多媒體應用影響了我們生活中許多方面，所以多媒體數據安全已經變成了一個很重要的議題。為了保護日益增長的多媒體數據，數據加密技術一直不斷的發展至今。
本文基於三維度Lorenz渾沌系統，重新設計出一個新四維度Lorenz渾沌系統。並且應用Matlab分析此新渾沌系統的特性。其中包含了二維相圖、三維相圖、平衡點分析、散度分析、功率頻譜密度分析及Lyapunov指數圖。之後藉由電路模擬軟體Multisim模擬此新渾沌系統，模擬無誤後我們將此系統的實際電路實現在麵包板上與模擬結果做比較。
在控制理論部分，我們設計順滑控制、積分順滑控制和適應性積分順滑控制三種控制器完成新四維度Lorenz渾沌系統同步並比較之間差異。之後對此系統做離散化和離散化同步並實現在現場可程式化閘陣列平台上。
最後藉由此渾沌系統特性對即時影片作安全加密演算法，且利用同步控制在FPGA上進行即時影片解密演算法。在這項研究中，我們將渾沌主系統轉成數位訊號，進而對即時影片加密，並利用同步後的從系統對即時影片進行解密。

Because multimedia applications affect many aspects of our life, multimedia data security is becoming an important problem. To protect the increasing use of multimedia, security technologies are being developed.
Based on the 3D Lorenz chaotic system, we redesign and produce the New 4D Lorenz chaotic system. And we apply the Matlab to analyze the new chaotic system’s properties which include 2D phase portraits, 3D phase portraits, equilibrium analysis, divergence analysis, power spectral density analysis and Lyapunov exponent diagrams. Then we simulate the new chaotic system by electronic circuit simulation software named Multisim. If the simulation is correct, we establish the real circuit on the breadboard and compare the result with simulation.
In the part of control theory, we use sliding mode control, integral sliding mode control and adaptive integral sliding mode control to implement the New 4D Lorenz chaotic system’s synchronization and compare the three kinds of controllers’ difference. After that, we discretize the new system and synchronize it. Therefore, we can implement on the FPGA platform.
Finally, we use the chaotic system’s property to implement real-time video secure encryption algorithm. Besides that, utilizing the synchronization of control for the real-time video decryption algorithm on FPGA. In this study, we convert the master and synchronized slave system to digital signals. The master system is used for real-time video encryption and the slave one is used for decrypting real-time video.

[1]L. D. Iasemidis and J. C. Sackellares, “REVIEW : Chaos Theory and Epilepsy,” SAGE Journals, vol. 2, no. 2, pp. 118-126, Mar 1996.
[2]M. Alshammari, M. Pavlovic and B. A. AL Qaied, “Chaos Theory in Strategy Research,” American Journal of Business and Management, vol. 5, no. 1, pp. 11-13, 2016.
[3]A. Nayfeh, Applied nonlinear dynamics. New York: Wiley, ISBN: 978-0-471-59348-5, 1995.
[4]G. Chen, X. Dong, From chaos to order: methodologies, perspectives and applications. Singapore: World Scientific, ISBN: 978-981-02-2569-8, 1998.
[5]E. N. Lorenz, “Deterministic non-periodic flows,” Journal of the atmospheric sciences, vol. 20, no. 2, pp. 130-141, Jan. 1963.
[6]J. C. Roux, R. H. Simoyi and H. L. Swinney, “Observation of a strange attractor,” Physica D: Nonlinear Phenomena, vol. 8, no. 1-2, pp. 257-266 Jul.1983.
[7]R. C. Hilborn, “Sea gulls, butterflies, and grasshoppers: A brief history of the butterfly effect in nonlinear dynamics,” American Journal of Physics, vol. 72, no. 425, Mar. 2004.
[8]J. Blackledge and N. Ptitsyn, “Encryption using Deterministic Chaos,” ISAST Transactions on Electronics and Signal Processing, vol. 4, no. 1, pp 6-17. Jan. 2011.
[9]G. Alvarez, “Some basic cryptographic requirements for chaos-based cryptosystems,” International Journal of Bifurcation and Chaos, vol. 16, no. 8, Aug. 2006.
[10]M. L. Barakat, A. S. Mansingka, A. G. Radwan and K. N. Salama, “Hardware stream cipher with controllable chaos generator for colour image encryption,” IET Image Processing, vol. 8, no. 1, pp. 33-43, 2014.
[11]M. A. Mohamed, M. E. Abou-Elsoud and W. M. K. El-din, “Hardware Implementation of Multimedia Encryption Techniques Using FPGA,” International Journal of Computer Science Issues, vol. 9, no 3, Mar. 2012.
[12]Z. Lin, S. Yu, J. Lü, S. Cai and G. Chen, “Design and ARM-Embedded Implementation of a Chaotic Map-Based Real-Time Secure Video Communication System,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 25, no. 7, pp. 1203-1216, Jul. 2015.
[13] R. Dogaru, I. Dogaru and H. Kim, “Chaotic Scan: A Low Complexity Video Transmission System for Efficiently Sending Relevant Image Features,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 20, no. 2, Feb. 2010.
[14]M. S. Azzaz, C. Tanougast, S. Sadoudi, A. Bouridane and A. Dandache, “An FPGA Implementation of a Feed-Back Chaotic Synchronization for Secure Communications,” Communication Systems Networks and Digital Signal Processing, pp. 239-243, 2010.
[15]A. J. Menezes, P.C. Van-Oorschot and S.A. Vanstone, Handbook of Applied Cryptography, 4th edition. Canada: CRC Press, ISBN: 9780849385230, 2010.
[16]R. A. Mollin, An Introduction to Cryptography, 4th edition. CRC Press, ISBN: 1584881275, 2006.
[17]M. Ciampa, Security+ Guide to Network Security Fundamentals, 4th edition. Course Technology, ISBN: 9781111640125, 2008.
[18]F. Harold and M. Krause, Information Security Management Handbook, 6th Edition. Auerbach Publications, ISBN: 9780849374951, 2007.
[19]M. Usama, M. K. Khan, K. Alghathbar and C. Lee “Chaos-Based Symmetric Key Cryptosystems,” Computers & Mathematics with Applications, vol. 60, no. 2,pp. 326-337, Jul. 2010.
[20]Y. Jeon, Y, Kim and J. Kim, “Implementation of a Video Streaming Security System for Smart Device,” IEEE International Conference on Consumer Electronics (ICCE), pp. 97-100, 2014.
[21]M. S. Azzaz, C. Tanougast, S. Sadoudi, A. Bouridane and A. Dandache, ”FPGA implementation of new Real-time Image Encryption based switching chaotic systems ,” Signals and Systems Conference, pp. 1-6, 2009.
[22] H. Kezia and G. F. Sudha, “Encryption of Digital Video Based on Lorenz Chaotic System,” Advanced Computing and Communications, 2008. ADCOM 2008. 16th International Conference, pp. 40-45, 2008.
[23]S. Sadoudi1, C. Tanougast, M. S. Azzaz1 and A. Dandache, “Design and FPGA implementation of a wireless hyperchaotic communication system for secure real-time image transmission,” EURASIP Journal on Image and Video Processing, Dec. 2013.
[24]B. Schneier, Applied Cryptography: Protocols, Algorithms, and Source Code in C. New York: John Wiley & Sons, Inc, ISBN:0471597562, 1993.
[25]X. Yi, C, H. Tan, C. K. Slew and M. R. Syed, “Fast encryption for multimedia,” IEEE Transactions on Consumer Electronics, vol. 47, no.1, pp. 101-107, 2001.
[26]C. Shen, S. Yu, J. Lü and G. Chen, “A Systematic Methodology for Constructing Hyperchaotic Systems With Multiple Positive Lyapunov Exponents and Circuit Implementation,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 61, no. 3 pp. 854-864, 2014.
[27]J. Lin, C. F. Huang, T. L. Liao and J. J. Yan, “Design and implementation of digital secure communication based on synchronized chaotic systems,” Digital Signal Processing, vol. 20, no. 1, pp 229-237 Jan. 2010.
[28]G. Millerioux, J. M. Amigo and J. Daafouz, ”Improving the security of a dynamic look-up table based chaotic cryptosystem,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 53, no. 6 pp. 502-506, 2006.
[29]N. Masuda; G. Jakimoski, K. Aihara and L. Kocarev, “Chaotic block ciphers: from theory to practical algorithms,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 53, no.6 pp. 1341-1352,2006.
[30]C. Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. Springer, ISBN: 978-0-387-90775-8.
[31]A. Hirose and H. Onishi, “Observation of positive Lyapunov exponent induced by gain increase of neuron nonlinearity in complex-valued associative memories,” Electronics Letters, vol. 32, no.8, pp. 745-746, 1996.
[32]M. Haeri and A. A. Emadzadeh, “Synchronizing different chaotic systems using active sliding mode control,” Chaos, Solitons & Fractals, vol. 31, no. 1, pp.119-129 Jan 2007.
[33] X. Guowei, W. Zhenkai and L. Chunqing, “Synchronization of Lorenz System Based on Fast Stabilization Sliding Mode Control,” Mathematical Problems in Engineering, 2015.
[34]M. Yahyazadeh, A. R. Noei and R. Ghaderi, “Synchronization of chaotic systems with known and unknown parameters using a modified active sliding mode control,” ISA Transactions, vol. 50, no. 2, pp.262-267, Apr. 2011.
[35]M. M. E. Dessoky, M.T. Yassen and E.S. Aly, “Bifurcation analysis and chaos control in Shimizu–Morioka chaotic system with delayed feedback Applied,” Mathematics and Computation, vol. 243, no. 15,pp. 283-297, Sep. 2014.
[36]Z. M. Ge and C. H. Yang, “Chaos synchronization and chaotization of complex chaotic systems in series form by optimal control,” Chaos, Solitons and Fractals, vol. 42, no. 2, pp. 994–1002, 2009.
[37]H. T. Yau and J. J. Van, “Design of sliding mode controller for Lorenz chaotic system with nonlinear input,” Chaos, Solitons and Fractals, vol. 19, pp. 891-898, 2004 .
[38]W. Ligang and W. Changhong, “Adaptive fuzzy sliding mode control of Lorenz chaotic system,” Front Electr Electron Eng, vol. 2, no. 3, pp. 277-281, 2007.
[39]L. Wu, H. Gao, “Sliding mode control of two dimentional systems in rossler model,” IET Control Theory and Applications, vol. 2, no. 4, pp.352-364, 2008.
[40]M. Yahyazadeh, A. R. Noe and R. Ghaderi, ”Synchronization of chaotic systems with known and unknown parameters using a modified active sliding mode control,” ISA Transactions, vol. 50, no. 2,pp. 262-267, Apr 2011.
[41]X. Zhang, H. Su, L. Xiao, and J. Chu, “Robust sliding mode control based on integral sliding surfaces,” Proceedings of the American Control Conference (ACC’05), pp. 4074-4077, Jun. 2005.
[42]F. Castanos and L. Fridman, “Analysis and design of integral sliding manifolds for systems with unmatched perturbations,” IEEE Transactions on Automatic Control, vol. 51, no. 5, pp. 853-858, 2006.
[43]T. T. V. Cao, L. Chen, F. He and K. Sammut, “Adaptive integral sliding mode control for active vibration absorber design Decision and Control,” Proceedings of the 39th IEEE Conference, vol. 3, pp. 2436-2437, 2000.
[44]S. Vaidyanathan, “adaptive controller and synchronizer design for hyperchaotic Zhou system with unknown parameters,” International Journal of Information Technology Modeling and Computing, vol.1, No.1, Feb. 2013.
[45]H. R. Karimi, M. Zapateiro and N. Luo, “Adaptive synchronization of master-slave systems with mixed neutral and discrete time-delays and nonlinear perturbations,” Asian Journal of Control, vol. 14, no. 1, pp. 251-257, 2012.
[46]M. M. Arefi and M. R. Jahed-Motlagh, “Adaptive robust synchronization of Rossler systems in the presence of unknown matched time-varying parameters,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 12, pp. 4149–4157, 2010.
[47]Y. Toopchi and J. Wang, “Chaos Synchronization of Hyperchaotic Zhou System by Adaptive Integral Sliding Mode Control,” Computing Communication Control and Automation (ICCUBEA) International Conference, pp. 73-77, 2015.
[48]I. Koyuncu, A. T. Ozcerit and I. Pehlivan, “Implementation of FPGA-based real time novel chaotic oscillator,” Nonlinear Dynamics, vol.77, pp. 49-59, 2014.
[49]T. Matsumoto, “Chaos in electronic circuits,” IEEE Inst. of Elec.and Elecs Eng, vol.75, no.8, pp. 1033-1046, Aug.1987.
[50]M. I. Sobhy, M. A. Aseeri and A. E. R. Shehata, “Real Time Implementation Of Continuous (Chua And Lorenz) Chaotic Generator Models Using Digital Hardware,” Proc. of the Third International Symposium on Communication Systems Networks and Digital Processing, pp.38-41, 1999.
[51]M.A. Aseeri, M.I. Sobhi and P. Lee, “Lorenz Chaotic Model Using Field Programmable Gate Array (FPGA),” Midwest Symposium on Circuit and Systems, pp. 686–699, 2002.
[52]H. Xue and W. B. LI, “Implementation of Chaos Synchronization on FPGA,” Advances in Information Sciences & Service Sciences, vol. 4, no. 6, pp. 42, Apr 2012.
[53]R. Karthikeyan, A. Prasina, R. Babu and S. Raghavendran, “FPGA Implementation of Novel Synchronization Methodology for a New Chaotic System,” Indian Journal of Science and Technology, vol. 8, no. 11, June 2015.
[54]R. Rameshbabu, R. Karthikeyan, R. Balamurali, A. Prasina, “FPGA Implementation of Adaptive Complete Synchronization Methodology for Novel Chaotic Systems Middle-East,” Journal of Scientific Research (Sensing, Signal Processing and Security), vol. 23, pp.36-44, 2015.
[55]Q. Zhang, W. Li and Q. Ding, “Discrete Design of Lorenz Chaotic System Based on Euler Method and Image Encryption,” 2015 Third International Conference on Robot, Vision and Signal Processing (RVSP) pp. 176-179, 2015.
[56]X. Li and S. Qian, “Controlling Unstable Discrete Chaos and Hyperchaos Systems,” Applied Mathematics, vol.4, pp.1-6, 2013.
[57]Z.Wang, Y. Liu, G.Wei, andX. Liu, “Anote on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances,” Automatica, vol. 46, no. 3, pp. 543-548, 2010.
[58]S. K. Spurgeon, “Hyperplane design techniques for discte-time variable structure control system,” Int. J. of Control, vol.55, no.2, pp. 445-456, 1992.
[59]S. T. Sarpturk, Y. Istefanopolos and O. Kaynak, “On the stability of Discrete-Time Sliding Mode Control,” IEEE Trans. On Automatic Control, vol. 32, no.1, pp. 930-932, Oct. 1987.
[60]A. Bartoszewicz, “Discrete time quasi-sliding-mode-control strategies,” IEEE Trans. On Industrial Electronics, vol. 45, pp. 633-637, 1998.
[61]B. Bandyopadhyay, Discrete-time Sliding Mode Control: A Multirate Output Feedback Approach. New York: Springer, 2006.
[62]K. Abidi, J. X. Xu, and J. H. She “A Discrete-Time Termina Sliding-Mode Control Approach Applied to a Motion Control Problem,” IEEE Trans. On Industrial Electronics, vol. 56, no. 9, Sep. 2009.
[63]Mentor Graphics, “Modelsim SE User’s Manuel, Sofware, Version 6.4,” Mentor Graphics, 2008.
[64]B. Zhang and M. Kahn, “Simulation of optical XOR encryption using MATLAB” 7th AFRICON Conference, vol. 2, pp. 995-1000, 2004.
[65]P. K. Shukla, A. Khare, M. A. Rizvi, S. Stalin and S. Kumar, “Applied Cryptography Using Chaos Function for Fast Digital Logic-Based Systems in Ubiquitous Computing,” Entropy, vol. 17, no.3, pp.1387-1410, 2015.
[66] S. Sadoudi1 and C. Tanougast , “Robust hyperchaotic synchronization via analog transmission line,” The European Physical Journal Special Topics, vol. 225, no. 1, pp. 119-126,Feb 2016.
[67]H. Ma, Y. Wang and G. Li, “Implementation of Audio Data Packet Encryption Synchronization Circuit,” Advances in Intelligent Systems and Computing, vol. 298, pp. 321-329.
[68]H. M. D. Kabir and S. B. Alam, “Hardware based real time, fast and highly secured speech communication using FPGA,” Information Theory and Information Security (ICITIS) IEEE International Conference, pp. 452-457, 2010.
[69]Y. Luo, S. Yu and J. Liu, “Design and Implementation of Image Chaotic Communication via FPGA Embedded Ethernet Transmission,” Chaos-Fractals Theories and Applications, IWCFTA. International Workshop, pp.148-152, 2009.
[70]W. Li, Q. Zhang and Q. Ding, “Digital Encryption Method Based on Lorenz Continuous Chaotic System,” Fifth International Conference on Instrumentation and Measurement, Computer, Communication and Control (IMCCC), pp.262-266, 2015.
[71]Qurban A. Memon, “A New Approach to Video Security over Networks,” International Journal of Computer Applications in Technology, vol. 25, no. 1, pp. 72-83, 2006.
[72]M. I. Sobhy and A. R. Shehata, "Chaotic algorithms for data encryption,” Proceedings of 2001 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’01), vol.2, pp. 997-1000, 2001.
[73] P. Tseng, Y. Chang, Y. Huang, H. Fang, C. Huang and L. Chen, “Advances in hardware architectures for image and video coding—a survey,” Proceedings of the IEEE, vol. 93, no. 1, pp. 184–197, 2005.
[74] C. E. Shannon, “Communication theory of secrecy systems,” The Bell System Technical Journal, vol. 28, no.4, pp. 656-715, 1949.
[75] J. Wen and M. Severa, W. Zeng and M. H. Luttrell, “A format-compliant configurable encryption framework for access control of video,” IEEE Transactions on Circuits and Systems for Video Technology Year, vol. 12,no. 6, pp. 545-557, 2002.
[76] F. Dufaux and T. Ebrahimi, “Scrambling for privacy protection in video surveillance systems,” IEEE Transactions on Circuits and Systems for Video Technology Year, vol. 18, no. 8, pp. 1168-1174, 2008.
[77] Y. Zhang and Z. Liu, “A chaos-based image encryption ASIC using reconfigurable logic,” IEEE Asia Pacific Conference, pp. 1782-1785, 2008.
[78]L. Kocarev, K. Halle, K. Eckert, and L. Chua, “Experimental demonstration of secure communication via chaotic synchronization,” Int. J. Bifur. Chaos, vol. 2, pp. 709-713, Sep. 1992.
[79]M. S. Azzaz, C. Tanougast, S. Sadoudi and A. Dandache, “Realtime FPGA implementation of Lorenz’s chaotic generator for ciphering telecommunications,” IEEE Internation Circuits and Systems and TAISA Conference, pp. 1-4, 2009.
[80]J. Lu, X. Wu and J. L, “Synchronization of a unified chaotic system and the application in secure communication,” Physics Letters A, vol. 305, pp. 365-370, 2002.