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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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On finite pseudorandom binary sequences II. The Champernowne, Rudin-Shapiro, and Thue-Morse sequences, a further construction

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JOURNAL OF NUMBER THEORY 1998年第2期73卷 256-276页

作者： Mauduit, C Sarkozy, A Inst Math Luminy CNRS UPR 9016 F-13288 Marseille 9 France Eotvos Lorand Univ Dept Algebra & Number Theory H-1088 Budapest Hungary

Special finite binary sequences are tested for pseudorandomness. As measures of pseudorandomness, well-distribution relative to arithmetic progressions and small (auto)correlation are used. These properties of the Champernowne, Thue-Morse, and Rudin-Shapiro sequences are studied and it is shown that although each of them possesses certain pseudorandom properties, none of them can be considered completely pseudorandom. Finally, by using the Legendre symbol and permutation polynomials, a nearly ideally pseudorandom sequence is constructed. (C) 1998 Academic Press.

关键词： Autocorrelation pseudorandom pseudorandom sequences Legendre symbol Finite Permutation pseudorandom binary sequences Arithmetic Progression sequences binary sequences

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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： Built-in self-test stimuli linear dependencies in m- sequences parallel LFSR sequences pseudorandom binary sequences pseudorandom sequences two-dimensional window property

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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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AN AIRJET ACTUATOR SYSTEM FOR IDENTIFICATION OF THE HUMAN ARM JOINT MECHANICAL-PROPERTIES

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING 1991年第11期38卷 1111-1122页

作者： XU, YM HUNTER, IW HOLLERBACH, JM BENNETT, DJ MIT DEPT BRAIN & COGNIT SCIARTIFICIAL INTELLIGENCE LABCAMBRIDGEMA 02139 MCGILL UNIV DEPT MECH ENGNMONTREAL H3A 2B4QUEBECCANADA

A system is described for determining the mechanical properties of the human arm during unconstrained posture and movement. An airjet perturbation device is attached to the wrist with a special cuff, and provides high-frequency stochastic perturbations in potentially three orthogonal directions. The airjet operates as a fluidic flip-flop utilizing the Coanda effect, and generates binary force sequences with a steady-state thrust of 4 N, a flat frequency response to 75 Hz, usable thrust to 150 Hz, and a rise time of 1 ms, when the static pressure at the nozzle inlet is 5.5 x 10(5) Pa (80 psi). These operating characteristics are adequate to identify the arm's mechanical properties efficiently and robustly.

关键词： moving parts white (color) actuator system Coanda effect Wrist frequency band widths Walsh functions perturbation Mechanical properties pseudorandom binary sequences

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A CONTROLLED PROBABILITY RANDOM PULSE-GENERATOR SUITABLE FOR VLSI IMPLEMENTATION

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 1990年第1期39卷 168-174页

作者： ALKHALILI, AJ ALKHALILI, DM ROYAL MIL COLL CANADA DEPT ELECT & COMP ENGNKINGSTON K7L 2W3ONTARIOCANADA

A method for generating a controlled number of pulses randomly within a specified time is presented. The number of random pulses is preset by an external device. The theory of maximal-length pseudorandom binary sequences is used as the basis for the method. An example of such a random generator implemented in a single VLSI chip using 3- mu m double-layer CMOS technology is presented. A controlled probability random generator based on the method proposed can be implemented in a single chip of not more than 500 gates.

关键词： pulse number Double layer Random Generator preset CMOS technology Computer equipment Very large scale integration dynamos Computer chips DNA Microarrays pseudorandom binary sequences gates

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

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