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研究生：	趙呈達 Chao, Cheng-Ta
論文名稱：	一串聯混沌系統的高安全性Baptista型數位混沌加密系統 A high security Baptista-type cryptosystem using cascaded chaotic maps
指導教授：	陳進興 Chen, Chin-Hsing
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 電腦與通信工程研究所 Institute of Computer & Communication Engineering
論文出版年：	2009
畢業學年度：	97
語文別：	英文
論文頁數：	103
中文關鍵詞：	串聯混沌系統、三角函數系統、Baptista型加密系統
外文關鍵詞：	trigonometric map, cascaded chaotic maps, Baptista-type cryptosystem
相關次數：	點閱：91 下載：1
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混沌系統擁有對初始值及參數的高敏感性，遍歷性…等，這些特性符合一加密系統的需求。混沌系統已被廣泛的應用於各類加密系統中，Baptista型加密系統便是其中一類。Baptista加密系統以疊代混沌系統使chaotic state到達明文相對應的區間，並以疊代的次數作為密文。在Baptista發表此加密系統後，相對應的攻擊不停的提出，但許多加強Baptista加密系統的演算法也為加強安全性而提出。

本論文修改J. Wei et al.於2006年所提出的一Baptista型加密系統並加強其安全性。本論文所提出的加密方法將原演算法中的logistic map改為串聯多個混沌系統，它包含三個PWLCM以及一個三角函數系統，每一個混沌系統的輸出均為下一個混沌系統的輸入。因每個混沌系統擁有不同的參數，這些參數使得keyspace大幅增加。本加密系統利用三角函數系統的大範圍混沌狀態來加強加密系統中的confusion以及diffusion效果。串聯混沌系統的技術抵擋混沌系統的退化，因而增強了本論文提出的加密系統的安全性。

本論文所提出的加密系統可以抵擋Baptista型加密系統的攻擊，而keyspace為256!x10^76足夠抵擋暴力破解法。本加密系統可將熵值為7.255686的256階灰階影像，提升到熵值7.999289。於效能方面，本加密系統加密速度為最快Baptista型加密系統之一，加密一張512x512的256階灰階影像平均花費0.48秒，而產生的密文大小只略大於明文。本加密系統的安全性與效能均高於現有的Baptista型加密系統，並可安全使用於實際應用。

Chaotic system properties, such as sensitivity to initial control parameter and initial condition, ergo-dicity and so on, are suitable to construct secure commun-ication schemes. Many chaos based cryptosystem have been proposed, one of them is the Baptista cryptosystem. The chaotic cryptosystem proposed by Baptista encrypts the ASCII code as the number of iterations applied in the chaotic map to reach the region corresponding to the ASCII code. After its publication, many variant versions and attacks have been proposed.

We modified the Baptista-type cryptosystem proposed by J. Wei et al. 2006. In our proposed cryptosystem, we exchange the logistic map to the cascaded chaotic maps. The cascaded maps include three PWLCMs and a trigonometric map. Four maps are cascaded and each output value of a map is input to the next one. The cascaded maps has different control parameter and these parameters increase the key-space. The chaotic state of the trigonometric map belong to [0,infinity), we utilize this huge interval to increase the confusion and diffusion of our cryptosystem. Cascading the chaotic maps increases the cycle length and against the digital degradation of the keystream of our cryptosystem.

Our proposed cryptosystem has ability against the attacks of the Baptista-type cryptosystems and the key-space of our proposed cryptosystem is 256!x10^76, which
is big enough to resist all kinds of brute-force attacks. For a 256-gray-scale image, our cryptosystem changed it entropy from 7.255686 to 7.999289 after encrypting. Our proposed cryptosystem is among the fastest Baptista-type cryptosystems, the time for encrypting a 512x512 256-gray-scale image is 0.48 seconds. The ciphertext size generated by our cryptosystem is only slightly larger than the plaintext size. Our proposed cryptosystem is more secure and efficient than current existing Baptista-type crypto-systems. It is suitable for practical applications.

Chapter 1 Introduction	                         1
1 Motivation	                                  1
2 Background	                                  1
3 Previous works	                         8
4 Research method	                        10
5 Organization of the thesis	               11
Chapter 2 Baptista type cryptosystems	      12
1 M. S. Baptista. 1998	                         12
1.1 Baptista original cryptosystem	      12
1.2 The drawbacks of Baptista original 
          cryptosystem	                        18
2 W. K. Wong et al. 2001	               18
3 K. W. Wong 2002	                        21
4 K. W. Wong 2003	                        24
5 K. W. Wong 2003(2)	                        28
6 S. Li et al. 2003 & S. Li et al. 2004	      31
7 F. J. Huang 2005	                        36
8 T. Xiang 2006 & Y. Wang et al. 2007	      39
8.1 T. Xiang 2006	                        39
8.2 Y. Wang et al. 2007	               43
Chapter 3 Cryptanalysis	                        45
1 Classical types of attacks	               45
2 Jakimoski- Kocarev attack	               46
3 One-time pad attacks	                        47
4 Entropy attacks	                        49
5 Key recovery of weakened version of 
      the cipher	                                 52
6 Cryptanalysis of dynamic look-up table 
      based chaotic cryptosystem	               54
Chapter 4 A Baptista type cryptosystem with 
          cascaded chaotic maps	               59
1 J. Wei et al. 2006	                        59
2 S. Behnia et al.	                        65
3 Cascading chaotic maps	               68
Chapter 5 Experimental results and discussion	      74
1 Security analysis	                        74
1.1 Key space analysis	               76
1.2 Statistical analysis	               76
1.3 Sensitivity analysis	               80
1.4 Information entropy	               82
2 Attack analysis	                        82
2.1 Jakimoski-Kocarev attack	               83
2.2 One-time pad attack	               83
2.3 Entropy attack	                        84
2.4 Key recovery attack	               85
2.5 Attack on dynamic look-up table	      86
2.6 Brute-force attack	               86
3 Performance comparison	               87
4 Discussion	                                 95
Chapter 6 Conclusion	                        97
                                    

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校內：2011-07-30公開
校外：2011-07-30公開

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