混沌PN序列的性能分析与比较
摘要
混沌是非线性确定性系统产生的一种类似随机的现象,广泛地存在于各种非线性系统之中。由于混沌表现出的非周期,宽频谱和对初始值非常敏感的特性,使得其产生的伪噪声(PN)序列性能优良,具随机性与长周期特性,适合于保密通信以及扩频码的产生。本文基于FPGA技术,在分析一个新的连续超混沌系统基础上,将混沌系统的各状态值抽位量化,得出PN序列,并对得到的PN序列进行随机性FIPS性能分析,结果表明该PN序列通过测试,在实际工程应用具有一定的价值。然后进行了几种成熟的混沌系统FIPS性能指标的分析比较,得出了相对于某种特定测试,哪个混沌系统的测试结果较为理想的结论。最后提出了PN序列发生器的可行性原理。
本文的主要工作有:
(1)通过Altera公司开发的DSPBuilder工具,构建多种混沌系统,再下载到FPGA芯片转化成VHDL语言,从而节省了硬件实现混沌的时间,使批量研究混沌系统及混沌PN序列成为可能。
(2)构造了一个新的Lu超混沌系统,并分析了其对称性,平衡点及稳定性,耗散性,吸引子相图,Lyapunov指数谱和分岔图等特性并构造了对应电路。
(3)利用FPGA数字技术得到该混沌的PN序列,并对该PN序列的FIPS各项指标进行了细致分析,得出其具有良好的随机性能,为工程实现提供了理论依据。
(4)对Lorenz,Chen,Lu, Sproott这四类经典混沌系统的数字PN序列性能进行了综合分析,得出:对于频率测试和串列测试,Lorenz系统的效果较好,而对于Poker测试和游程测试,Lu系统的效果更好,最后对于自相关测试,四个混沌系统则相差无几。
(5)在分析众多混沌系统的基础上,提出了PN序列发生器的原理和可行性。
Chaos is a quasi stochastic phenomenon occurring in the non-linear determinate dynamic systems, which is ubiquitous in very nonlinear system. In virtue of its characteristics such as non-cycle, wide spectrum and sensitivity to the initial values. The chaotic PN sequences are highly random and have long periods which mean that it’s suitable for secret communication and spreading code generation. Based on the analysis of a new continuous hyperchaotic system which is based on the use of FPGA technology and quantify the state value of chaotic system to arrive PN sequence, and analyse the randomness FIPS performance, then know the PN sequence get through the test and have practical engineering application value. Then test several mature chaotic system through FIPS performance analysis and comparison of obtained results which is better. Finally, this paper proposes with the feasibility of PN sequence generator principle. The main work of this paper includes:
(1) DSP Builder Toolbag, which is developed by Altera, is employed to firstly construct chaotic systems in MATLAB. The systems are then coverted into VHDL language and downloaded into FPGA chip. This process shortens the development cycle of chaos hardware realization and makes it possible to analyze a large amount of chaotic PN sequences.
(2) Constructed a new hyperchaotic Lu system, and an analysis of its symmetry, balance and stability, dissipative attractor phase diagram, Lyapunov exponent spectra and bifurcation diagram and other properties, and construct the corresponding circuit.
(3) Based on FPGA Digital technology, get the chaotic PN sequences. Analyse the PN sequence of FIPS performance is quite good, provided a theoretical basis for the engineering implementation.
(4) As for Lorenz, Chen, Lu, Sproott four categories of classical chaotic system, conducted a comprehensive analysis of the PN sequences obtained: for the Frequency test and Serial test, Lorenz system is the best, and for testing and Poker test-Runs test, Lu system is the best.
(5) On the analysis of many chaotic systems, proposed the principle and feasibility of PN sequence generator
本文的主要工作有:
(1)通过Altera公司开发的DSPBuilder工具,构建多种混沌系统,再下载到FPGA芯片转化成VHDL语言,从而节省了硬件实现混沌的时间,使批量研究混沌系统及混沌PN序列成为可能。
(2)构造了一个新的Lu超混沌系统,并分析了其对称性,平衡点及稳定性,耗散性,吸引子相图,Lyapunov指数谱和分岔图等特性并构造了对应电路。
(3)利用FPGA数字技术得到该混沌的PN序列,并对该PN序列的FIPS各项指标进行了细致分析,得出其具有良好的随机性能,为工程实现提供了理论依据。
(4)对Lorenz,Chen,Lu, Sproott这四类经典混沌系统的数字PN序列性能进行了综合分析,得出:对于频率测试和串列测试,Lorenz系统的效果较好,而对于Poker测试和游程测试,Lu系统的效果更好,最后对于自相关测试,四个混沌系统则相差无几。
(5)在分析众多混沌系统的基础上,提出了PN序列发生器的原理和可行性。
Chaos is a quasi stochastic phenomenon occurring in the non-linear determinate dynamic systems, which is ubiquitous in very nonlinear system. In virtue of its characteristics such as non-cycle, wide spectrum and sensitivity to the initial values. The chaotic PN sequences are highly random and have long periods which mean that it’s suitable for secret communication and spreading code generation. Based on the analysis of a new continuous hyperchaotic system which is based on the use of FPGA technology and quantify the state value of chaotic system to arrive PN sequence, and analyse the randomness FIPS performance, then know the PN sequence get through the test and have practical engineering application value. Then test several mature chaotic system through FIPS performance analysis and comparison of obtained results which is better. Finally, this paper proposes with the feasibility of PN sequence generator principle. The main work of this paper includes:
(1) DSP Builder Toolbag, which is developed by Altera, is employed to firstly construct chaotic systems in MATLAB. The systems are then coverted into VHDL language and downloaded into FPGA chip. This process shortens the development cycle of chaos hardware realization and makes it possible to analyze a large amount of chaotic PN sequences.
(2) Constructed a new hyperchaotic Lu system, and an analysis of its symmetry, balance and stability, dissipative attractor phase diagram, Lyapunov exponent spectra and bifurcation diagram and other properties, and construct the corresponding circuit.
(3) Based on FPGA Digital technology, get the chaotic PN sequences. Analyse the PN sequence of FIPS performance is quite good, provided a theoretical basis for the engineering implementation.
(4) As for Lorenz, Chen, Lu, Sproott four categories of classical chaotic system, conducted a comprehensive analysis of the PN sequences obtained: for the Frequency test and Serial test, Lorenz system is the best, and for testing and Poker test-Runs test, Lu system is the best.
(5) On the analysis of many chaotic systems, proposed the principle and feasibility of PN sequence generator
引文
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[2]. Kocarev L, Chaos-based cryptography: A brief overview, IEEE Circuits and Systems, 2001, 1(3): 6-21.
[3].吕金虎,陆君安,陈士华.混沌时间序列分析及其应用.武汉大学出版社,2002.
[4].冯登国著.密码分析学.北京:清华大学出版社,2000.
[5]. Wang, Haiyan; Pan, Dihong; Shen, Xiaohong. Research on two UWA frequency-hopped spread-spectrum communication methods in low sonic energy condition[C]. Wireless, Mobile and Multimedia Networks, 2006:1– 4
[6]. Mazzini, G.; Setti, G.; Rovatti, R. Chaotic complex spreading sequences for asynchronous DS-CDMA. I. System modeling and results[C].Circuits and Systems I: Fundamental Theory and Applications, 1997:937– 947
[7]. Xulei Bao; Guangyi Wang; Cuiping Wang; Wei Feng. Experimental Investigation on Impulsive Synchronization of Chaotic PN Sequences Based on FPGA[C]. .Young Computer Scientists, 2008:2914– 2918
[8]. Mozaary A, Zaainari L, Keol K, Porra V. Theoretical connection between PN-sequences and chaos makes simple FPGA pseudo-chaos sources possible [J]. Electronics and Computer Engineering, 2007: 1539-1542
[9]. Fengling Han, Jinhu Lü, Xionghuo Yu, Guanrong Chen and Yong Feng. Generating multi-scroll chaotic attractors via a linear second-order hysteresis system [J]. Dynamics of Continuous, Discete and Impulsive Systems Series B: Applications. 2005, 12: 95-110
[10]. Rosslor O. E. An equation for continuous chaos. Physics Letters A,1976,57(5):397-398.
[11]. Yuxia Li,Wallace K S Tang,Guanrong Chen,Hyperchaos evolved from the generalized Lorenz equation. International Journal of circuit theory and applications,Apple,2005,33:235-251
[12].何海莲;王光义.一个新的Rossler超混沌系统.杭州电子科技大学学报. 2008. 4.
[13]. Drutarovsky.M, Galajda.P. A robust chaos-based true random number generator embedded in reconfigurable switched-capacitor hardware [J]. Radioelektronika, 17th International Conference. 2007: 1-6.
[14]. A.S.Poznyak, Yu Wen, E.N. Sanche. Identification and control of unknown chaotic systems via dynamic neural networks [J]. IEEE Trans. on Circuits and Systems. 1995, 46(12): 1491-1495.
[15]. R. Vicente, H.Dauden, P. Colet, R.Toral. Analysis and characterization of the hyperchaos generated by a semiconductor laser subject [J]. IEEE Quantum Electron. 2005, 41(4): 541-548
[16]. V. S. Udaltsov, J. P. Goedgebuter, L. Larger, J. B. Cuenot, et al. Communication with hyperchaos: the dynamics of a DNLF emitter and recovery of transmitted information [J]. Opt. Spectrosc. 2003, 95(1): 114-118.
[17]. C.P.Li,W.H.Deng,D.Xu.Chaos synchronization of the Chua system with a fractional order[J].Physcia A.2006;360:171-185
[18]. Dept. of Electron. Eng., Kon-kuk Univ., Seoul, South Korea. A new family of frequency hopping patterns with good Hamming autocorrelation and crosscorrelation[C]. Military Communications Conference, IEEE. 1993,2:451-454.
[19]. Junwei Wang,Xiaohua Xiong,Yanbin Zhang. Extendingsynchro fractional-order Chen systems[J].Physica A.2006; 370: 279-285.
[20].张雪锋;范九伦;一种改进的混沌序列产生方法[J].数学的实践与认识. 2009. 18.
[21]. C. Beck, G. Roepstorff, Effects of phase space discretization on the long-time behavior of dynamical systems, Physica D: Nonlinear Phenomena, Vol. 25, pp. 173-180, 1987
[22].徐赐文.一类新型的混沌密码体制[J],中央民族大学学报,2001.6(2):106-112
[23].张波;王光义;韩春艳基于Logistic映射PN序列的FPGA实现现代电子技术.2009.7
[24]. Wang Guangyi, Bao Xulei, Wang Zhong Lin. Design and FPGA Implementation of a new hyperchaotic system [J]. Chinese Physics B. 2008, 17(10): 3596-3602.
[25]. Mozaary A, Zaainari L, Keol K, Porra V. Theoretical connection between PN-sequences and chaos makes simple FPGA pseudo-chaos sources possible [J]. Electronics and Computer Engineering, 2007. 2007: 1539-1542.
[26].蔡兆波.基于FPGA技术的混沌信号产生与语音保密通信的研究[D].广东工业大学. 2008
[27].王亥,胡健东.改进型Logistic-Map混沌扩频序列[J].通信学报. 1997, 18(8): 71-77
[28]. Mazzini, G.; Setti, G.; Rovatti, R. Chaotic complex spreading sequences for asynchronous DS-CDMA. I. System modeling and results[C].Circuits and Systems I: Fundamental Theory and Applications, 1997:937– 947
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