol Fac Sci Nanchang 330099 Peoples R China Huazhong Univ Sci & Technol Sch Automat Wuhan 430074 Peoples R China

pseudorandom binary sequences play a significant role in many fields, such as error control coding, spread spectrum communications, and cryptography. In recent years, chaotic system is regarded as an important pseudorandom source in the design of pseudorandom bit generators (PRBGs). Among them, most are based on one or more fixed chaotic systems, and the generated binary sequences come to be stationary. However, these kinds of chaotic PRBGs can be attacked by reconstructing the phase space or using some statistical analysis methods. In this study, a scheme for chaotic PRBG based on non-stationary logistic map is proposed. The authors design a dynamic algorithm to change the driven parameter sequence (not random) into a random-like sequence. The variable parameters disrupt the phase space of the system, which can resist the phase space reconstruction attacks effectively. They prove that the non-stationary logistic map is still chaotic under Wiggins' chaos definition. The numerical analysis shows that the generated binary sequences have good cryptographic properties and can pass the well-known statistical tests. The authors' chaotic PRBG based on non-stationary logistic map is a novel scheme in the design of PRBG, and is more secure than the PRBGs based on fixed chaotic systems.

关键词： Wiggins chaos definition statistical analysis Other numerical methods numerical analysis pseudorandom bit generators Codes binary sequences PRBGs design phase space reconstruction attacks statistical tests parameter sequence Cryptography chaos random sequences nonstationary logistic maps dynamic algorithm random number generation cryptography chaotic PRBG scheme pseudorandom binary sequences Cryptography theory statistical analysis methods fixed chaotic systems nonstationary sequence cryptographic property Other topics in statistics

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On error linear complexity of new generalized cyclotomic binary sequences of period p²

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INFORMATION PROCESSING LETTERS 2019年 144卷 9-15页

作者： Wu, Chenhuang Xu, Chunxiang Chen, Zhixiong Ke, Pinhui Univ Elect Sci & Technol China Sch Comp Sci & Engn Chengdu 611731 Sichuan Peoples R China Putian Univ Prov Key Lab Appl Math Putian 351100 Fujian Peoples R China Fujian Normal Univ Coll Math & Informat Fujian Prov Key Lab Network Secur & Cryptol Fuzhou 350117 Fujian Peoples R China

We consider the k-error linear complexity of a new generalized cyclotomic binary sequence of period p(2) for an odd prime p. The new sequences were introduced recently by Z. Xiao, X. Zeng, C. Li and T. Helleseth by defining a new kind of generalized cyclotomic classes modulo p(2). They proved that the sequences had large linear complexity. In this work, we determine the values of the k-error linear complexity in terms of the theory of Fermat quotients. The results indicate that such sequences have good stability, that is, the linear complexity does not significantly decrease by changing a few terms. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Cryptography pseudorandom binary sequences k-Error linear complexity Generalized cyclotomic classes Fermat quotients

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Bit pattern dependence in optical DQPSK modulation

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ELECTRONICS LETTERS 2007年第22期43卷 1223-1225页

作者： van den Borne, D. Gottwald, E. Khoe, G. D. de Waardt, H. Eindhoven Univ Technol COBRA Inst NL-5600 MB Eindhoven Netherlands Nokia Siemens Networks GmbH & Co KG D-81379 Munich Germany

A strong bit pattern dependence in optical transmission links employing multilevel modulation formats when pseudorandom binary sequences are used for modulation is demonstrated. The use of pseudorandom quaternary sequ... 详细信息

关键词： pseudorandom quaternary sequences multilevel modulation optical transmission links pseudorandom binary sequences optical modulation optical links multilevel modulation formats quadrature phase shift keying optical DQPSK modulation bit pattern dependence Modulation and coding methods Free-space optical links

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