基于超混沌同步的数字保密通信研究
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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,混沌运动的动力学特性可用来描述和量化许多复杂现象,混沌信号具有遍历性、非周期、连续宽带频谱、似噪声的特性,特别适合于保密通信领域。混沌同步的实现为混沌保密通信提供了理论基础,使得混沌同步及其应用研究成为当代相关学科的研究热点。
本论文对超混沌同步及其在保密通信中的应用进行了深入研究,主要内容如下:
首先,系统地论述了混沌同步及其应用的研究现状,重点研究了驱动-响应混沌同步、基于反馈方法的混沌同步和基于状态观测器方法的混沌同步,采用这三种方法设计了三种同步方案,并对三种方案进行数值仿真分析,可以看到基于状态观测器方法的混沌同步方案具有一定的优越性。超混沌系统的特性使其更适合应用于数字保密通信领域,接下来,设计了一种基于状态观测器方法的超混沌同步方案,并通过数值仿真验证了该方案的正确性及实现混沌同步的有效性。
其次,对混沌掩盖、混沌参数调制、混沌键控和混沌扩频进行理论分析,设计了一种基于状态观测器方法的混沌掩盖方案,通过数值仿真,验证了该方案的有效性。并针对传统的混沌掩盖技术存在的不足,设计了一种基于状态观测器的超混沌同步保密通信方案,通过理论推导及数值仿真实验得出,这是一种有效的保密通信方案,且保密性较高。
Chaos is a quasi-stochastic phenomenon appearing possibly in definite nonlinear dynamic systems. Chotic motion is a complex nonlinear motion and the chaotic phenomenon has been observed in a lot of real systems.The dynamic properties of chaos signal such as ergodicity, aperiodic, uncorrelated, broadband and noise-like have been proved to be useful for secure communication. The chaotic synchronization is the theory basis of secure communication.The research of the chaotic synchronization and its application becomes a new research focus in nonlinear science fields.
The main content of this paper contains the analysis of hyperchaotic synchronization and application of hyperchaotic secure communication. In this dissertation, the main contributions are as follows:
Firstly, the application of chaotic synchronization and its current situation is described systematiclly, then three chaotic synchronization schemes are designed with three different methods, which are the drive-response chaotic synchronization, the synchronization method based on feedback and the observer-based synchronization method. Then make numerical simulations with the three schemes, from the results, we can see that the observer-based chaotic synchronization method has more advantages than the others. Hyperchaotic systems have the features with which can make them more suitable for digital secure communications, then, a method based on state observer hyperchaotic program is designed and verified by numerical simulation of the correctness and chaotic synchronization effectiveness.
Secondly, three chaotic synchronization methods used for secure communication are in depth study, namely, chaotic masking, chaotic parameter modulation, chaotic shift keying and chaotic spread-spectrum theoretical analysis. A state observer based on chaotic masking method program is designed, through numerical simulation, the effectiveness of the program is demonstrated. Because the traditional chaotic masking technology has some shortcomings, a hyperchaotic observer-based synchronization secure communication scheme is designed, from theoretical analysis and numerical simulation results, we can get that it is an effective secure communication scheme, and has higher confidentiality.
本论文对超混沌同步及其在保密通信中的应用进行了深入研究,主要内容如下:
首先,系统地论述了混沌同步及其应用的研究现状,重点研究了驱动-响应混沌同步、基于反馈方法的混沌同步和基于状态观测器方法的混沌同步,采用这三种方法设计了三种同步方案,并对三种方案进行数值仿真分析,可以看到基于状态观测器方法的混沌同步方案具有一定的优越性。超混沌系统的特性使其更适合应用于数字保密通信领域,接下来,设计了一种基于状态观测器方法的超混沌同步方案,并通过数值仿真验证了该方案的正确性及实现混沌同步的有效性。
其次,对混沌掩盖、混沌参数调制、混沌键控和混沌扩频进行理论分析,设计了一种基于状态观测器方法的混沌掩盖方案,通过数值仿真,验证了该方案的有效性。并针对传统的混沌掩盖技术存在的不足,设计了一种基于状态观测器的超混沌同步保密通信方案,通过理论推导及数值仿真实验得出,这是一种有效的保密通信方案,且保密性较高。
Chaos is a quasi-stochastic phenomenon appearing possibly in definite nonlinear dynamic systems. Chotic motion is a complex nonlinear motion and the chaotic phenomenon has been observed in a lot of real systems.The dynamic properties of chaos signal such as ergodicity, aperiodic, uncorrelated, broadband and noise-like have been proved to be useful for secure communication. The chaotic synchronization is the theory basis of secure communication.The research of the chaotic synchronization and its application becomes a new research focus in nonlinear science fields.
The main content of this paper contains the analysis of hyperchaotic synchronization and application of hyperchaotic secure communication. In this dissertation, the main contributions are as follows:
Firstly, the application of chaotic synchronization and its current situation is described systematiclly, then three chaotic synchronization schemes are designed with three different methods, which are the drive-response chaotic synchronization, the synchronization method based on feedback and the observer-based synchronization method. Then make numerical simulations with the three schemes, from the results, we can see that the observer-based chaotic synchronization method has more advantages than the others. Hyperchaotic systems have the features with which can make them more suitable for digital secure communications, then, a method based on state observer hyperchaotic program is designed and verified by numerical simulation of the correctness and chaotic synchronization effectiveness.
Secondly, three chaotic synchronization methods used for secure communication are in depth study, namely, chaotic masking, chaotic parameter modulation, chaotic shift keying and chaotic spread-spectrum theoretical analysis. A state observer based on chaotic masking method program is designed, through numerical simulation, the effectiveness of the program is demonstrated. Because the traditional chaotic masking technology has some shortcomings, a hyperchaotic observer-based synchronization secure communication scheme is designed, from theoretical analysis and numerical simulation results, we can get that it is an effective secure communication scheme, and has higher confidentiality.
引文
1王兴元.复杂非线性系统中的混沌.北京:电子工业出版社, 2003: 59-83
2郝柏林.分岔、混沌、奇怪吸引子及其他.物理学进展, 1983, 3(3): 329-416
3巩华荣,官玉彬,唐昌建.微波管中离子张弛振荡的混沌现象.物理学报, 2008, 54(1): 159-163
4 M.S.Baptista, E.E.Macau, C.Grebogi. Integrated Chaos-Based Communication. Acta Astrpmaitica, 2006, 54: 153-157
5郝柏林.从抛物线谈起——混沌动力学引论.上海:上海科技教育出版社, 1993: 126-178
6 E.N.Lorenz. Deterministic Non-Periodic Flows. Atoms Sci, 1963, 20: 130-141
7黄润生.混沌及其应用.武汉:武汉大学出版社, 2000: 94-157
8 T.Y.Li, J.A.Yorke. Period Three Implies Chaos. America Math Month, 1975, 82: 985-992
9 R.M.May. Simple Mathematical Models with Very Complicated Dynamics. Nature, 1976, 261: 459-467
10 M.J.Feigenbaum. Quantitative Universality for A Class of Nonlinear Transformations. Stat Phys, 1978, 19(1): 25-52
11刘建东.变型蔡氏电路中混沌控制的实验研究.物理实验, 2007, 25(3): 7-10
12 M.P.Keneedy. Three Steps to Chaos-Part2: A Chua’s Circuit Primer. IEEE Trans. CAS, 1993, 40(10): 657-674
13 H.Dedieu, M.P.Keneedy, M.Hasler. Chaos Shift Keying: Modulation and Demodulation of A Chaotic Carrier Using Self-Synchronizing Chua’s Circuits. IEEE Trans. CAS, 1993, 40(10): 634-642
14 P.Arena. An Integrated Chua’s Cell for the Implementation of A Chua’s Array. Bifuration and Chuas, 2007, 14(1): 93-105
15 L. M. Pecora, T. L. Carroll. Synchronization in Chaotic Systems. Phys. Rev. Lett, 1990,64: 821-823
16孙克辉,高冬花,张泰山.混沌系统同步控制方法研究进展.桂林电子工学院学报, 2008, 24(1): 21-24
17刘国刚,赵怡.参数不确定混沌系统的自适应同步控制.电路与系统学报, 2007, 10(1): 24-27
18齐冬莲,魏金岭,赵光宙.基于系统辨识的自适应混沌同步控制研究.控制与决策, 2001, 16(1): 120-122
19 Anil Maybhate, R.E.Amritkar. Use of Synchronization and Adaptive Control in Parameter Estimation from A Time Series, Physical Review Letters, 1999, 59(1): 284-292
20 Moez Feki. An Adaptive Chaos Synchronization Scheme Applied to Secure Communication. Chaos, Solitons and Fractals, 2006, 18: 141-148
21兰祝刚,彭巍,丘水生.混沌同步方法的研究.通信技术, 2000, 1: 28-31
22赵辽英.混沌同步控制及其在保密通信中的应用.杭州电子工业学院学报, 2003, 23(1): 20-23
23 Ju H. Park. Adaptive Synchronization of Rossler System with Uncertain Parameters. Chaos, Solitons and Fractals, 2008, 25(2): 325-331
24姚明海.混沌控制的研究进展和展望.浙江工业大学学报, 2001, 29(4): 332-336
25赵耿,方锦清.现代信息安全与混沌保密通信应用研究的进展.物理学进展, 2003, 23(2): 212-256
26 G.Y.He. Synchronous Chaos in the Coupled System of Two Logistic Maps. Chaos, Solitons and Fractals, 2008, 23: 909-913
27关新平,范正平,陈彩莲.混沌控制及其在保密通信中的应用.北京:国防工业出版社, 2002: 159-251
28吴祥兴.混沌学导论.上海:上海科学技术文献出版社, 1996: 25-48
29 H.Fujisaka, T.Yamada. Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. Porg Theor Phys, 1983, 69: 32-47
30杨涛,邵惠鹤.一类混沌系统的同步方法. 2006, 51(4): 742-748
31李丽香.混沌同步和参数辨识及其在保密通信中的应用.物理学报, 2003, 32(5):79-84
32 X.S.Yang. A Framework for Synchronization Theory. Chaos, Solitons and Fractals, 2006, 11: 1365-1368
33 J.W.Shuai. Dominique.M.D. Phase Synchronization in Two Coupled Chaotic Neurons. Phys.Lett.A, 2005, 264: 289-297
34 L.Q.Zhu, Y.C.Lai. Experimental Observation of Generalized Time-Lagged Chaotic Synchronization. Phys.Rev.E, 2008, 64: 145-161
35王燕舞.混沌同步的控制与应用研究.计算机应用与研究, 2007, 31(7): 63-75
36强浩.混沌同步及其在保密通信中的应用.计算机工程, 2006, 26(6): 98-113
37王光瑞,于熙玲,陈式刚.混沌的控制、同步与利用.北京:国防工业出版社, 2001: 86-153
38 O.Morgul, E.Solak. Observer Based Synchronization of Chaotic Systems. Phys.Rev.E, 1996, 54(5): 4803-4811
39 H. Nijmeijer, I. M. Ymareels. An Observer Looks at Synchronization. IEEE Trans. Circuit Sys. Syst.Ι: Fundam Theory. Appl, 1997, 44(10): 882-890
40高铁杠,陈增强,袁著祉.基于观测器的混沌系统的同步研究.物理学报, 2006, 53(5): 1305-1308
41 Richter H. The Generalized Hénon Maps: Examples for Higher-Dimensional Chaos. International Journal of Bifurcation and Chaos, 2002, 12(6): 1371-1381
42王国红,段小虎.基于变形蔡氏电路的混沌掩盖保密通信研究.空军工程大学学报, 2005, 6(4): 49-51
43韩建群,朱义胜.一种提高调频差分混沌移相键控调制传输效率方法.电子学报, 2005, 33(6): 1032-1035
44张涛,刘宗才,刘佩田.利用相移键控实现混沌通信.量子学报, 2006, 19(4): 334-336
45王冬光,刘文.一种差分混沌键控通信方案的研究.哈尔滨工程大学学报, 2006, 25 (3): 375-379
46李建芬,李农,林辉.适合传输快变信息信号的混沌调制保密通信.物理学报, 2007, 53 (6): 1694-1698
47兀旦晖,宋玲芳.一种基于两级混沌调制保密通信方案的研究.陕西科技大学学报, 2006, 24(3): 104-109
48王亥,胡建栋.数字混沌扩频通信系统.北京邮电大学学报, 2008, 21(4): 7-11
49凌聪,孙松庚.用于CDMA的四相混沌扩频序列.通信学报, 2008, 19(3): 40-44
50 T.Yang, L.O.Chua. Secure Communication via Chaotic Parameter Modulation. IEEE Trans on CAS(I), 1996, 43(9): 817-819
51 K.S.Halle, C.W.Wu, M.Itoh. Spread Spectrum Communication through Modulation of Chaos. International Journal of Bifuration and Chaos. 1993, 3(2):469-477
52 Stinson DR. Cryptography: Theory and Practice. CRC Press, 1995: 258-349
53浦晨岚,李为相,林锦国.一种混沌同步系统及其在保密通信中的应用.科技通报, 2006, 22(6): 841-845
54赵新彦,曹国雄,朱双鹤.数字混沌保密通信的发展及前景.电子工程, 2005, 20(4): 27-31
55 Li G-H, Zhou S-P. An Observer-Based Anti-Synchronization. Chaos, Solitons & Fractals 2006, 31(29): 495-498
56于茜,李春萍,冯秀琴.基于两级混沌同步保密通信方案的设计.物理实验, 2009, 44(11): 159-174
57刘凌,苏燕辰,刘崇新.一个新混沌系统及其电路仿真实验.物理学报, 2006, 38(8): 18-26
58江浩,褚衍东.超混沌Liu系统的同步研究.南通大学学报, 2008, 51(2): 35-46
59潘凯.非线性动力系统及复杂网络的混沌同步研究.通信学报, 2008, 54(6): 147-165
60周平.一类三维连续混沌系统观测器.物理学报, 2006, 21(5): 58-74
2郝柏林.分岔、混沌、奇怪吸引子及其他.物理学进展, 1983, 3(3): 329-416
3巩华荣,官玉彬,唐昌建.微波管中离子张弛振荡的混沌现象.物理学报, 2008, 54(1): 159-163
4 M.S.Baptista, E.E.Macau, C.Grebogi. Integrated Chaos-Based Communication. Acta Astrpmaitica, 2006, 54: 153-157
5郝柏林.从抛物线谈起——混沌动力学引论.上海:上海科技教育出版社, 1993: 126-178
6 E.N.Lorenz. Deterministic Non-Periodic Flows. Atoms Sci, 1963, 20: 130-141
7黄润生.混沌及其应用.武汉:武汉大学出版社, 2000: 94-157
8 T.Y.Li, J.A.Yorke. Period Three Implies Chaos. America Math Month, 1975, 82: 985-992
9 R.M.May. Simple Mathematical Models with Very Complicated Dynamics. Nature, 1976, 261: 459-467
10 M.J.Feigenbaum. Quantitative Universality for A Class of Nonlinear Transformations. Stat Phys, 1978, 19(1): 25-52
11刘建东.变型蔡氏电路中混沌控制的实验研究.物理实验, 2007, 25(3): 7-10
12 M.P.Keneedy. Three Steps to Chaos-Part2: A Chua’s Circuit Primer. IEEE Trans. CAS, 1993, 40(10): 657-674
13 H.Dedieu, M.P.Keneedy, M.Hasler. Chaos Shift Keying: Modulation and Demodulation of A Chaotic Carrier Using Self-Synchronizing Chua’s Circuits. IEEE Trans. CAS, 1993, 40(10): 634-642
14 P.Arena. An Integrated Chua’s Cell for the Implementation of A Chua’s Array. Bifuration and Chuas, 2007, 14(1): 93-105
15 L. M. Pecora, T. L. Carroll. Synchronization in Chaotic Systems. Phys. Rev. Lett, 1990,64: 821-823
16孙克辉,高冬花,张泰山.混沌系统同步控制方法研究进展.桂林电子工学院学报, 2008, 24(1): 21-24
17刘国刚,赵怡.参数不确定混沌系统的自适应同步控制.电路与系统学报, 2007, 10(1): 24-27
18齐冬莲,魏金岭,赵光宙.基于系统辨识的自适应混沌同步控制研究.控制与决策, 2001, 16(1): 120-122
19 Anil Maybhate, R.E.Amritkar. Use of Synchronization and Adaptive Control in Parameter Estimation from A Time Series, Physical Review Letters, 1999, 59(1): 284-292
20 Moez Feki. An Adaptive Chaos Synchronization Scheme Applied to Secure Communication. Chaos, Solitons and Fractals, 2006, 18: 141-148
21兰祝刚,彭巍,丘水生.混沌同步方法的研究.通信技术, 2000, 1: 28-31
22赵辽英.混沌同步控制及其在保密通信中的应用.杭州电子工业学院学报, 2003, 23(1): 20-23
23 Ju H. Park. Adaptive Synchronization of Rossler System with Uncertain Parameters. Chaos, Solitons and Fractals, 2008, 25(2): 325-331
24姚明海.混沌控制的研究进展和展望.浙江工业大学学报, 2001, 29(4): 332-336
25赵耿,方锦清.现代信息安全与混沌保密通信应用研究的进展.物理学进展, 2003, 23(2): 212-256
26 G.Y.He. Synchronous Chaos in the Coupled System of Two Logistic Maps. Chaos, Solitons and Fractals, 2008, 23: 909-913
27关新平,范正平,陈彩莲.混沌控制及其在保密通信中的应用.北京:国防工业出版社, 2002: 159-251
28吴祥兴.混沌学导论.上海:上海科学技术文献出版社, 1996: 25-48
29 H.Fujisaka, T.Yamada. Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. Porg Theor Phys, 1983, 69: 32-47
30杨涛,邵惠鹤.一类混沌系统的同步方法. 2006, 51(4): 742-748
31李丽香.混沌同步和参数辨识及其在保密通信中的应用.物理学报, 2003, 32(5):79-84
32 X.S.Yang. A Framework for Synchronization Theory. Chaos, Solitons and Fractals, 2006, 11: 1365-1368
33 J.W.Shuai. Dominique.M.D. Phase Synchronization in Two Coupled Chaotic Neurons. Phys.Lett.A, 2005, 264: 289-297
34 L.Q.Zhu, Y.C.Lai. Experimental Observation of Generalized Time-Lagged Chaotic Synchronization. Phys.Rev.E, 2008, 64: 145-161
35王燕舞.混沌同步的控制与应用研究.计算机应用与研究, 2007, 31(7): 63-75
36强浩.混沌同步及其在保密通信中的应用.计算机工程, 2006, 26(6): 98-113
37王光瑞,于熙玲,陈式刚.混沌的控制、同步与利用.北京:国防工业出版社, 2001: 86-153
38 O.Morgul, E.Solak. Observer Based Synchronization of Chaotic Systems. Phys.Rev.E, 1996, 54(5): 4803-4811
39 H. Nijmeijer, I. M. Ymareels. An Observer Looks at Synchronization. IEEE Trans. Circuit Sys. Syst.Ι: Fundam Theory. Appl, 1997, 44(10): 882-890
40高铁杠,陈增强,袁著祉.基于观测器的混沌系统的同步研究.物理学报, 2006, 53(5): 1305-1308
41 Richter H. The Generalized Hénon Maps: Examples for Higher-Dimensional Chaos. International Journal of Bifurcation and Chaos, 2002, 12(6): 1371-1381
42王国红,段小虎.基于变形蔡氏电路的混沌掩盖保密通信研究.空军工程大学学报, 2005, 6(4): 49-51
43韩建群,朱义胜.一种提高调频差分混沌移相键控调制传输效率方法.电子学报, 2005, 33(6): 1032-1035
44张涛,刘宗才,刘佩田.利用相移键控实现混沌通信.量子学报, 2006, 19(4): 334-336
45王冬光,刘文.一种差分混沌键控通信方案的研究.哈尔滨工程大学学报, 2006, 25 (3): 375-379
46李建芬,李农,林辉.适合传输快变信息信号的混沌调制保密通信.物理学报, 2007, 53 (6): 1694-1698
47兀旦晖,宋玲芳.一种基于两级混沌调制保密通信方案的研究.陕西科技大学学报, 2006, 24(3): 104-109
48王亥,胡建栋.数字混沌扩频通信系统.北京邮电大学学报, 2008, 21(4): 7-11
49凌聪,孙松庚.用于CDMA的四相混沌扩频序列.通信学报, 2008, 19(3): 40-44
50 T.Yang, L.O.Chua. Secure Communication via Chaotic Parameter Modulation. IEEE Trans on CAS(I), 1996, 43(9): 817-819
51 K.S.Halle, C.W.Wu, M.Itoh. Spread Spectrum Communication through Modulation of Chaos. International Journal of Bifuration and Chaos. 1993, 3(2):469-477
52 Stinson DR. Cryptography: Theory and Practice. CRC Press, 1995: 258-349
53浦晨岚,李为相,林锦国.一种混沌同步系统及其在保密通信中的应用.科技通报, 2006, 22(6): 841-845
54赵新彦,曹国雄,朱双鹤.数字混沌保密通信的发展及前景.电子工程, 2005, 20(4): 27-31
55 Li G-H, Zhou S-P. An Observer-Based Anti-Synchronization. Chaos, Solitons & Fractals 2006, 31(29): 495-498
56于茜,李春萍,冯秀琴.基于两级混沌同步保密通信方案的设计.物理实验, 2009, 44(11): 159-174
57刘凌,苏燕辰,刘崇新.一个新混沌系统及其电路仿真实验.物理学报, 2006, 38(8): 18-26
58江浩,褚衍东.超混沌Liu系统的同步研究.南通大学学报, 2008, 51(2): 35-46
59潘凯.非线性动力系统及复杂网络的混沌同步研究.通信学报, 2008, 54(6): 147-165
60周平.一类三维连续混沌系统观测器.物理学报, 2006, 21(5): 58-74