基于延迟超混沌Chen系统的保密通信方法研究
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摘要
混沌是指在确定性非线性系统中出现的类似随机的行为,混沌信号具有遍历性、非周期、连续宽带频谱、类噪声的特性,特别适合于保密通信领域。前期的研究已经表明,延迟反馈控制Chen系统中能够产生无穷维超混沌现象,如何实现具有延迟的超混沌系统的同步,并利用超混沌实现混沌保密通信得到更好的保密性能是本文的主要研究内容。具体内容如下：
对现有混沌同步方法进行了研究,主要包括驱动—响应同步法、主动—被动同步法、变量反馈同步法及自适应同步法,总结了现有的同步方法的特点,为进一步选择混沌同步方法实现具有延迟的混沌系统之间的同步奠定了基础。
分析了现有一些混沌保密通信方法,包括混沌掩盖、混沌参数调制和混沌键控。在此基础上,采用Chen系统作为混沌加密器,研究了基于密钥流的保密通信方案及其破解方法。
提出了基于直接延迟反馈的超混沌Chen系统的保密通信方法,延迟的混沌系统比一般的超混沌系统具有更复杂的混沌特性。为了进一步提高保密通信的安全性能,本文还使用了密钥流迭代函数。采用正弦信号和语音信号作为明文信号,同时在信道中加入噪声,通过仿真表明在接收端可以很好的恢复出明文信号。理论分析和仿真结果表明这种新的保密通信方法增强了保密通信的安全性。
Chaos is a quasi-stochastic phenomenon appearing in definite nonlinear dynamic systems. Chaotic signal has its special dynamic properties such as ergodicity, non-periodic, continuous broadband spectra and noise like etc. Prior researches have shown that Chen system with time delay feedback control can generate hyper-chaos with infinite dimension. How to realize hyper-chaotic synchronization with time delay, and then realizing hyper-chaotic secure communication with better security performance are the main contents of this paper. The details are as follows:
Several existing methods of chaotic synchronization are discussed in this paper, such as drive-response synchronization, active-passive synchronization, state feedback synchronization and adaptive synchronization. The features of the existing synchronization methods are given through simulation and analytical results which are helpful for selecting the synchronization method to realize time delay chaotic system synchronization.
Analyzing the existing methods of secure communication including the chaotic masking, chaotic parameter modulation and chaos shift keying. Chen system is used as chaotic encryption system in the secure communication scheme with key-stream iteration. The attacking methods are also studied to show the security fault of the low dimensional chaotic attractor.
A new approach of secure communication based on hyper-chaotic Chen system with direct time delay feedback is proposed. Meanwhile, for the purpose of improving the security of message transmission, a hyper-chaotic communication method based on multi-shift ciphering is presented. To inspect the performance of the proposed scheme, the sinusoidal waveform and voice signals are used as the plain signals. The results have shown that the legal receiver could recover the plain signals effectively even though there exist the noise from the public channel. Theoretical analysis and simulation results have shown that this new secure communication method enhanced the security performance.
对现有混沌同步方法进行了研究,主要包括驱动—响应同步法、主动—被动同步法、变量反馈同步法及自适应同步法,总结了现有的同步方法的特点,为进一步选择混沌同步方法实现具有延迟的混沌系统之间的同步奠定了基础。
分析了现有一些混沌保密通信方法,包括混沌掩盖、混沌参数调制和混沌键控。在此基础上,采用Chen系统作为混沌加密器,研究了基于密钥流的保密通信方案及其破解方法。
提出了基于直接延迟反馈的超混沌Chen系统的保密通信方法,延迟的混沌系统比一般的超混沌系统具有更复杂的混沌特性。为了进一步提高保密通信的安全性能,本文还使用了密钥流迭代函数。采用正弦信号和语音信号作为明文信号,同时在信道中加入噪声,通过仿真表明在接收端可以很好的恢复出明文信号。理论分析和仿真结果表明这种新的保密通信方法增强了保密通信的安全性。
Chaos is a quasi-stochastic phenomenon appearing in definite nonlinear dynamic systems. Chaotic signal has its special dynamic properties such as ergodicity, non-periodic, continuous broadband spectra and noise like etc. Prior researches have shown that Chen system with time delay feedback control can generate hyper-chaos with infinite dimension. How to realize hyper-chaotic synchronization with time delay, and then realizing hyper-chaotic secure communication with better security performance are the main contents of this paper. The details are as follows:
Several existing methods of chaotic synchronization are discussed in this paper, such as drive-response synchronization, active-passive synchronization, state feedback synchronization and adaptive synchronization. The features of the existing synchronization methods are given through simulation and analytical results which are helpful for selecting the synchronization method to realize time delay chaotic system synchronization.
Analyzing the existing methods of secure communication including the chaotic masking, chaotic parameter modulation and chaos shift keying. Chen system is used as chaotic encryption system in the secure communication scheme with key-stream iteration. The attacking methods are also studied to show the security fault of the low dimensional chaotic attractor.
A new approach of secure communication based on hyper-chaotic Chen system with direct time delay feedback is proposed. Meanwhile, for the purpose of improving the security of message transmission, a hyper-chaotic communication method based on multi-shift ciphering is presented. To inspect the performance of the proposed scheme, the sinusoidal waveform and voice signals are used as the plain signals. The results have shown that the legal receiver could recover the plain signals effectively even though there exist the noise from the public channel. Theoretical analysis and simulation results have shown that this new secure communication method enhanced the security performance.
引文
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[10]Fang Jinqing. Transition to hyperchaos in coupled generalized During equation[M], IAE-oll,1991
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[18]Ren H P, Han C Z, Liu D. Breaking Chaotic Shift Key Communication via Adaptive Key Identification [J]. Chinese Physics B.2008,17(4):1202-1208
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[21]Ponomarenko V I, Prokhorov M D. Extracting information masked by the chaotic signal of a time-delay system [J]. Physics Review E.2002,66,026215
[22]Chin Yi Chee, Daolin Xu, Steven R Bishop. A Zero-crossing approach to uncover the mask by chaotic encryption with periodic modulation [J]. Chaos, Solution and Fractals.2004, 21(4):1129-1134
[23]Andrew T Parker, Kevin M Short. Reconstructing the key stream from a chaotic encryption scheme [J].IEEE Transaction on Circuits and Systems-Ⅰ.2001,48(5):624-630
[24]Gonzalo Alvarez, F Montoya, G Pastor and M Romera. Breaking a secure communication scheme based on the phase synchronization of chaotic system [J]. Chaos.2004,14(2):274-278
[25]Shujun Li, Gonzalo Alvarez, Guanrong Chen, Xuanqing Mou. Breaking a chaos-noise-based secure communication scheme [J]. Chaos.2005,15(1):137-148
[26]Bu S, Wang B H. Improving the security of chaotic encryption by using simple modulating method [J]. Chaos, Solution and Fractal.2004,19(3):919-924
[27]J Y Chen, K W Wang, L M Cheng and J W Shuai. A secure communication scheme based on the phase synchronization of chaotic systems [J]. Chaos.2003,13(4):508-514
[28]J.C. Sprott, J.C. Wildenberg, Yousef Azizi. A simple spatiotemporal chaotic Lotka-Volterra model [J]. Chaos, Solitons and Fractals.2005,26(2):1035-1043
[29]P. L. Ramazza, U. Bortolozzo, and S. Boccaletti. Experimental synchronization of spatiotemporal chaos in nonlinear optics [J]. Physics Review E.2006,73(4):1-5
[30]A A Minai, T D Pandian. Communication with noise:How chaos and noise combine to generate secure encryption [J]. Chaos.1998,8(3):621-628
[31]C.E.Shannon. Communication Theory of Secrecy Systems [J].Bell System Technical journal.1994, 28(4):656-715
【32】杨维明编著.时空混沌和耦合映象格子[M].上海科技教育出版社,1994
[33]Pecora L M, Carroll T L. Synchronization in chaotic systems [J]. Physics Letter.1990,64(8): 821-824
[34]Femat R, Jauregui-Ortiz R A. Chaos-based communication scheme via robust asymptotic feedback [J]. IEEE Transaction on Circuits and Systems.2001.48(10):1161 — 1169
[35]王胜远.Lorenz和Rossler混沌系统的两驱动一响应同步研究[J].量子力学学报,1998,15(5)：460-464,
【36】杨涛. 一类混沌系统的同步方法[J].物理学报,2002,51(4)：742-748
[37]L. Kolcarev and U. Parlitz. General approach for chaotic synchronization with applications to communication [J]. Physics Review Letter.1995,74(3):5028-5031.
[38]A.Tesi, A.de Angeli, R.Genesio. On system decomposition synchronizing chaos [J]. International Journal of Bifuration and Chaos.1994,6(2):1675-1684.
【39】王金兰,陈光旨等. 超混沌系统的混沌同步[J].广西科学,1999,6(3)：184-188
[40]K. Pyragas. Experimental control of chaos by delayed self-controlling feedback. Physics Letter A. 1999,180:99-102.
【41】罗晓曙.用线性和非线性反馈实现混沌的同步化[J]. 广西物理,1997,18(2)：1-5
【42】邓林.混沌同步及其在保密通信中的应用[D].2005,重庆大学硕士论文
【43】尹海欣.混沌系统的控制与同步理论研究[D].2003,燕山大学硕士学位论文
[44]Agization. HN. Chaos synchronization of LU dynamical [J]. Nonlinear Analysis,2004,58 (10):11-20
【45】贺明峰,穆云明,赵立中.基于参数自适应控制的混沌同步[J].物理学报,2000,35(5)：830-831.
【46】贺明锋,穆云,赵立中.基于参数自适应控制的混沌同步[J].2000,35(3)：830-834
【47】赵晓红,巍学业,杨涛.洛伦兹系统的混沌自适应控制与同步研究[J]. 北方交通大学学报,2002,26(3)：25-29
[48]蒲兴成.混沌同步控制及应用研究[D].2006,重庆大学博士学位论文
【49】禹思敏,丘水生罗伟民.二进制混沌键控信号相关解调的实验研究[J].电路与系统学报,2000,5(3)：31-35
[50]葛志平,蒋铃鸽,何晨.一种改进的差分混沌键控通信方案及其性能分析[J].上海交通大学学报,2004,38：14-18
【51】凌聪,孙松庚. 用于CDMA的四相混沌扩频序列[J].通信学报,1998,19(3)：40-44
[52]Rulkov.N.F, Sushchik.M.M, Tsimring.L.S, Volkovskii.A.R. Digital Communication Using Chaotic Pulse Position Modulation[J].EEE Trans.CAS-Ⅰ.2001,48(2):1436-1444
[53]Maggio.GM, Rulkov.N, Reggiani.L. Pseudo-Chaotic time hopping for UWB Impulse Radio [J]. IEEE Trans.CAS-L2001,48(12):1424-1435.
[54]Dmitriev.A.S et.al. Basic Principles of Direct Chaotic Communications [J]. Nonlinear Phenomena in Complex Systems.2002,4(1):1-14
[55]车会生,邵毅. 激光混沌保密通信[J].激光与光电子学进展,2003,40(5)：7-13.
[56]黄报星.Lorenz系统的混沌同步与保密通信[J].吉林大学学报,2003,33(3)：60-63
[57]鞠磊,翁贻方.主动—被动混沌同步保密通信系统设计[J].北京工商大学学报,2002,20(1)：33-36
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【60】潘家民.多进制混沌键控调制方法研究[D].2003,吉林大学硕士学位论文
[61]Ueta T, Chen G R. Bifurcation analysis of Chen's equation [J]. International Journal of Bifurcation and Chaos.2000,10(8):1917-1931
[62]Vanecek, Celikovsky S. Control systems:from linear analysis to synthesis of chaos [M].London: Pretice Hall,1996.
[63]Tao Yang, Chai Wah Wu, Leon O. Chua. Cryptography based on chaotic systems [J]. IEEE Transaction on Circuits and System.1997,44(5):469-472
[64]Andrew T. Parker, Kevin M. short. Reconstructing the key-stream from a chaotic encryption scheme [J]. IEEE Transaction on Circuits and Systems.2001,48(5):624-630
[65]任海鹏,刘丁,韩崇昭.基于直接延迟反馈的混沌反控制[J].物理学报,2006,55(06)：2694-08
[66]张晓丹,李志萍,张丽丽.一类基于奇异值分解的Lyapunov指数计算方法[J].北京科技大学学报,2005,27(3)：371.374
[67]J.C.Sprott.Lyapunov Exponents for Delay Differential Equations. http://sprott.physics.wisc.edu/chaos /ddele.htm.2007
【2】 刘孝贤等.Lorenz系统的动力学特性及对称性[J].山东工业大学学报,1998,28(3)54-59
[3]Li T Y, Yorke J A. Period three implies chaos [J]. Amer, Math, Monthly,82,1975
【4】 方锦清.驾驭混沌与发展高新技术[M].北京,原子能出版社,2001,12
[5]GQ.Zhong, F.Ayrom. Periodicity and chaos in Chua's circuit [J]. IEEE Trans, On CAS,1985,32(5): 501-503
[6]G.Q.Zhong, F.Ayrom, Experimental confirmation of chaos from Chua's circuit [J]. International Journal of Circuits Theory and Application.1985,13 (1):93-98
【7】 葛真,徐云,段瑜龙.非线性电路及混沌[M].重庆,重庆大学出版社,1989
[8]方锦清：非线性系统中混沌控制方法、同步原理及其应用前景(二)[J].物理学进展,2002,16(2)：174-179
[9]O.R.Rossler. Chaotic oscillations-an example of hyper chaos in nonlinear oscillations in biology[C], Lectures in Applied Mathematics.1979,17(4):114-156
[10]Fang Jinqing. Transition to hyperchaos in coupled generalized During equation[M], IAE-oll,1991
[11]Kapitaniak T, Chua L O.Hyperchaotics attractors of unidirectionally-coupled Chua's circuits [J]. International Journal of Bifurcation and Chaos.1994,4(2):483-488
[12]Udaltsov VS, Goedgebuer J P, Larger L, et al. communicating with hyper-chaos:the dynamics of a DNLF emitter and recovery of transmitted information [J]. Optics Spectroscopic.2003, 95(1):114-121.
[13]Kevin M Short. Steps towards unmasking secure communications [J]. International Journal of Bifurcation and Chaos.1994,4(4):959-977
[14]Perez G, Cerdeira H A. Extracting messages masked by chaos [J]. Physics Review Letter.1995,74: 1970-1972.
[15]Tao Yang, Recovery of digital signal from chaotic switching [J]. International Journal of Circuits Theory and Application.1995,23(6):611-615
[16]Yang T, Yang L B, Yang C M. Breaking chaotic secure communications using a spectrogram [J]. Physics Letter A.1998,247:105-11
[17]Yang T, Yang L B, Yang C M. Breaking chaotic switching using generalized synchronization: examples [J]. IEEE Transactions on Circuits and Systems-1.1998,45(10):1062-1067
[18]Ren H P, Han C Z, Liu D. Breaking Chaotic Shift Key Communication via Adaptive Key Identification [J]. Chinese Physics B.2008,17(4):1202-1208
[19]Kevin M Short, Andrew T Parker. Unmasking a hyper-chaotic communication scheme [J]. Physics Review E.1998,58(1):1159-1162
[20]Zhou C, Lai C H. Extracting messages masked by chaotic signals of time-delay systems [J]. Physics Review E.1999,60(1):320-322.
[21]Ponomarenko V I, Prokhorov M D. Extracting information masked by the chaotic signal of a time-delay system [J]. Physics Review E.2002,66,026215
[22]Chin Yi Chee, Daolin Xu, Steven R Bishop. A Zero-crossing approach to uncover the mask by chaotic encryption with periodic modulation [J]. Chaos, Solution and Fractals.2004, 21(4):1129-1134
[23]Andrew T Parker, Kevin M Short. Reconstructing the key stream from a chaotic encryption scheme [J].IEEE Transaction on Circuits and Systems-Ⅰ.2001,48(5):624-630
[24]Gonzalo Alvarez, F Montoya, G Pastor and M Romera. Breaking a secure communication scheme based on the phase synchronization of chaotic system [J]. Chaos.2004,14(2):274-278
[25]Shujun Li, Gonzalo Alvarez, Guanrong Chen, Xuanqing Mou. Breaking a chaos-noise-based secure communication scheme [J]. Chaos.2005,15(1):137-148
[26]Bu S, Wang B H. Improving the security of chaotic encryption by using simple modulating method [J]. Chaos, Solution and Fractal.2004,19(3):919-924
[27]J Y Chen, K W Wang, L M Cheng and J W Shuai. A secure communication scheme based on the phase synchronization of chaotic systems [J]. Chaos.2003,13(4):508-514
[28]J.C. Sprott, J.C. Wildenberg, Yousef Azizi. A simple spatiotemporal chaotic Lotka-Volterra model [J]. Chaos, Solitons and Fractals.2005,26(2):1035-1043
[29]P. L. Ramazza, U. Bortolozzo, and S. Boccaletti. Experimental synchronization of spatiotemporal chaos in nonlinear optics [J]. Physics Review E.2006,73(4):1-5
[30]A A Minai, T D Pandian. Communication with noise:How chaos and noise combine to generate secure encryption [J]. Chaos.1998,8(3):621-628
[31]C.E.Shannon. Communication Theory of Secrecy Systems [J].Bell System Technical journal.1994, 28(4):656-715
【32】杨维明编著.时空混沌和耦合映象格子[M].上海科技教育出版社,1994
[33]Pecora L M, Carroll T L. Synchronization in chaotic systems [J]. Physics Letter.1990,64(8): 821-824
[34]Femat R, Jauregui-Ortiz R A. Chaos-based communication scheme via robust asymptotic feedback [J]. IEEE Transaction on Circuits and Systems.2001.48(10):1161 — 1169
[35]王胜远.Lorenz和Rossler混沌系统的两驱动一响应同步研究[J].量子力学学报,1998,15(5)：460-464,
【36】杨涛. 一类混沌系统的同步方法[J].物理学报,2002,51(4)：742-748
[37]L. Kolcarev and U. Parlitz. General approach for chaotic synchronization with applications to communication [J]. Physics Review Letter.1995,74(3):5028-5031.
[38]A.Tesi, A.de Angeli, R.Genesio. On system decomposition synchronizing chaos [J]. International Journal of Bifuration and Chaos.1994,6(2):1675-1684.
【39】王金兰,陈光旨等. 超混沌系统的混沌同步[J].广西科学,1999,6(3)：184-188
[40]K. Pyragas. Experimental control of chaos by delayed self-controlling feedback. Physics Letter A. 1999,180:99-102.
【41】罗晓曙.用线性和非线性反馈实现混沌的同步化[J]. 广西物理,1997,18(2)：1-5
【42】邓林.混沌同步及其在保密通信中的应用[D].2005,重庆大学硕士论文
【43】尹海欣.混沌系统的控制与同步理论研究[D].2003,燕山大学硕士学位论文
[44]Agization. HN. Chaos synchronization of LU dynamical [J]. Nonlinear Analysis,2004,58 (10):11-20
【45】贺明峰,穆云明,赵立中.基于参数自适应控制的混沌同步[J].物理学报,2000,35(5)：830-831.
【46】贺明锋,穆云,赵立中.基于参数自适应控制的混沌同步[J].2000,35(3)：830-834
【47】赵晓红,巍学业,杨涛.洛伦兹系统的混沌自适应控制与同步研究[J]. 北方交通大学学报,2002,26(3)：25-29
[48]蒲兴成.混沌同步控制及应用研究[D].2006,重庆大学博士学位论文
【49】禹思敏,丘水生罗伟民.二进制混沌键控信号相关解调的实验研究[J].电路与系统学报,2000,5(3)：31-35
[50]葛志平,蒋铃鸽,何晨.一种改进的差分混沌键控通信方案及其性能分析[J].上海交通大学学报,2004,38：14-18
【51】凌聪,孙松庚. 用于CDMA的四相混沌扩频序列[J].通信学报,1998,19(3)：40-44
[52]Rulkov.N.F, Sushchik.M.M, Tsimring.L.S, Volkovskii.A.R. Digital Communication Using Chaotic Pulse Position Modulation[J].EEE Trans.CAS-Ⅰ.2001,48(2):1436-1444
[53]Maggio.GM, Rulkov.N, Reggiani.L. Pseudo-Chaotic time hopping for UWB Impulse Radio [J]. IEEE Trans.CAS-L2001,48(12):1424-1435.
[54]Dmitriev.A.S et.al. Basic Principles of Direct Chaotic Communications [J]. Nonlinear Phenomena in Complex Systems.2002,4(1):1-14
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