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研究生:鍾隆宇
研究生(外文):Long-Yeu, Chung
論文名稱:私匙密碼系統應用混沌系統和哈爾小波理論之研究
論文名稱(外文):The Development of a Novel Symmetric Cryptography Based on Chaotic System with Haar Wavelets Theory
指導教授:羅仁權羅仁權引用關係
指導教授(外文):Ren C. Luo
學位類別:博士
校院名稱:國立中正大學
系所名稱:電機工程研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:英文
論文頁數:179
中文關鍵詞:私匙密碼系統混沌系統哈爾小波安全通訊電子商務私匙分配協定遠端控制
外文關鍵詞:Private-Key CryptographyChaotic SystemHaar WaveletsSecure CommunicationElectronic CommerceSymmetric-Key Distribution ProtocolRemote control
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中文摘要
近年來,由於電腦網路技術的蓬勃發展和廣泛應用,使得資訊流通與存取更為快速與便捷。諸如政府推動之行政電子化,民間企業之電子商務(Electronic Business)、線上購物(On-line Shopping)、金融機構之金流機制和民眾生活型態重大改變之資訊家電(Information Appliance)、電子交易行為等,均已將網路技術應用於實務上。所以可謂在過去的十年間,電腦與電腦網路帶給人類社會的重大影響,媲美工業革命,如同汽車對人類的影響一樣,重大而且深遠。然而當電腦網路應用方興未艾之際,相隨地卻也激起了人們的某種危機意識,資訊在眾目睽睽下之電腦網路上傳輸時應如何保護,以確保資訊(a)秘密性(Secrecy or Privacy),(b)鑑定性(Authenticity),(c)完整性(Integrity),(d)不可否認性(Non repudiation)。因而為有效合理地對電腦網路上傳輸訊息加以保密,以防止傳輸的資訊被非法竊聽(Eavesdropped )或篡改(Tampered illegally),則必須對明文(Plaintext)作保密的動作,以確保通訊安全。在目前廣泛使用的私匙加密技術(Private-key Cryptography)中,最引人注目地莫過於IBM公司於1977年發表的DES(Data Encryption Standard)。由於DES的加解密速度非常地快速,因此十分受到各界的青睞並應用於各層面上;然而近些年,美國政府支持的DES Hall 計劃研究發現也證實了56 bits的DES不安全,112 bits的DES也可以結合一定數量的計算機在合理地時間內破解。此項事實發現,將對目前廣泛採用DES為加密方法的應用(如電子銀行之金流)產生重大負向影響。因而激起了本文的研究動機。
本文乃針對上述問題加以克服,發展另一新型而且具高度安全的公眾網路(Internet)私匙密碼系統。本文第四章,應用混沌(Chaos)理論和哈爾小波(Haar Wavelets) 創造了一嶄新加解密方法,不僅使得在公眾通道上傳輸的資料具有高度的混淆性,以防止惡意的第三者的閱讀、竊取、甚至篡改。再者,經由Haar 小波理論設計一Encoder和Decoder不僅保有增強加解密方法的安全度外,既另保持傳輸資訊具有完整性,原資料些微變動皆可輕易檢驗,用以偵測傳輸區塊是否受到雜訊的干擾或人為的篡改。基本而言,混沌(Chaos)是一種看似隨機的不規則運動現象,是非線性定率系統(Deterministic) 中具有內在隨機性的一種表現。以典型的混沌現象紊流(Turbulence)而言,當流體在低速時,流體的流動狀態是規律且可預測的。而若流速超過臨界速度以後,則其流動狀態就變得無法掌握。以較科學的眼光來看,所謂的變得無法掌握就是我們說的可預測性降低。因此,我們可以對混沌做一般性的描述:混沌是由於某個決定性的動態系統(Deterministic dynamical system)對起始狀態的敏感,因而產生的長時期(Long-term)不可預測行為(Non-prediction)。進一步地說,當起始條件產生微小的偏差時,對於非混沌系統而言,如此的偏差會導致隨著時間增加而呈線性成長的預測誤差,而對於混沌系統而言,這樣的預測誤差就會著時間增加而呈指數成長(Exponential growth)。也因此混沌系統對初始條件的敏感性,造成其運動軌跡(狀態)具有強限制性的預測能力。因此在非常短的時間之後,系統的狀態基本上是無法預知的。事實上,這種對於起始條件的敏感,是僅有在系統的主導方程式(Governing equations)為非線性時才會產生的現象。本文所提出之異於傳統之私匙加密系統,就是基於此項理論基礎發展。經由本文的研究和實作,驗證本方法為一高度安全性的私匙加密系統。本文第五章提出一以私匙分配中心(Key Distribution Center,KDC)模式之認證協定(Authentication Protocol)用以安全分配通信私匙(Private-key)於網路上要求連線通訊雙方,透過KDC居中協調,任何通訊主體只須記住自己和KDC之間的秘密鑰匙,不須記錄與其他通訊主體間的通信私匙,如此方式即可解決大型網路上複雜的私匙管理問題。本文也提出一嶄新有效率且安全地私匙分配之認證協定,經與文獻中著名和重要方法比較,本協定在通訊安全條件下之加解密次數大幅減少,可節省許多寶貴的通訊時間和成本。本文實驗部分以具有跨平台能力的Java Code實作本文所提出之私匙加解密方法,並利用TCP/IP之通訊協定傳輸資料成功地在Internet上運作。不論任何型式的數位資料,如語音、圖像、文字皆可安全的在公眾網路上傳送。再者,新近根據國際知名的產業分析公司『Forester Research Inc.』的預測,全球電子商務的營業額在公元二○○一年將達到兩千億美元的巨量交易額。從美國總統柯林頓發表『電子商務白皮書』之後,所有的國家都以快速的步伐來建構屬於自己的電子商務空間,用以迎向全球資訊化、網路商業化的未來。在此前提下,我國政府亦積極推動NII計劃,並以建立亞太營運中心為目標。電子商務的應用可以說徹底的改變了我們購物的型態,可以用『秀才不出門,能購天下物』來形容。這裡所牽涉到的問題是商品的展出方式、購物者的身份識別、訂購的資訊如何傳遞至商家、購物者如何付款、銀行如何扮演支付角色(金流)、所購貨品如何送至買者(物流)、傳遞的資訊又如何能在不可靠而又不安全的網際網路上進行可靠又安全的資訊傳遞而又不容許任何差錯(資料完整性)、傳遞過程中資料如何保密而不被攔截篡改(私密性)等等一連串的問題都要尋求解答。這裡面每一項問題都需要用現代資訊科技來解決。譬如說,商品展出的方式有用虛擬實境(Virtual Reality,簡稱V.R.)的技術把整個電子大型購物中心或Shopping Mall都能隨購物者腳步的移動而連續的呈現在螢幕上而隨心所欲的閒逛,進入有興趣的商店,挑選看中的商品,使用信用卡付完商品的價款,而所挑選的商品便透過物流、郵遞送到家裡,這就是未來電子購物的模式。然而用信用卡付款(Payment)以及挑選商品(Ordering),首先訂購者的身份要能唯一的識別(Authentication, Digital Signature),不能被造假(Fraud Detection),而所訂的貨物不能否認(Non-repudiation),付款資料不能絲毫有錯(Data Integrality),亦不能洩漏給第三者(Data Encryption),面商家收到銀行或金融機構的付款後也不能否認(Non-repudiation),所送金額又不能送錯商家(Uniqueness of Reception),訂貨的資料以及付款的數額均需保密(Privacy),以防被攔截或被纂改。在本文第六章就此項課題配合本文所提出之新型私匙密碼系統設計一可行之「消費者導向電子商務」架構。第七章結論中我們對未來再深入研究提出建議。

Abstract
Private-key mechanisms are also called symmetric cryptography such as DES (Data encryption standard), which was developed in the middle of 1970’s by IBM and was officially announced as the standard of data encryption by the National Bureau of standard, U.S. In the current state of the art, DES has been defeated and this has been proved by the widely publicized DESHALL project. However, this is a defeat for the key size (56 bits), but with the increase of computer capability and the constantly improving technology of cryptanalysis. Long key DES would become more and more insecure and therefore, the consequences would be not less serious than those of Y2K. In order to meet this crisis and to prevent information transmitted on the public channels from being eavesdropped on or tampered with illegally, plaintext should be encrypted to ensure secure communication. It is, therefore, necessary and urgent to develop a new and more secure private cryptosystem than DES. The core of this dissertation, we proposed a novel hybrid cryptosystem by combining the advantages of private key cryptosystem, Haar wavelets encoder and chaotic masking. In this scheme, we use the seven chaotic parameters (a, b, a, b, x0, y0, z0 ) and the dimension of Haar wavelet encoder matrix Hn , the combining form of Hn with sub wavelet basis {h0, h1, ….,hn-1}, the pre-specified time span ts, as well as the coefficients ai, i = 1,…, n, and the prime number k of the collision-free one-way function to serve as the “encryption keys”. The security property of the proposed cryptosystem results from two main parts: the first one, the high sensitivity of synchronization versus parameter or initial condition small variation. One of them is sensitive enough to make the state trajectories separate from each other at exponential rate. The second part depends on the Haar wavelets encoder Hn with its various combining form from the sub wavelets basis {h0, h1, ….,hn-1}; it is composed the way as the lottery. Furthermore, due to the collision free one-way function, the chaotic behavior control parameters are always different. Therefore, the system can be secured as long as the first chaotic parameters are kept secret. Moreover, transmitting error-detection function of the proposed cryptosystem is also addressed. And the new concept of chaos-based cryptosystem had been successfully implemented by JAVA code and operated on Internet.
Otherwise, regarding the private-key distribution protocol, it is essential not only to deliver the private key with security but also to prevent the system from malicious attacks, especially over the Internet. It has been imaged that the destroyers are omnipresent. The private-key systems are governed by the major challenges in the key management, generating, storing, and transmitting of private keys. Thus, the provision of a proper key distribution protocol is a significant issue in the private-key cryptosystem. Although several good protocols for private key distribution are available, some potential problems such as the necessity of synchronous clocks or the lack of proper semaphore for the both participators to conclude a conversation exist. This thesis also presents a new authentication protocol for key distribution by incorporating counter values in the operation to avoid the dependence on system clocks and to provide semaphore for both entities to conclude a conversation properly. We validate the effectiveness of the protocol by illustrating its defense capability to some attacking scenarios. In addition, the proposal has less computational burden relative to the existing and widely using protocols.
For E-commerce applications consider, we propose an Internet based consumer oriented E-commerce model, which apply the algorithm as stated above chapter. Finally, we make some concluding remarks and present future researches related to the topics in the last Chapter.

Contents
Acknowledgments
中文摘要…………………………………………………………………I
Abstract……………………………….…………………….……….IV
Captions for figures and tables…………………………………IX
Chapter 1 Introduction……..…………………………………….1-1
1.1. Application of Cryptography in the Real World…… …1-3
1.1.1 Secure Communication……………..…………………...…1-3
1.1.2 Identification and Authentication…………………..…1-4
1.1.3 Secret Sharing…………………………….…….………….1-5
1.1.4 Electronic Commerce…………………………………………1-5
1.1.5 Certification………………………………………………..1-6
1.1.6 Remote Access………………………………….……..…….1-7
1.2. Research Motivations………………………………………..1-7
1.3. Contributions………………………………………… .…….1-9
1.4.Organization of Dissertation………………………. …….1-14
Chapter 2 An Overview of Some Popular Techniques in Cryptography…2-1
2.1.The Private-key Cryptography…………………. ………...2-2
2.1.1 The Data Encryption (DES)……………………….……….2-4
2.1.2 DES is not secure………………………..…….…….……2-10
2.2. The Public-key Cryptography……………………. ….…..2-11
2.3 Digital Signatures…………………………………………….2-13
2.4 Authentication Protocol for Key Distribution………...2-14
Chapter 3 Novel Computer-Oriented Method Based upon the Haar Wavelets for Solving System Time Response................3-1
3.1 Integration of Haar wavelets………………….…………..3-3
3.2 Theoretical Derivation……………………….………………3-9
3.3 Numerical Experiments……………………………………….3-12
3.4 Conclusion Remarks…………………………………..….….3-14
Chapter 4 A Novel Symmetric Cryptography Based on the Hybrid Haar Wavelets Encoder and Chaotic Masking Scheme……... 4-1
4.1 Introduction……………….……………………………….…4-1
4.1.1 Background………………………………………...……...4-1
4.1.2 Scope of the Chapter………………..…… ……….4-3
4.2 Basic Principles Involved in the Proposed Scheme…..4-4
4.2.1 Haar wavelets multiplex system……………………4-4
4.2.2 The Phenomenon and Theorem of Chaos.….….…….4-9
4.2.3 Chaotic Masking……………………………………….4-15
4.3 The Proposed Hybrid Cryptosystem…………………………4-23
4.4 Experience Results……………………………………………4-28
4.5 Attack and Security Issues…………………………………4-35
4.5.1 Ciphertext Only Attack…………………………….…… 4-36 4.5.2 Known-plaintext Attack…………………… ……..…….4-39
4.6 Conclusion and Further Work……………………….…….4-43
Chapter 5 Novel Authentication Protocol for Symmetric Cryptography
Key distribution…………………………………………………....5-1
5.1 Related Authentication Protocol………….…….………….5-3
5.1.1 The Initial Authentication Protocol Phase…..….5-5
5.1.2 The Subsequent Authentication Phase………… ……5-5
5.1.3 Weakness of Hwang’s Protocol………………… ……5-6
5.2 Proposed Authentication Protocol………………………… 5-7
5.2.1 Initial Authentication: Getting Session key Certificate 5-7
5.2.2 Subsequent Authentication: Exchanging the Certificates…-8
5.3 Security Analysis of the Protocol and Discussions……..5-8
5.3.1 Man-in-the-Middle Attack……………………………….…..5.8
5.3.2 Replay Attack………………………………………......5.9
5.3.3 The Paradox Attack…………………….…………....…5.9
5.3.4 The Parallel Session Attack…………………….....5.10
5.4 Discussions………………………………………....………….5.11
5.5 Conclusion Remarks……………………………………………….5.12
Chapter 6 The design for Internet Based Consumer-Oriented Electronic Commerce ………………………………………………….6.1
6.1 Introduction……………………………..………….…….…….6.1
6.2 The Consumer-Oriented Electronic Business……………..6 -4
6.3 The Survey of the Electronic Business of the Encryption u-Path…6-11
Chapter 7 Conclusion and Discussions..…………….….………7-1
References
Appendix
Captions for figures and tables
Figure 1.1 Secret writing.
Figure 2.1 Flow of information in conventional cryptographic system.
Figure 2.1.1 DES enciphering algorithm.
Figure 2.1.2 Calculation of f(Ri-1,Ki).
Figure 2. 2 Flow of information in public key system.
Figure 3.1 Haar Wavelets (The first eigth Haar functions defined in the domain [0,1] shows the localized).
Figure 3.2 Integration of Haar wavelets.
Figure 3.3 Haar wavelets approach for Problem 3. 1.
Figure 3.4 Haar wavelets approach for Problem 3. 2.
Figure 4.1 The first sixteen Haar functions defined in the domain [0,1] shows the localized.
Figure 4.2(a) The bifurcation diagram of the logistic difference equation Xn+1=AXn(1-Xn).
Figure 4.2(b) The bifurcation diagram from period-2 to period-8 of the logistic difference equation Xn+1=AXn(1-Xn).
Figure 4.3 Presented the sensitivity to initial conditions on the chaotic attactor by RÖssler’s system with a=0.55,b=2,c=4, and initial condition (0.1,0.1,0.1).
Figure 4.4 (a) Chua’s circuit.
Figure 4.4 (b) The Chua’s diode (VR vs iR).
Figure4.4(c)Double scroll behavior generated by α=9,β=14.286, a=-1.1428,b=- 0.7142 and initial value of (x0,y0,z0 ) =(0.5,0.5,0.5).
Figure 4.4 (d) Phase plot of Chua’s circuit, x vs. y.
Figure4.4 (e), (f), (g), Time series of Lorenz system with , b=45.92, r=4.0, (e) x vs. t (f) y vs. t (g) z vs. t.
Figure4.4 (h), (i), (j) Phase plot of Lorenz system with , b=45.92, r=4.0, (h) x vs. y (i) y vs. z (j) x vs. z.
Figure 4.5 Three channels, (a) x, (b) y, and (c) z, of chaotic signals generated from the Chua's circuit described by Equ. (4.7). In Figure4.3 (a),(b),(c), the top subplot shows the x of chaotic signals whenα=9,β=14.286, a=-1.1428,b=- 0.7142 and initial value of (x0,y0,z0) =(0.5,0.5,0.5) are applies; the bottom subplot shows only small changeΔα=0.0001 on parameter α.
Figure 4.6 Schematics of the proposed hybrid cryptosystem.
Figure 4.7 A brain computer tomogram picture.
Figure 4.8. An arbitrary selected segment (128 Bytes) shows that the underlying structure in Figure 4.7.
Figure 4.9 (a) The ciphertext by (a, b, a, b, x0, y0, z0 )=(9,14.286, -1.1428, -0.7142, 0.5, 0.5, 0.5) for Figure 4.7 (c).
Figure 4.9 (b) The ciphertext by (a, b, a, b, x0, y0, z0)=(8.9999, 14.286, -1.1428, -0.7142, 0.5, 0.5, 0.5) for Figure 4.7(c).
Figure 4.10 Threshold vs rank of Haar wavelets encoder matrix.
Figure 4.11 Loss of information about of initial state of the chaotic system as time progresses.
Figure 4.12 The K=(a, b, a, b, x0, y0, z0 ); Mi: the plaintext, by adaptive technique observing the chaotic signals could be deduce the K, when |x- |→0.
Figure 4.13 Known Plaintext Attack Procedure using the identification methodology.
Figure 4.14(a) Experiences Though over Internet.
Figure 4.14(b) Software Implement for Figure 4.6 by Java code.
Figure 4.15 Experimental result for the proposed hybrid cryptographic scheme; (a)original image (a jade-tree-frog on Taiwan), (b) Haar wavelets applied, (c) both chaotic signal streams and Haar wavelets signal streams are applied, (d) the decrypted image.
Figure4.16 and Figure 4.17 Experimental result for the proposed hybrid cryptographic scheme; (a) original image (a credit card), (b) Haar wavelets applied, (c) both chaotic signal streams and Haar wavelets signal streams are applied, (d) the decrypted image.
Figure 4.18 Experimental result for the proposed hybrid cryptographic scheme; (a) original image (a check), (b) Haar wavelets applied, (c) both chaotic signal streams and Haar wavelets signal streams are applied, (d) the decrypted image.
Figure 4.19. Experimental result for the proposed hybrid cryptographic scheme; (a) original image (a temple characters named as eight-generals on Taiwan), (b) Haar wavelets applied, (c) both chaotic signal streams and Haar wavelets signal streams are applied, (d) the decrypted image.
Figure 4.20 (a) Client site flow Chart.
Figure 4.20 (b) Server site flow Chart.
Figure 5.1 The initial authentication protocol of Hwang’s protocol.
Figure 5.2 The subsequent authentication protocol of Hwang’s protocol.
Figure 5.3 The initial authentication protocol of the proposed protocol.
Figure 5.4 The subsequent authentication protocol of the proposed protocol.
Figure 5.5 Parallel session attack scenarios in subsequent protocol.
Figure 5.6. Paradox attack scenarios in initial authentication protocol.
Figure 6.1 Internet-based consumer-oriented Model E-Commerce.
Figure 6.2 The Electronic Business of the Encryption u-Path.
Figure 6.3(a) Generating a Digitally Signed Message.
Figure 6.3(b) Verifying a Digitally Signed Message.
Table 2.1.1 Initial permutation IP.
Table 2.1.2 Initial permutation IP-1 .
Table 2.1.3 Bit-selection Table E.
Table 2.1.4 Permutation P .
Table 2.1.5 Selection functions(S-boxes).
Table 2.1 6 Key search machine cost vs Expected search time(For 56 bits DES, using 2000 technology)[RSA Corp.].
Table 4.1.Critical parametric values of the Chua’s circuits for different dynamical behaviors.
Table 4.2 Spectra of Lyapunov exponents and Associated Attactors Three-Dimensional State Space.
Table 4.3 The relative errors between the source and recovered images.
Table 5.1 Characteristic comparisons of different protocols.

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