混沌密码及其在多媒体保密通信中应用的进展

doi:10.11999/JEIT151356

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Abstract

This paper reviews the past situation and existing problems in chaotic cipher theories and applications, and reports the recent progress of some issues on theoretical design and hardware implementation of ciphers based on high-dimensional chaos system, including basic theory, design methods, typical applications, and ideas coping with the problems. In the aspect of design of chaotic cipher and its security evaluation, the following progress is summarized: counteracting dynamics degradation of digital chaotic systems with anti-control methods; designing no-degeneration chaotic systems in digital domain; proposing a multi-round chaotic stream cipher with the high-dimensional digital chaotic systems and feedback mechanism of self-loop; evaluating security level of the proposed chaotic ciphers with various methods. In the aspect of application and hardware implementation of multimedia secure communication, the following developments are reported: optimizing a cross platform conducting real-time remote chaotic secure communication, targeting different application businesses of hand-held devices, such as smartphone, computer, ARM, FPGA; and establishing a demonstration platform on chaotic secure communications to verify the effectiveness.

Key words： No-degeneration high-dimensional chaotic cipher Multimedia secure communications Chaos anti- control Security evaluation Hardware implementation

Received: 01 December 2015 Published: 26 January 2016

PACS:	TN918.7
	O415.5

Fund:

The National Natural Science Foundation of China (61532020)

Corresponding Authors: YU Simin E-mail: siminyu@163.com

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	YU Simin
	Lü Jinhu
	LI Chengqing

Cite this article:

YU Simin,Lü Jinhu,LI Chengqing. Some Progresses of Chaotic Cipher and Its Applications in Multimedia Secure Communications[J]. JEIT, 2016, 38(3): 735-752.

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http://jeit.ie.ac.cn/EN/10.11999/JEIT151356 OR http://jeit.ie.ac.cn/EN/Y2016/V38/I3/735

[1]	陈关荣, 吕金虎. Lorenz系统族的动力学分析、控制与同步[M]. 北京: 科学出版社, 2003: 9-32.
	CHEN Guanrong and Jinhu. Dynamics Analysis, Control and Synchronization of Lorenz System Family[M]. Beijing: Science Press, 2003: 9-32.
[2]	吕金虎, 陆君安, 陈士华. 混沌时间序列分析及其应用[M]. 武汉: 武汉大学出版社, 2002: 11-56.
	Jinhu, LU Junan, and CHEN Shihua. Chaotic Time Series Analysis and Its Application[M]. Wuhan: Wuhan University Press, 2002: 11-56.
[3]	廖晓峰, 肖迪, 陈勇, 等. 混沌密码学原理及其应用[M]. 北京: 科学出版社, 2009: 232-263.
	LIAO Xiaofeng, XIAO Di, CHEN Yong, et al. Principle and Application of Chaos-based Cryptography[M]. Beijing: Science Press, 2009: 232-263.
[4]	王兴元. 复杂非线性系统中的混沌[M]. 北京: 电子工业出版社, 2003: 1-14.
	WANG Xingyuan. Chaos in Complex Nonlinear Systems[M]. Beijing: Publishing House of Electronics Industry, 2003: 1-14.
[5]	王兴元. 混沌系统的同步及在保密通信中的应用[M]. 北京: 科学出版社, 2012: 25-41.
	WANG Xingyuan. Synchronization of Chaotic Systems and Its Application in Secure Communications[M]. Beijing: Science Press, 2012: 25-41.
[6]	朱从旭, 胡玉平, 孙克辉. 基于超混沌系统和密文交错扩散的图像加密新算法[J]. 电子与信息学报, 2012, 34(7): 1735-1743. doi: 10.3724/SP.J.1146.2011.01004.
	ZHU Congxu, HU Yuping, and SUN Kehui. New image encryption algorithm based on hyperchaotic system and ciphertext diffusion in crisscross pattern[J]. Journal of Electronics & Information Technology, 2012, 34(7): 1735-1743. doi: 10.3724/SP.J.1146.2011.01004.
[7]	刘泉, 李佩玥, 章明朝, 等. 基于可Markov分割混沌系统的图像加密算法[J]. 电子与信息学报, 2014, 36(6): 1271-1277. doi: 10.3724/SP.J.1146.2013.01246.
	LIU Quan, LI Peiyue, ZHANG Mingchao, et al. Image encryption algorithm based on chaos system having Markov portion[J]. Journal of Electronics & Information Technology, 2014, 36(6): 1271-1277. doi: 10.3724/SP.J.1146.2013.01246.
[8]	邓晓衡, 廖春龙, 朱从旭, 等. 像素位置与比特双重置乱的图像混沌加密算法[J]. 通信学报, 2014, 35(3): 216-223. doi: 10.3969/j.issn.1000-436x.2014.03.025.
	DENG Xiaoheng, LIAO Chunlong, ZHU Congxu, et al. Image encryption algorithms based on chaos through dual scrambling of pixel position and bit[J]. Journal on Communications, 2014, 35(3): 216-223. doi: 10.3969/j.issn. 1000-436x.2014.03.025.
[9]	张顺, 高铁杠. 基于类 DNA 编码分组与替换的加密方案[J]. 电子与信息学报, 2015, 37(1): 150-157. doi: 10.11999/ JEIT140091.
	ZHANG Shun and GAO Tiegang. Encryption based on DNA coding codon grouping and substitution[J]. Journal of Electronics & Information Technology, 2015, 37(1): 150-157. doi: 10.11999/JEIT140091.
[10]	文昌辞, 王沁, 黄付敏, 等. 基于仿射和复合混沌的图像自适应加密算法[J]. 通信学报, 2012, 33(11): 119-127. doi: 10.3969/j.issn.1000-436x.2012.11.015.
	WEN Changci, WANG Qin, HUANG Fumin, et al. Self- adaptive encryption algorithm for image based on affine and composed chaos[J]. Journal on Communications, 2012, 33(11): 119-127. doi: 10.3969/j.issn.1000-436x.2012.11.015.
[11]	陈铁明, 葛亮. 面向无线传感器网络的混沌加密与消息鉴别算法[J]. 通信学报, 2013, 5: 012. doi: 10.3969/j.issn.1000- 436x.2013.05.013.
	CHEN Tieming and GE Liang. Chaos-based encryption and message authentication algorithm for wireless sensor network [J]. Journal on Communications, 2013, 34(5): 113-120. doi: 10.3969/ j.issn.1000-436x.2013.05.013.
[12]	谭良, 吴波, 刘震, 等. 一种基于混沌和小波变换的大容量音频信息隐藏算法[J]. 电子学报, 2010, 38(8): 1812-1818.
	TAN Liang, WU Bo, LIU Zhen, et al. An audio information hiding algorithm with high-capacity which based on chaotic and wavelet transform[J]. Acta Electronica Sinica, 2010, 38(8): 1812-1818.
[13]	郭建胜, 张锋. 一种图像加密算法的等效密钥攻击方案[J]. 电子学报, 2010, 38(4): 781-785.
	GUO Jiansheng and ZHANG Feng. An equivalent key attack on an image cryptosystem[J]. Acta Electronica Sinica, 2010, 38(4): 781-785.
[14]	葛辛, 刘粉林, 芦斌, 等. 基于搜索机制混沌加密算法的密文特性分析[J]. 电子与信息学报, 2008, 30(7): 1625-1629.
	GE Xin, LIU Fenlin, LU Bin, et al. Analysis for the cipherext characteristic of based on search mechanism chaotic cryptosystem[J]. Journal of Electronics & Information Technology, 2008, 30(7): 1625-1629.
[15]	杨吉云, 廖晓峰, 肖迪, 等. 对一种基于logistic 映射的分组加密机制的分析和改进[J]. 通信学报, 2008, 29(12): 86-90.
	YANG Jiyun, LIAO Xiaofeng, XIAO Di, et al. Cryptanalysis and improvement of a block cryptographic scheme based on logistic map[J]. Journal on Communications, 2008, 29(12): 86-90.
[16]	SCHARINGER J. Fast encryption of image data using chaotic Kolmogorov flows[J]. Journal of Electronic Imaging, 1998, 7(2): 318-325.
[17]	FRIDRICH J. Symmetric ciphers based on two-dimensional chaotic maps[J]. International Journal of Bifurcation and Chaos, 1998, 8(6): 1259-1284.
[18]	BAPTISTA M S. Cryptography with chaos[J]. Physics Letters A, 1998, 240(1/2): 50-54.
[19]	PISARCHIK A N, FLORES-CARMONA N J, and CARPIO-VALADEZ M. Encryption and decryption of images with chaotic map lattices[J]. Chaos, 2006, 16(3): 033118.
[20]	胡汉平, 刘双红, 王祖喜, 等. 一种混沌密钥流产生方法[J]. 计算机学报, 2004, 27(3): 408-412. doi: 10.3321/j.issn: 0254-4164.2004.03.019.
	HU Hanping, LIU Shuanghong, WANG Zuxi, et al. A method for generating chaotic key stream[J]. Chinese Journal of Computers, 2004, 27(3): 408-412. doi: 10.3321/j.issn: 0254-4164.2004.03.019.
[21]	CHEN G, MAO Y, and CHUI C. A symmetric image encryption scheme based on 3D chaotic cat maps[J]. Chaos Solitons & Fractals, 2004, 21(3): 749-761.
[22]	PAREEK N, et al. Image encryption using chaotic logistic map[J]. Image and Vision Computing, 2006, 24(9): 926-934.
[23]	BOSE R. Novel public key encryption technique based on multiple chaotic systems[J]. Physical Review Letters, 2005, 95: 098702.
[24]	CHEN Y and LIAO X. Cryptanalysis on a modified Baptista-type cryptosystem with chaotic masking algorithm [J]. Physics Letters A, 2005, 342(5/6): 389-396.
[25]	SHEN Chaowen, YU Simin, LÜ Jinhu, et al. A systematic methodology for constructing hyperchaotic systems with multiple positive Lyapunov exponents and circuit implementation[J]. IEEE Transactions on Circuits and Systems-I: Regular Papers, 2014, 61(3): 854-864.
[26]	SHEN Chaowen, YU Simin, LÜ Jinhu, et al. Designing hyperchaotic systems with any desired number of positive Lyapunov exponents via a simple model[J]. IEEE Transactions on Circuits and Systems-I: Regular Papers, 2014, 61(8): 2380-2389.
[27]	SHEN Chaowen, YU Simin, LÜ Jinhu, et al. Constructing hyperchaotic systems at will[J]. International Journal of Circuit Theory and Applications, 2015, 43(12): 2039-2056.
[28]	GAN Qiuye, YU Simin, LI Chengqing, et al. Design and ARM-embedded implementation of a chaotic map-based multicast scheme for multiuser speech wireless communication[J]. Submitted to IEEE Transactions on Circuits and Systems for Video Technology, 2015.
[29]	LIN Zhuosheng, YU Simin, LÜ Jinhu, et al. Design and ARM-embedded implementation of a chaotic map-based real-time secure video communication system[J]. IEEE Transactions on Circuits and Systems for Video Technology, 2015, 25(7): 1203-1216.
[30]	ZHENG Hanzhong, YU Simin, and XU Xiangqian. A systematic methodology for multi-images encryption and decryption based on single chaotic system and FPGA embedded implementation[J]. Mathematical Problems in Engineering, 2014: 698608-1-698608-15.
[31]	CHEN Shikun, YU Simin, LÜ Jinhu, et al. Theoretical design and FPGA-based implementation of real-time chaos-based video encryption-decryption communication systems[J]. Submitted to IEEE Transactions on Circuits and Systems for Video Technology, 2016.
[32]	ZHENG Hanzhong, YU Simin, and LÜ Jinhu. Design and ARM platform-based realization of digital color image encryption and decryption via single state varible feedback control[J]. International Journal of Bifurcation and Chaos, 2014, 24(4): 1450049-1-1450049-11.
[33]	YU Simin, Jinhu, and CHEN Guanrong. Demostratioin and hardware realization of multimedia chaotic secure communications[OL]. http://www.ee.cityu.edu.hk/~gchen/ VideoCrypt.htm. 2014.5.
[34]	方锦清. 混沌通信及其相关网络信息安全研究的若干进展[J]. 系统工程学报, 2010: 25(6): 725-741.
	FANG Jinqing. Several advances in chaos-based communication and research of information security associated with networks[J]. Journal of Systems Engineering, 2010: 25(6): 725-741.
[35]	BOURBAKIS N and ALEXOPOULOS C. Picture data encryption using scan patterns[J]. Pattern Recognition, 1992, 25(6): 567-581.
[36]	LI Shujun, LI Chengqing, CHEN Guanrong, et al. A general quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks[J]. Signal Processing: Image Communication, 2008, 23(3): 212-223.
[37]	LI Chengqing and LO K T. Optimal quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks[J]. Signal Processing, 2011, 91(4): 949-954.
[38]	ARROYO D, RHOUMA R, ALVAREZ G, et al. On the security of a new image encryption scheme based on chaotic map lattices[J]. Chaos, 2008, 18(3): 033112-1-033112-8.
[39]	SOLAK E andÇOKAL C. Algebraic break of image ciphers based on discretized chaotic map lattices[J]. Information Sciences, 2011, 181(1): 227-233.
[40]	WANG Kai, PEI Wenjiang, ZOU Liuhua, et al. On the security of 3D Cat map based symmetric image encryption scheme[J]. Physics Letters A, 2005, 343(6): 432-439.
[41]	LI Chengqing and CHEN Guanrong. On the security of a class of image encryption schemes[C]. Proceeding of IEEE International Symposium on Circuits and Systems, Seattle, 2008: 3290-3293.
[42]	SOLAK Ercan,ÇOKAL Cahit, YILDIZ Olcaytaner, et al. Cryptanalysis of Fridrich’s chaotic image encryption[J]. International Journal of Bifurcation and Chaos, 2010, 20(5): 1405-1413.
[43]	LI Chengqing, LI Shujun, ASIM Muhammad, et al. On the security defects of an image encryption scheme[J]. Image and Vision Computing, 2009, 27(9): 1371-1381.
[44]	FRANZ M. Comment on ‘Novel public key encryption technique based on multiple chaotic systems’[J]. Physical Review Letters, 2006, 96(6): 069401-1-069401-5.
[45]	WANG Kai, PEI Wenjiang, ZOU Liuhua, et al. Security of public key encryption technique based on multiple chaotic systems[J]. Physics Letters A, 2006, 360(2): 259-262.
[46]	李树钧. 数字化混沌密码的分析与设计[D]. [博士论文], 西安交通大学, 2003.
	LI Shujun. Analyses and new designs of digital chaotic ciphers[D]. [Ph.D. dissertation], Xi’an Jiaotong University, 2003.
[47]	ALVAREZ G and LI Shujun. Some basic cryptographic requirements for chaos-based cryptosystems[J]. International Journal of Bifurcation and Chaos, 2006, 16(8): 2129-2151.
[48]	KOCAREV L. Chaos-based cryptography: a brief overview[J]. IEEE Circuits and Systems Magazine, 2001, 1(3): 6-21.
[49]	SOLAK E. Partial identification of Lorenz system and its application to key space reduction of chaotic cryptosystems [J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2004, 51(10): 557-560.
[50]	金晨辉, 杨阳. 对自同步混沌密码的分割攻击方法[J]. 电子学报, 2006, 34(7): 1337-1341. doi: 10.3321/j.issn:0372-2112. 2006.07.031.
	JIN Chenhui and YANG Yang. A divide-and-conquer attack on self-synchronous chaotic ciphers[J]. Acta Electronica Sinica, 2006, 34(7): 1337-1341. doi: 10.3321/j.issn:0372-2112. 2006.07.031.
[51]	ZHU Zhiliang, ZHANG Wei, WONG Kwokwo, et al. A chaos-based symmetric image encryption scheme using a bit-level permutation[J]. Information Sciences, 2011, 181(6): 1171-1186.
[52]	BHATNAGAR G and WU Q M J. Chaos-based security solution for fingerprint data during communication and transmission[J]. IEEE Transactions on Instrumentation and Measurement, 2012, 61(4): 876-887.
[53]	KWOK H S and TANG W K S. A fast image encryption system based on chaotic maps with finite precision representation[J]. Chaos, Solitons & Fractals, 2007, 32(4): 1518-1529.
[54]	RÖSSLER O E. An equation for hyperchaos[J]. Physics Letters A, 1979, 71A(2/3): 155-157.
[55]	MATSUMOTO T, CHUA L O, and KOBAYASHI K. Hyperchaos: laboratory experiment and numerical confirmation[J]. IEEE Transactions on Circuits and Systems, 1986, 33(11): 1143-1147.
[56]	RECH P and ALBUQUERQUE H A. A hyperchaotic Chua system[J]. International Journal of Bifurcation and Chaos, 2009, 19(11): 3823-3828.
[57]	BARBOZA R. Dynamics of a hyperchaotic Lorenz system[J]. International Journal of Bifurcation and Chaos, 2007, 17(12): 4285-4294.
[58]	HU Guosi. Generating hyperchaotic attractors with three positive Lyapunov exponents via state feedback control[J]. International Journal of Bifurcation and Chaos, 2009, 19(2): 651-660.
[59]	LI Yuxiang, CHEN Guanrong, and TANG W K S. Controlling a unified chaotic system to hyperchaotic[J]. IEEE Transactions on Circuits and Systems-II: Express Briefs, 2005, 52(4): 204-207.
[60]	WANG Xingyuan and WANG Mingjun. A hyperchaos generated from Lorenz system[J]. Physica A, 2008, 387(14): 3751-3758.
[61]	CHEN Aimin, LU Junan, LÜ Jinhu, et al. Generating hyperchaotic Lü attractor via state feedback control[J]. Physica A, 2006, 364: 103-110.
[62]	KAPITANIAK T, CHUA L O, and ZHONG G Q. Experimental hyperchaos in coupled Chua’s circuits[J]. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 1994, 41(7): 499-503.
[63]	CANNAS B and CINCOTTI S. Hyper chaotic behaviour of two bi-directionally coupled Chua’s circuits[J]. International Journal of Circuit Theory and Applications, 2002, 30(6): 625-637.
[64]	CAFAGNA D and GRASSI G. Hyperchaotic coupled Chua circuits: An approach for generating new n×m-scroll attractors[J]. International Journal of Bifurcation and Chaos, 2003, 13(9): 2537-2550.
[65]	CAFAGNA D and GRASSI G. Decomposition method for studying smooth Chua’s equation with application to hyperchaotic multiscroll attractors[J]. International Journal of Bifurcation and Chaos, 2007, 17(1): 209-226.
[66]	THAMILMARAN K, LAKSHMANAN M, and VENKATESAN A. Hyperchaos in a modified canonical Chua’s circuit[J]. International Journal of Bifurcation and Chaos, 2004, 14(1): 221-243.
[67]	LI Yuxia, TANG W K S, and CHEN Guanrong. Hyperchaotic evolved from the generalized Lorenz system[J]. International Journal of Circuit Theory and Applications, 2005, 33(4): 235-251.
[68]	WANG Jiezhi, CHEN Zengqiang, CHEN Guanrong, et al. A novel hyperchaotic system and its complex dynamics[J]. International Journal of Bifurcation and Chaos, 2008, 18(11): 3309-3324.
[69]	陈关荣, 汪小帆. 动力系统的混沌化理论、方法与应用[M]. 上海: 上海交通大学出版社, 2006: 1-49.
	CHEN Guanrong and WANG Xiaofan. Chaotification of Dynamical Systems: Theory, Methods and Applications [M]. Shanghai: Shanghai Jiao Tong University Press, 2006: 1-49.
[70]	禹思敏, 吕金虎, 陈关荣. 动力系统反控制方法及其应用[M]. 北京: 科学出版社, 2013: 270-324.
	YU Simin, Jinhu, and CHEN Guanrong. Anti-control Method of Dynamical Systems and Its Applications[M]. Beijing: Science Press, 2013: 270-324.
[71]	禹思敏. 新型混沌电路与系统的设计原理及其应用[M]. 北京: 科学出版社, 2016: 35-71.
	YU Simin. Design Principle of New Chaotic Circuits and Systems and Its Applications[M]. Beijing: Science Press, 2016: 35-71.
[72]	YU Simin and CHEN Guanrong. Anti-control of continuous- time dynamical systems[J]. Communications in Nonlinear Science and Numerical Simulation, 2012, 17(6): 2617-2627.
[73]	YU Simin and CHEN Guanrong. Chaotifying continuous- time nonlinear autonomous systems[J]. International Journal of Bifurcation and Chaos, 2012, 22(9): 1250232-1-1250232-17.
[74]	LIU Ling, WU Xiaogang, and HU Hanping. Estimating system parameters of Chua’s circuit from synchronizing signal[J]. Physics Letters A, 2004, 324(1): 36-41.
[75]	盛利元, 贾伟尧. 一个截断误差诱导下的随机数字振荡系统[J]. 物理学报, 2005, 54(12): 5574-5580.
	SHENG Liyuan and JIA Weiyao. A stochastic digital oscillating system induced by the truncation error[J]. Acta Physica Sinica, 2005, 54(12): 5574-5580.
[76]	WHEELER D and MATTHEWS R. Supercomputer investigations of a chaotic encryption algorithm[J]. Cryptologia, 1991, 15(2): 140-151.
[77]	HEIDARI B G and MCGILLEM C D. A chaotic direct- sequence spread-spectrum communication system[J]. IEEE Transactions on Communication, 1994, 42(2): 1524-1527.
[78]	CERNÁK J. Digital generators of chaos[J]. Physics Letters A, 1996, 214(3): 151-160.
[79]	王相生, 甘骏人. 一种基于混沌的序列密码生成方法[J]. 计算机学报, 2002, 25(4): 351-356. doi: 10.3321/j.issn:0254-4164. 2002.04.003.
	WANG Xiangsheng and GAN Junren. A chaotic sequence encryption method[J]. Chinese Journal of Computers, 2002, 25(4): 351-356. doi: 10.3321/j.issn:0254-4164.2002.04.003.
[80]	HU Hanping, DENG Yashuang, and LIU Lingfeng. Counteracting the dynamical degradation of digital chaos via hybrid control[J]. Communications in Nonlinear Science and Numerical Simulation, 2014, 19(6): 1970-1984.
[81]	DENG Yashuang, HU Hanping, et al. Analysis and design of digital chaotic systems with desirable performance via feedback control[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2015, 45(8): 1187-1200.
[82]	GUYEUX C and BAHI J M. Topological chaos and chaotic iterations application to hash functions[C]. IEEE International Joint Conference on Neural Networks, Barcelona, 2010: 1-7.
[83]	BAHI J M and GUYEUX C. Discrete Dynamical Systems and Chaotic Machines Theory and Applications[M]. Boca Raton: CRC Press, Taylor & Francis Group, 2013: 47-70.
[84]	BAHI J M, FANG Xiaole, GUYEUX C, et al. Suitability of chaotic iterations schemes using XOR shift for security applications[J]. Journal of Network and Computer Applications, 2014, 37(1): 282-292.
[85]	WANG Qianxue, YU Simin, GUYEUX C, et al. Theoretical design and circuit implementation of integer domain chaotic systems[J]. International Journal of Bifurcation and Chaos, 2014, 24(10): 1450128-1-1450128-10.
[86]	WANG Qianxue, YU Simin, GUYEUX C, et al. Study on a new chaotic bitwise dynamical system and its FPGA implementation[J]. Chinese Physics B, 2015, 24(6): 060503-1-060503-8.
[87]	WANG Qianxue, YU Simin, LI Chengqing, et al. Theoretical design and FPGA-based implementation of higher- dimensional digital chaotic systems[J]. IEEE Transactions on Circuits and Systems-I: Regular Papers, arXiv: 1509.04469, 2016.
[88]	禹思敏. 混沌系统与混沌电路原理、设计及其在通信中的应用[M]. 西安: 西安电子科技大学出版社, 2011: 313-334.
	YU Simin. Chaotic Systems and Chaotic Circuits: Principle, Design and Its Application in Communications[M]. Xi,an: Xidian University Press, 2011: 313-334.
[89]	YU Simin, LÜ Jinhu, LEUNG H, et al. Design and implementation of n-scroll chaotic attractors from a general Jerk circuit[J]. IEEE Transactions on Circuits and Systems-I: Regular Papers, 2005, 52(7): 1459-1476.
[90]	LÜ Jinhu, YU Simin, LEUNG H, et al. Experimental verification of multidirectional multiscroll chaotic attractors [J]. IEEE Transactions on Circuits and Systems-I: Regular Papers, 2006, 53(1): 149-165.
[91]	YU Simin, LÜ Jinhu, and CHEN Guanrong. Theoretical design and circuit implementation of multi-directional multi-torus chaotic attractors[J]. IEEE Transactions on Circuits and Systems-I: Regular Papers, 2007, 54(9): 2087-2098.
[92]	YU Simin, TANG W K S, LÜ Jinhu, et al. Generation of n m-wing Lorenz-like attractors from a modified Shimizu- Morioka model[J]. IEEE Transactions on Circuits and Systems-I: Regular Papers, 2008, 55(11): 1168-1172.
[93]	YU Simin, LÜJinhu, CHEN Guanrong, et al. Design and implementation of grid multi-wing butterfly chaotic attractors from a piecewise Lorenz system[J]. IEEE Transactions on Circuits and Systems-I: Regular Papers, 2010, 57(10): 803-807.
[94]	YU Simin, LÜ Jinhu, CHEN Guanrong, et al. Generating grid multi-wing chaotic attractors by constructing heteroclinic loops into switching systems[J]. IEEE Transactions on Circuits and Systems-I: Regular Papers, 2011, 58(5): 314-318.
[95]	YU Simin, LÜ Jinhu, CHEN Guanrong, et al. Design and implementation of grid multiwing hyperchaotic Lorenz system family via switching control and constructing super- heteroclinic loops[J]. IEEE Transactions on Circuits and Systems-I: Regular Papers, 2012, 59(5): 1015-1028.
[96]	CALLEGARI S, ROVATTI R, and SETTI G. First direct implementation of a true random source on programmable hardware[J]. International Journal of Circuit Theory and Applications, 2005, 33(1): 1-16.
[97]	RECAI KILIC. Universal programmable chaos generator: design and implementation issues[J]. International Journal of Bifurcation and Chaos, 2010, 20(2): 419-435.
[98]	SCHLOTTMANN C R and HASLER J. High-level modeling of analog computational elements for signal processing applications[J]. IEEE Transactions on Very Large Scale Integration Systems, 2014, 22(9): 1945-1953.
[99]	SANTO B and KURTHS J. Chaos and cryptography: A new dimension in secure communications[J]. European Physical Journal Special Topics, 2014, 223(8): 1441-1445.
[100]	CHOU Haogong, CHUANG Chunfu, WANG Wenjune, et al. A fuzzy-model-based chaotic synchronization and its implementation on a secure communication system[J]. IEEE Transactions on Information Forensics and Security, 2013, 8(12): 2177-2185.
[101]	BARAKAT M L, MANSINGKA A S, RADWAN A G, et al. Hardware stream cipher with controllable chaos generator for colour image encryption[J]. IET Image Processing, 2014, 8(1): 33-43.
[102]	AZZAZ M S, TANOUGASTB C, SADOUDI S, et al. Synchronized hybrid chaotic generators: Application to real-time wireless speech encryption[J]. Communications in Nonlinear Science and Numerical Simulation, 2013, 18(8): 2035-2047.
[103]	ANNOVAZZI L V, BENEDETTI M, MERLO S, et al. Optical chaos masking of video signals[J]. IEEE Photonics Technology Letters, 2005, 17(9): 1995-1997.
[104]	SADOUDI S, TANOUGAST C, AZZAZ M S, et al. Design and FPGA implementation of a wireless hyperchaotic communication system for secure real-time image transmission[J]. EURASIP Journal on Image and Video Processing, 2013, 2013(43): 1-18.
[105]	BLAYA A B and LOPEZ V J. On the relations between positive Lyapunov exponents, positive entropy, and sensitivity for interval maps[J]. Discrete and Continuous Dynamical Systems, 2012, 32(2): 433-466.
[106]	TERMONIA Y. Kolmogorov entropy from a time series[J]. Physical Review A, 1984, 29(3): 1612-1614.
[107]	EPSTEIN M, HARS L, KRASINSKI R, et al. Design and implementation of a true random number generator based on digital circuit artifacts[J]. Lecture Notes in Computer Science, 2003, 2779: 152-165.
[108]	SUNAR B, MARTIN W, and STINSON D. A provably secure true random number generator with built-in tolerance to active attacks[J]. IEEE Transactions on Computers, 2007, 56(1): 109-119.
[109]	BANKS J, BROOKS J, CAIRNS G, et al. On Devaney's definition of chaos[J]. The American Mathematical Monthly, 1992, 99(4): 332-334.
[110]	KOCAREV L and LIAN S. Chaos-based Cryptography Theory, Algorithms and Applications[M]. Berlin Heidelberg Springer-Verlag, 2011: 67-98.