臺灣博碩士論文加值系統

在本篇的研究中，我們提出一種結合Logistic-Map與AES-256的影像加密演算法。首先，我們使用量化後的Logistic-Map所產生的多個混沌替換盒（CS-BOX）來代替原本的單個替換盒（S-BOX），在使用量化後的Logistic-Map產生的混沌虛擬亂數作為CS-BOX的隨機選擇器。我們提出的影像加密演算法可以使密文影像有更好的隨機性及安全性，對於加密影像分析方法如：直方圖、相關性分析等方法都有較好的結果。

本篇的研究提出的方法可以分為以下五個部分。第一部分是透過期望值方式量化Logistic-Map，使產生的混沌序列有最佳化的期望值，第二部分是使用量化後的Logistic-Map產生多個CS-BOX及InvCS-BOX並替換掉AES中的S-BOX及InvS-BOX，第三部分使用經過量化後的Logistic-Map產生一組混沌虛擬亂數作為隨機選擇器，用於選擇CS-BOX及InvS-BOX，第四部分是將整合後的影像加/解密演算法開始進行影像處理的部分，第五部分則是將實驗結果進行影像分析如：直方圖、相關性分析、熵分析、差異性分析及高對比度影像分析，此外，我們也與標準的AES演算法進行比對，而根據實驗的結果，我們提出的方法有較為出色的表現。

本研究提出的方法貢獻如下：
1.均勻性，透過期望值方式量化混沌序列：
使用期望值方式量化混沌序列，使得量化後的結果更為平衡。

2.安全性，提出新的S-BOX演算法：
使用量化方法量化基於Logistic-Map產生的混沌序列，並根據最佳化期望值產生均勻的多個CS-BOX。

3.隨機性，提出混沌虛擬亂數產生器：
使用Logistic-Map產生的混沌虛擬亂數作為多個CS-BOX的選擇器。

4.創新性，打破舊有的加密演算法：
相較於其他學者提出加密演算法，大多是組成單一個S-BOX應用於AES，而我們則是提出多個CS-BOX並使用選擇器隨機選擇CS-BOX。

In this study, we propose an image encryption algorithm that combines the Logistic Map with AES-256. Initially, we use multiple chaotic substitution boxes (CS-BOX) generated by quantized Logistic Map to replace the original single substitution box (S-BOX). Then, we use chaotic pseudorandom numbers generated by the quantized logistic map as the random selector for the CS-BOX. Our proposed image encryption algorithm improves the randomness and security of the encrypted images, which leads to better results in image encryption analysis methods such as histogram analysis and correlation analysis.

The proposed method in this study is divided into five parts. The first part involves quantifying the Logistic Map using the expected value approach to ensure that the generated chaotic sequences have optimized expected values. The second part uses the quantized Logistic Map to generate multiple CS-BOX and InvCS-BOX, replacing the S-BOX and InvS-BOX in AES. The third part involves generating a set of chaotic pseudo-random numbers using the quantized Logistic Map, which serve as random selectors for choosing the CS-BOX and InvCS-BOX. The fourth part applies the integrated image encryption/decryption algorithm to image processing. The fifth part analyzes the experimental results using various image analysis methods such as histogram analysis, correlation analysis, entropy analysis, differential analysis, and high-contrast image analysis. For image decryption. Additionally, we compare our proposed method with the standard AES algorithm, and the experimental results show that our method achieves better outcomes.

The contributions of the proposed method in this study are as follows:

1.Uniformity, Using the expected value approach to quantify chaotic sequences:
Using the expected value approach to quantify chaotic sequences results in a more balanced quantification.

2.Security, A new S-BOX algorithm:
Using a quantization method to quantify chaotic sequences generated by the Logistic Map, multiple uniform CS-BOX are produced based on optimized expected values.

3.Randomness, A chaotic pseudo-random number generator:
The chaotic pseudo-random numbers generated by the Logistic Map are used as selectors for the multiple CS-BOX.

4.Innovation, Breaking the old encryption algorithms:
Compared to encryption algorithms proposed by other researchers, which mostly consist of a single S-BOX applied to AES, our method introduces multiple CS-BOX and uses selectors to randomly choose a CS-BOX.

中文摘要 I
Abstract III
致謝詞 V
Contents VI
List of Figures VIII
List of Tables XI

1.Chapter 1 Introduction 1
1.1 Research Background 1
1.2 Research Motivation and Purposes 3
1.3 Organization of this thesis 4

2.Chapter 2 Research Background 5
2.1 Cryptography 5
2.2 Advance Encryption Standard（AES）10
2.3 Image Encryption 21
2.4 Chaos Theorem and Logistic Map 26

3.Chapter 3 The propused Chaostic AES S-BOX encryption method 29
3.1 The Encryption and Decryption Process of Chaotic AES 29
3.2 Quantifying Chaotic Sequences Using the Method of Expected Values 32
3.3 Generating a S-BOX based on The Logistic-Map 35
3.4 Generating an Inverse S-BOX based on The Logistic-Map 38
3.5 Generating S-BOX selector based on The Logistic-Map 41

4.Chapter 4 The Experimental Results and Analysis 43
4.1 Histogram Analysis 43
4.2 Correlation Analysis 47
4.3 Entropy Analysis 53
4.4 Defferential Analysis 55
4.5 High Contrast Image Analysis 57
4.6 SA Analysis 59

5.Chapter 5 Conclusions and Future Research 61
5.1 Conclusions 61
5.2 Futrue Research 61

6.Reference 62


List of Figures
FIGURE 2-1 CLASSIFICATION OF ENCRYPTION ALGORITHMS 6
FIGURE 2-2 SYMMMETRIC ENCRYPTION AND DECRYPTION PROCESS FLOW CHAR 6
FIGURE 2-3 AES SHIFTROWS 7
FIGURE 2-4 AES S-BOX 8
FIGURE 2-5 ASYMMETRIC ENCRYPTION AND DECRYPTION PROCESS FLOW CHAR 8
FIGURE 2-6 SUBSTITUTION-PERMUTATION NETWORK 11
FIGURE 2-7 AES FLOWCHART 13
FIGURE 2-8 AES S-BOX 16*16 TABLE 14
FIGURE 2-9 AES INVS-BOX 16*16 TABLE 14
FIGURE 2-10 AES S-BOX 14
FIGURE 2-11 AFFINE TRANSFORMATION 15
FIGURE 2-12 AES SHIFTROWS 16
FIGURE 2-13 AES INVSHIFTROWS 16
FIGURE 2-14 AES MIXCOLUMNS 17
FIGURE 2-15 AES FIXED MATRIX 17
FIGURE 2-16 AES FIXED INVMATRIX 17
FIGURE 2-17 AES ADDROUNDKEY 18
FIGURE 2-18 AES-128 KEYEXPANSION 19
FIGURE 2-19 KEYEXPANSION RCON 20
FIGURE 2-20 ORIGINAL HISTOGRAM 23
FIGURE 2-21 ENCRYPTION HISTOGRAM 23
FIGURE 2-22 ORIGINAL CORRELATION ANALYSIS 24
FIGURE 2-23 ENCRYPTION CORRELATION ANALYSIS 24
FIGURE 2-24 LORENZ STRANGE ATTRACTORS 27
FIGURE 2-25 LOGISTIC MAP BIFURCATION DIAGRAM 28
FIGURE 3-1 IMAGE ENCRYPTION 29
FIGURE 3-2 IMAGE DECRYTION 31
FIGURE 3-3 CHAOSTIC RANDOM NUMBER 34
FIGURE 3-4 CS-BOX PARAMETER R= 3.7677 36
FIGURE 3-5 CS-BOX PARAMETER R= 3.9111 36
FIGURE 3-6 CS-BOX PROCESS 37
FIGURE 3-7 INVCS-BOX PARAMETER R= 3.7677 39
FIGURE 3-8 INVCS-BOX PARAMETER R= 3.9111 39
FIGURE 3-9 INVCS-BOX PROCESS 40
FIGURE 3-10 CHAOSTIC PSEUDO-RANDOM VALUE 42
FIGURE 3-11 CHAOSTIC PSEUDO-RANDOM NUMBER PROCESS 42
FIGURE 4-1 LENA ORGINAL IMAGE 43
FIGURE 4-2 LENA ORGINAL IMAGE HISTOGRAM 43
FIGURE 4-3 LENA ENCRYPTION IMAGE 43
FIGURE 4-4 LENA ENCRYPTION IMAGE HISTOGRAM 43
FIGURE 4-5 MANDRIL ORGINAL IMAGE 44
FIGURE 4-6 MANDRIL ORGINAL IMAGE HISTOGRAM 44
FIGURE 4-7 MANDRIL ENCRYPTION IMAGE 44
FIGURE 4-8 MANDRIL ENCRYPTION IMAGE HISTOGRAM 44
FIGURE 4-9 PEPPERS ORGINAL IMAGE 44
FIGURE 4-10 PEPPERS ORGINAL IMAGE HISTOGRAM 44
FIGURE 4-11 PEPPERS ENCRYPTION IMAGE 44
FIGURE 4-12 PEPPERS ENCRYPTION IMAGE HISTOGRAM 44
FIGURE 4-13 JETPLANE ORGINAL IMAGE 45
FIGURE 4-14 JETPLANE ORGINAL IMAGE HISTOGRAM 45
FIGURE 4-15 JETPLANE ENCRYPTION IMAGE 45
FIGURE 4-16 JETPLANE ENCRYPTION IMAGE HISTOGRAM 45
FIGURE 4-17 WALKBRIDGE ORGINAL IMAGE 45
FIGURE 4-18 WALKBRIDGE ORGINAL IMAGE HISTOGRAM 45
FIGURE 4-19 WALKBRIDGE ENCRYPTION IMAGE 45
FIGURE 4-20 WALKBRIDGE ENCRYPTION IMAGE HISTOGRAM 45
FIGURE 4-21 WOMAN1 ORGINAL IMAGE 46
FIGURE 4-22 WOMAN1 ORGINAL IMAGE HISTOGRAM 46
FIGURE 4-23 WOMAN1 ENCRYPTION IMAGE 46
FIGURE 4-24 WOMAN1 ENCRYPTION IMAGE HISTOGRAM 46
FIGURE 4-25 WOMAN2 ORGINAL IMAGE 46
FIGURE 4-26 WOMAN2 ORGINAL IMAGE HISTOGRAM 46
FIGURE 4-27 WOMAN2 ENCRYPTION IMAGE 46
FIGURE 4-28 WOMAN2 ENCRYPTION IMAGE HISTOGRAM 46
FIGURE 4-29 LENA ORGINAL CORRELATION ANALYSIS 47
FIGURE 4-30 LENA ENCRYPTION CORRELATION ANALYSIS 47
FIGURE 4-31 MANDRIL ORGINAL CORRELATION ANALYSIS 48
FIGURE 4-32 MANDRIL ENCRYPTION CORRELATION ANALYSIS 48
FIGURE 4-33 PEPPERS ORGINAL CORRELATION ANALYSIS 48
FIGURE 4-34 PEPPERS ENCRYPTION CORRELATION ANALYSIS 48
FIGURE 4-35 JETPLANE ORGINAL CORRELATION ANALYSIS 49
FIGURE 4-36 JETPLANE ENCRYPTION CORRELATION ANALYSIS 49
FIGURE 4-37 WALKBRIDGE ORGINAL CORRELATION ANALYSIS 49
FIGURE 4-38 WALKBRIDGE ENCRYPTION CORRELATION ANALYSIS 49
FIGURE 4-39 WOMAN1 ORGINAL CORRELATION ANALYSIS 50
FIGURE 4-40 WOMAN1 ENCRYPTION CORRELATION ANALYSIS 50
FIGURE 4-41 WOMAN2 ORGINAL CORRELATION ANALYSIS 50
FIGURE 4-42 WOMAN2 ENCRYPTION CORRELATION ANALYSIS 50
FIGURE 4-43 ECB MODE CIRCULAR ENCRYPRION 57
FIGURE 4-44 ECB MODE CHUNG YUAN ENCRYPRION 57
FIGURE 4-45 ECB MODE PENGUIN ENCRYPRION 58
FIGURE 4-46 CHAOS CIRCULAR ENCRYPRION 58
FIGURE 4-47 CHAOS MODE CHUNG YUAN ENCRYPRION 58
FIGURE 4-48 CHAOS MODE PENGUIN ENCRYPRION 58


List of Tables
TABLE 2-2-1 AES-128 AND DES COMPARE 10
TABLE 2-2AES PARAMETER 11
TABLE 2-3 KEY OF NUMBER 18
TABLE 4-1 CORRELATION ANALYSIS RESULT 51
TABLE 4-2 ENTROPY ANALYSIS RESULT 53
TABLE 4-3 DEFFERENTIAL ANALYSIS RESULT 55
TABLE 4-4 SA ANALYSIS RESULT 59

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