臺灣博碩士論文加值系統

在本論文中，我們設計一種基於四維混沌系統生成金鑰及改進進階加密標準的影像加密演算法，並以Altera FPGA DE10-Standard實現整個加密與傳輸系統，利用FPGA的流水線與平行運算特性對其演算法優化。
首先，利用相圖分析、平衡點分析與李亞普諾夫指數對渾沌系統的特性進行驗證。經驗證後的混沌系統當作金鑰產生器，用於加密演算法中。在改進的進階加密標準中，以旋轉排序和立方替換盒修改了列移位與位元組替換，並減少加密循環次數。接下來我們將加密演算法和有線圖像傳輸系統實現到基於ARM的SoC-FPGA，HPS軟體運行在Linux上，用於控制FPGA加密演算法與影像傳輸。當影像加密完成後，使用Socket傳輸到接收端，進行影像解密並透過VGA端口即時顯示。
在加密安全性分析中，我們進行直方圖分析、相關性係數分析、差異性分析和熵值分析，其中，熵值分析包含全局與區域性。從加密安全性分析的結果表明，所提出的圖像加密演算法是安全有效的。

In this thesis, we design an image encryption algorithm based on four-dimensional chaotic system to generate key and improve advanced encryption standard, and implement the encryption and transmission system with Altera FPGA DE10-Standard. The encryption algorithm is optimized by using the pipeline and parallel computing features of FPGA.
First, the phase portraits analysis, equilibrium point analysis and Lyapunov exponent are used to verify the characteristics of the chaotic system. The verified chaotic system is used as a key generator for the encryption algorithm. In the improved advanced encryption standard, ShiftRows and SubByres are modified with Spin-Sort and Cubic S-Box, and the round of encryption is reduced. Next, we implement the encryption algorithm and the wired image transmission system to the ARM-based SoC-FPGA. The HPS software runs on Linux and is used to control the FPGA encryption algorithm and image transmission. After complete image encryption, use Socket to transmit to the receive side. Then decrypt the image and display it instantly through the VGA port.
In the analysis of cryptographic security, we perform histogram analysis, correlation coefficient analysis, difference analysis and entropy analysis. The entropy analysis includes global and local. The results from the encryption security analysis show that the proposed image encryption algorithm is safe and effective.

摘要 i
Abstract iii
誌謝 iiiii
CONTENTS iv
List of Figure vii
List of Table xii
Chapter 1 Introduction 1
1.1 Background 1
1.2 Motivation and Objectives 1
1.3 Literature Review 2
1.4 Outline 3
Chapter 2 Design Encryption Algorithm 5
2.1 Chaotic System 5
2.1.1 Description of the system 5
2.1.2 Phase Portraits 5
2.1.3 Equilibrium Analysis 7
2.1.4 Lyapunov Exponent Analysis 9
2.2 Fundamental Principles of AES 12
2.3 Fundamental Principles of breadth-first search 14
2.4 Fundamental of Cubic S-box 17
2.5 Key Generator Design 20
2.6 Purpose of new chaotic encryption algorithm 21
2.6.1 AddRoundKey 21
2.6.2 Cubic S-Box replace SubBytes 25
2.6.3 Spin-Sort replace ShiftRows 25
2.6.4 MixColumns 29
2.6.5 Diversion of pixel 31
2.7 Process of decryption algorithm 32
2.6.1 Inverse Cubic S-Box 32
2.6.2 Inverse Spin-Sort 33
2.6.1 Inverse MixColumns 34
2.8 Flow chart of encryption and decryption 35
Chapter 3 FPGA Implementation 38
3.1 Development environment 38
3.1.1 FPGA 38
3.1.2 DE10-Standard 39
3.1.3 Intel Quartus Prime 40
3.1.4 SignalTap II Logic Analyzer 41
3.2 Euler's method for FPGA chaotic system implementation 42
3.2.1 IEEE Standard for Floating-Point Arithmetic 42
3.2.2 Chaos System Discretization 43
3.2.3 Chaotic Generator Implementation 43
3.2.4 Chaotic Generator Verification 47
3.3 HPS and Communication 50
3.3.1 Internal communication between HPS and FPGA 50
3.3.2 Wired communication between two DE10-Standard boards 52
3.4 Encryption System Hardware Implementation 54
3.4.1 SDRAM access 54
3.4.2 Encryption system 56
3.5 Demonstration 58
Chapter 4 Security Analysis 61
4.1 Histogram Analysis 61
4.2 Correlation Analysis 66
4.3 Differential Attack Analysis 82
4.4 Information Entropy Analysis 85
Chapter 5 Conclusion 88
5.1 Conclusion 88
5.2 Future Work 89
Reference 90

[1] Wu J, Liao X and Yang B. (2017). Color image encryption based on chaotic systems and elliptic curve ElGamal scheme. Signal Processing, 141: 109-124.
[2] J.M. Amigó, L. Kocarev and J. Szczepanski. (2007). Theory and practice of chaotic cryptography. Physics Letters A, 366: 211-216.
[3] Jakimoski G and Kocarev L. (2001). Chaos and cryptography: block encryption ciphers based on chaotic maps. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 48(2): 163-169.
[4] Matthews, R. (1989). On the Derivation of a “Chaotic” Encryption Algorithm. Cryptologia, 13(1): 29-42.
[5] Fridrich J. (1998). Symmetric ciphers based on two–dimensional chaotic maps. International Journal of Bifurcation and Chaos, 8(6): 1259-1284.
[6] Fabio Pareschi, Gianluca Setti and Riccardo Rovatti. (2010). Implementation and testing of high-Speed CMOS true random number generators based on chaotic systems. IEEE Transactions on Circuits and Systems-I: Regular Papers, 57(12): 3124-3137.
[7] Fatih Özkaynak. (2014). Cryptographically secure random number generator with chaotic additional input. Nonlinear Dynamics, 78(3): 2015-2020.
[8] J. C. Yen and J. I. Guo. (2000). Efficient hierarchical chaotic image encryption algorithm and its VLSI realisation, IEE Proceedings - Vision Image and Signal Processing, 147(2): 167-175.
[9] Shannon, C. E. (1949). Communication theory of secrecy systems. Bell Labs Technical Journal, 28(4): 656-715.
[10] Cao, C., Sun, K. and Liu, W. (2018). A Novel Bit-Level Image Encryption Algorithm Based on 2D-LICM Hyperchaotic Map. Signal Processing, 143: 122-133.
[11] Qi Yin and Chunhua Wang. (2018). A New Chaotic Image Encryption Scheme Using Breadth-First Search and Dynamic Diffusion. International Journal of Bifurcation and Chaos, 28(4): 1850047.
[12] Yong Zhang. (2018). The unified image encryption algorithm based on chaos and cubic S-Box. Information Sciences, 450: 361-377.
[13] Xingyuan Wang, Yuanyuan Zhao, Huili Zhang and Kang Guo. (2016). A novel color image encryption scheme using alternate chaotic mapping structure. Optics and Lasers in Engineering, 82: 79-86.
[14] Benyamin Norouzi and Sattar Mirzakuchaki. (2014). A fast color image encryption algorithm based on hyper-chaotic systems. Nonlinear Dynamics, 78(2): 995-1015.
[15] Boriga, R., Dăscălescu, A. C., and Priescu, I. (2014). A new hyperchaotic map and its application in an image encryption scheme. Signal Processing: Image Communication, 29(8): 887-901.
[16] Yue Wu, Yicong Zhou, George Saveriades, Sos Agaian, Joseph P. Noonan and Premkumar Natarajan. (2013). Local Shannon entropy measure with statistical tests for image randomness. Information Sciences, 222: 323-342.
[17] V. Rijmen, and J. Daemen. (2001). Advanced encryption standard. Proceedings of Federal Information Processing Standards Publications, National Institute of Standards and Technology: 19-22,
[18] Mrinal K. Mandal, Madhumita Kar, Sandesh K. Singh and Vivek K. Barnwal. (2013). Symmetric key image encryption using chaotic Rossler system. Security and Communication Networks, 7(11): 2145-2152
[19] Jeyamala Chandrasekaran, B. Subramanyan, and Raman Selvanayagam. (2011). A Chaos Based Approach for Improving Non Linearity in S Box Design of Symmetric Key Cryptosystems. Advances in Networks and Communications: 516-522.
[20] K. SunSun. (2016). Chaotic Secure Communication: Principles and Technologies. De Gruyter Gruyter.
[21] Pak, C. and Huang, L. (2017) A New Color Image Encryption Using Combination of the 1D Chaotic Map. Signal Processing, 138: 129-137.
[22] Xiaolin Wu, Bin Zhu, Yutong Hu and Yamei Ran. (2017). A novel colour image encryption scheme using rectangular transform-enhanced chaotic tent maps. IEEE Access, 1-1.
[23] Xingyuan Wang and Hui-li Zhang. (2015). A color image encryption with heterogeneous bit-permutation and correlated chaos. Optics Communications, 342: 51-60.
[24] Abolfazl Yaghouti Niyat, Mohammad Hossein Moattar and Masood Niazi Torshiz. (2017). Color image encryption based on hybrid hyper-chaotic system and cellular automata. Optics and Lasers in Engineering, 90: 225-237.
[25] Wu, Y., Noonan, J. P. and Agaian, S. (2011). NPCR and UACI randomness tests for image encryption. Cyber journals: multidisciplinary journals in science and technology, Journal of Selected Areas in Telecommunications (JSAT), 1(2): 31-38.
[26] Radu Boriga, Ana Cristina Dăscălescu, Iustin Priescu. (2014). A new hyperchaotic map and its application in an image encryption scheme. Signal Processing: Image Communication, 29(8): 887-901.
[27] Yue Wu, Yicong Zhou, George Saveriades, Sos Agaian, Joseph P. Noonan and Premkumar Natarajan. (2013). Local Shannon entropy measure with statistical tests for image randomness. Information Sciences, 222: 323-342.
[28] Cheng-Hsiung Yang, Hou-Cheng Wu and Shun-Feng Su (2019). Implementation of Encryption Algorithm and Wireless Image Transmission System on FPGA. IEEE Access, 7, 50513-50523.
[29] Xing-Yuan Wang, Ying-Qian Zhang and Xue-Mei Bao. (2015). A Colour Image Encryption Scheme Using Permutation-Substitution Based on Chaos. Entropy, 17: 3877-3897.
[30] Copyright © Terasic Inc. (2017) DE10-Standard_User_manual. Retrieved from https://www.intel.com/content/dam/altera-www/global/en_US/portal/dsn/42/doc-us-dsnbk-42-5505271707235-de10-standard-user-manual-sm.pdf
[31] Gaurav Bhatnagar and Q. M. Jonathan Wu (2014). Biometric Inspired Multimedia Encryption Based on Dual Parameter Fractional Fourier Transform. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 44(9): 1234-1247.
[32] Younan Zhao, Wei Zhang, Housheng Su and Junqi Yang (2018). Observer-Based Synchronization of Chaotic Systems Satisfying Incremental Quadratic Constraints and Its Application in Secure Communication. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 1-12.
[33] Weiguo Sheng, Shengyong Chen, Gang Xiao, Jiafa Mao and Yujun Zheng. (2015). A Biometric Key Generation Method Based on Semisupervised Data Clustering. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 45(9): 1205-1217.
[34] Dong Yue and Qing-Long Han. (2019). Guest Editorial Special Issue on New Trends in Energy Internet: Artificial Intelligence-Based Control, Network Security, and Management. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49(8): 1251-1253.
[35] Manju Khari, Aditya Kumar Garg, Amir H. Gandomi, Rashmi Gupta, Rizwan Patan and Balamurugan Balusamy. (2019). Securing Data in Internet of Things (IoT) Using Cryptography and Steganography Techniques. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 1-8.
[36] Xingyuan Wang, Yutao Hou, Shibing Wang and Rui Li. (2018). A new image encryption algorithm based on CML and DNA sequence. IEEE Access, 6, 62272-62285.
[37] Xiaoqiang Zhang and Xuesong Wang. (2018). Digital Image Encryption Algorithm Based on Elliptic Curve Public Cryptosystem. IEEE Access, 6, 70025-70034.
[38] Ahmed A. Abd El-Latif, Bassem Abd-El-Atty and Muhammad Talha. (2018). Robust Encryption of Quantum Medical Images. IEEE Access, 6, 1073-1081.
[39] Mohamed Elhoseny, Gustavo Ramírez-González, Osama M. Abu-Elnasr, Shihab A. Shawkat, Arunkumar N and Ahmed Farouk. (2018). Secure Medical Data Transmission Model for IoT-Based Healthcare Systems. IEEE Access, 6, 20596-20608.
[40] Xingyuan Wang, Xiaoqiang Zhu and Yingqian Zhang. (2018). An Image Encryption Algorithm Based on Josephus Traversing and Mixed Chaotic Map. IEEE Access, 6, 23733-23746.