臺灣博碩士論文加值系統

混沌系統對初始條件具有高靈敏度及良好的隨機特性，此特性可應用於密碼系統。低維度的混沌系統計算速度雖然快，但簡單的系統參數有安全方面的疑慮；高維度的混沌系統較為安全，但因為使用較為複雜的系統參數，這將導致運算負載過重。交換式混沌系統融合多個低維度的混沌系統，以增進系統安全以及攻擊者的困難。
目前全球流通最頻繁的圖像格式為JPEG，JPEG為一圖像壓縮檔，具有節省數位圖像儲存空間，並大大節省圖像傳輸時間，JPEG圖像之安全研究無論在學術研究與實際應用上皆為一重要研究主題，在本論文中，我們基於交換式混沌系統提出針對JPEG圖像安全的加密演算法，使用交換式混沌序列，對JPEG圖像進行置換和擴散運算。此外，我們進一步運用所提出的交換式混沌之圖像加密演算法對JPEG內部的編碼器和解碼器進行安全加密。
實驗結果顯示，本圖像加密算法的密文圖像具有較低的相鄰像素相關性，金鑰空間大，良好的金鑰靈敏度，較佳的統計分析。本交換式混沌系統應用在JPEG安全架構部分，從實驗結果顯示，該演算法具有良好的PSNR（峰值雜訊比）以及較低的MSE（均方誤差）。

Chaotic system has the high sensitivity to initial conditions and excellent random behaviors. It can be applied to cryptosystem. The computation of low-dimensional chaotic systems is fast, but there are some concerns on their security for the simple system parameters. The high-dimensional chaotic systems are more secure, but have more complex parameters that lead to high computation complexity. The switching chaotic system is introduced by adopting multiple low-dimensional chaotic systems, to promote the security of the system and the difficulties of attackers.
JPEG is the most popular format of digital image. It is a common compress format of image which saves the storage space and transmission time greatly. The security of JPEG is an important topic for both theoretic research and practical application. For JPEG, we present an image encryption algorithm based on switching chaotic system. By the switching chaotic sequence, permutation operation and diffusion operation are performed on the JPEG images. In this thesis, we further apply the proposed switching image encryption algorithm to the JPEG internal encoder and decoder.
The experimental results show that the proposed image encryption algorithm has less correlation between adjacent pixels, large key space, good key sensitivity and a better security for statistical analysis. In secure JPEG structure, the experimental results have good PSNR (Peak Signal to Noise Ratio) and less MSE (Mean Square Error).

致謝 i
摘要 ii
Abstract iii
Contents iv
List of Figures vi
List of Tables viii
Chapter 1 Introduction 1
Chapter 2 Background knowledge 3
2.1 Introduction to Chaos Theory 3
2.1.1 Logistic Map 3
2.1.2 Tent Map 4
2.1.3 Sine Map 5
2.1.4 Lorenz Chaotic System 6
2.1.5 Chen’s Chaotic System 6
2.2 Introduction of JPEG 7
2.3 JPEG Coding Process 8
2.3.1 Image Segmentation 8
2.3.2 Color Space Conversion 9
2.3.3 Discrete Cosine Transform 10
2.3.4 Data Quantization 10
2.3.5 Zig-Zag Reordering 11
2.3.6 Huffman Coding 12
Chapter 3 The Related Image Encryption Algorithm 15
3.1 A Symmetric Color Image Encryption Scheme Based on Chaotic Maps by Fu 15
3.2 An Image Encryption Scheme Based on Lorenz Chaos System by Jiang 18
3.3 Image Encryption Algorithm Based on Logistic Chaotic System and S-box Scrambling by Zhao 19
3.4 JPEG Encryption with File Size Preservation by Niu 22
3.5 Securing JPEG Architecture Based on Enhanced Chaotic Hill Cipher Algorithm by Hamissa 25
Chapter 4 The Proposed Image Encryption Scheme 29
4.1 Design of the Proposed Encryption Algorithm 29
4.2 Design of the Proposed Decryption Algorithm 30
4.3 Switching Chaotic System 31
4.4 Data Scrambling System 32
4.5 Diffusion of Pixel Values 36
4.6 Encryption Effect of the Proposed Algorithm 38
4.7 Secure JPEG Structure 39
Chapter 5 Experimental Results 41
5.1 Histograms Analysis of Encrypted Image 41
5.2 Encryption Key Space Analysis 43
5.3 Analysis of Correlation of Two Adjacent Pixels Test 44
5.4 Key Sensitivity Test 45
5.5 Experimental Results of Secure JPEG Structure 46
5.5.1 Key Space Analysis 48
5.5.2 Key Sensitivity Test with JPEG Structure 49
5.5.3 Image Experimental Measurements 50
Chapter 6 Conclusions 54
References 55

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