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Complexity of chaotic binary sequence and precision of its numerical simulation

NONLINEAR DYNAMICS 2012年第1期67卷 549-556页

作者： Liu, Niansheng Guo, Donghui Parr, Gerard Jimei Univ Sch Comp Engn Xiamen 361021 Fujian Peoples R China Xiamen Univ Sch Informat Sci & Technol Xiamen 361005 Fujian Peoples R China Univ Ulster Sch Comp & Informat Engn Coleraine BT52 1SA Londonderry North Ireland

Numerical simulation is one of primary methods in which people study the property of chaotic systems. However, there is the effect of finite precision in all processors which can cause chaos to degenerate into a periodic function or a fixed point. If it is neglected the precision of a computer processor for the binary numerical calculations, the numerical simulation results may not be accurate due to the chaotic nature of the system under study. New and more accurate methods must be found. A quantitative computable method of sequence complexity evaluation is introduced in this paper. The effect of finite precision is evaluated from the viewpoint of sequence complexity. The simulation results show that the correlation function based on information entropy can effectively reflect the complexity of pseudorandom sequences generated by a chaotic system, and it is superior to the other measure methods based on entropy. The finite calculation precision of the processor has significant effect on the complexity of chaotic binary sequences generated by the Lorenz equation. The pseudorandom binary sequences with high complexity can be generated by a chaotic system as long as the suitable computational precision and quantification algorithm are selected and behave correctly. The new methodology helps to gain insight into systems that may exist in various application domains such as secure communications and spectrum management.

关键词： Complexity of sequence Lorenz equations chaotic binary sequence Finite calculation precision

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Orthogonal chaotic binary sequences Based on Tent Map and Walsh Functions

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2021年第9期E104A卷 1349-1352页

作者： Tsuneda, Akio Kumamoto Univ Div Informat & Energy Fac Adv Sci & Technol Kumamoto 8608555 Japan

In this letter, we will prove that chaotic binary sequences generated by the tent map and Walsh functions are i.i.d. (independent and identically distributed) and orthogonal to each other.

关键词： tent map orthogonal sequence Walsh functions chaotic binary sequence correlation function i.i.d.

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Auto-Correlation Properties of binary sequences Obtained by Switching Two Bernoulli chaotic binary sequences 14

Auto-Correlation Properties of Binary Sequences Obtained by ...

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14th International Conference on Information and Communication Technology Convergence, ICTC 2023

作者： Tsuneda, Akio Fujikawa, Masahiro Kumamoto University Department of Computer Science and Electrical Engineering Kumamoto Japan

ISBN: (纸本)9798350313277

In Monte-Carlo simulations, various types of random numbers are necessary for simulating various kinds of stochastic phenomena. Using one-dimensional chaotic maps, we can design statistical properties of the chaotic sequences, which implies that chaotic sequences may be useful for Monte-Carlo methods. In this paper, we examine auto-correlation properties of binary sequences obtained by switching two chaotic binary sequences generated by Bernoulli map. It is shown that binary sequences with various new types of auto-correlation properties can be generated. © 2023 IEEE.

关键词： Auto-correlation function Bernoulli map chaotic binary sequence

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Evaluating the Randomness of chaotic binary sequences Via a Novel Period Detection Algorithm

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INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 2022年第5期32卷

作者： Fan, Chunlei Ding, Qun Tse, Chi K. Heilongjiang Univ Elect Engn Coll Harbin 150080 Peoples R China City Univ Hong Kong Dept Elect Engn Hong Kong Peoples R China

When chaotic systems are applied to stream ciphers, chaotic real-valued sequences generally need to be converted into binary sequences with the purpose of encrypting data. However, the performance of binary sequences will be degraded under the joint influence of round-off and quantization errors. In this case, the randomness of some chaotic binary sequences may be weakened in a local range. Taking advantage of parallel computing, a fast period detection algorithm is designed to locate all local "periodicities" contained in chaotic binary sequences quickly and accurately. This algorithm evaluates the randomness of a chaotic binary sequence from a new perspective of periodicity which enriches the randomness test methods for binary sequences. Different logistic binary sequences are analyzed to demonstrate the effectiveness and practicability of the proposed algorithm.

关键词： chaotic binary sequence local period binary quantization randomness test

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Periodic performance of the chaotic spread spectrum sequence on finite precision

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Journal of Systems Engineering and Electronics 2008年第4期19卷 672-678页

作者： Zhu Canyan Zhang Lihua Wang Yiming Liu Jiasheng Mao Lingfeng School of Electronic & Information Engineering Soochow Univ. Suzhou 215021 P. R. China School of Electronic and Electric Engineering East China Jiaotong Univ. Nanchang 310013 P. R. China

It is well known that the periodic performance of spread spectrum sequence heavily affects the correlative and secure characteristics of communication systems. The chaotic binary sequence is paid more and more attention since it is one kind of applicable spread spectrum sequences. However, there are unavoidable short cyclic problems for chaotic binary sequences in finite precision. The chaotic binary sequence generating methods are studied first. Then the short cyclic behavior of the chaotic sequences is analyzed in detail, which are generated by quantification approaches with finite word-length. At the same time, a chaotic similar function is defined for presenting the cyclic characteristics of the sequences. Based on these efforts, an improved method with scrambling control for generating chaotic binary sequences is proposed. To quantitatively describe the improvement of periodic performance of the sequences, an orthogonal estimator is also defined. Some simulating results are provided. From the theoretical deduction and the experimental results, it is concluded that the proposed method can effectively increase the period and raise the complexity of the chaotic sequences to some extent.

关键词： chaotic binary sequence finite precision periodic performance orthogonal estimator

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Research on the quantifications of chaotic random number generators

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INTERNATIONAL JOURNAL OF SENSOR NETWORKS 2014年第1期15卷 32-39页

作者： Zheng, Yan-bin Pan, Jing Song, Yu Cheng, Hai Ding, Qun Heilongjiang Univ Key Lab Elect Engn Harbin 150080 Peoples R China

It has been proved that Local-Period phenomena widely exist in any chaotic binary sequences. Among the reasons of Local-Period phenomena, the quantifications of chaotic binary random number generators are the key factors. This paper proposed that different quantifications could make the generated sequences from the same chaotic real value sequence appear different randomness. Moreover, the simulation results illustrated that for the same Logistic real value sequence quantified by different quantifications, such as L-bits quantification, C-threshold quantification and Region quantification, Local-Period phenomena are located in different places by binary sequence period detection (BSPD) detecting method. Meanwhile, statistical data inferred that C-threshold quantification has less effect on the randomness of original chaotic real value sequence.

关键词： chaotic binary sequence quantification chaotic random number generator Local-Period phenomenon

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Pseudo-randomness and complexity of binary sequences generated by the chaotic system

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2011年第2期16卷 761-768页

作者： Nian-Sheng, Liu Jimei Univ Sch Comp Engn Xiamen 361021 Fujian Peoples R China

The pseudo-randomness and complexity of binary sequences generated by chaotic systems are investigated in this paper. These chaotic binary sequences can have the same pseudo-randomness and complexity as the chaotic real sequences that are transformed into them by the use of Kohda's quantification algorithm. The statistical test, correlation function, spectral analysis, Lempel-Ziv complexity and approximate entropy are regarded as quantitative measures to characterize the pseudo-randomness and complexity of these binary sequences. The experimental results show the finite binary sequences generated by the chaotic systems have good properties with the pseudo-randomness and complexity of sequences. However, the pseudo-randomness and complexity of sequence are not added with the increase of sequence length. On the contrary, they steadily decrease with the increase of sequence length in the criterion of approximate entropy and statistical test. The constraint of computational precision is a fundamental reason resulting in the problem. So only the shorter binary sequences generated by the chaotic systems are suitable for modern cryptography without other way of adding sequence complexity in the existing computer system. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Chaos sequence complexity Pseudo-randomness chaotic binary sequence

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Watermark embedded in permuted domain

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ELECTRONICS LETTERS 2001年第2期37卷 80-81页

作者： Yen, JC Natl Lien Ho Inst Technol Dept Elect Engn Maioli Taiwan

A scheme is proposed in which a watermark is transformed and then used to modify the third, fourth, or fifth bit of the pixels in a permuted image according to a chaotic binary sequence. The PSNR is larger than 44dB a... 详细信息

关键词： Image and video coding chaotic binary sequence data compression permuted domain chaos binary sequences copy protection image coding compression ratio PSNR watermark Computer vision and image processing techniques

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