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Title: A cryptosystem based on chaotic and elliptic curve cryptography
Other Titles: Yi ge li yong hun dun ji tuo yuan qu xian jia mi fa de jia mi xi tong
Authors: Ho, Sun Wah (何新華)
Department: Dept. of Computer Engineering and Information Technology
Degree: Master of Philosophy
Issue Date: 2005
Publisher: City University of Hong Kong
Subjects: Computer security
Curves, Elliptic -- Data processing
Notes: CityU Call Number: QA76.9.A25 H58 2005
Includes bibliographical references (leaves 109-111)
Thesis (M.Phil.)--City University of Hong Kong, 2005
xii, 111 leaves : ill. ; 30 cm.
Type: Thesis
Abstract: With the huge growth of computer usage among modern people, there is more and more information transmitted over the Internet everyday. This information may be personal email, electronic bank transactions or even corporation business information which should be accessed only by authorized persons. In order to protect the confidential information, efficient and secure cryptographic algorithms and applications are required. New cryptographic approaches other than traditional ones need to be explored. Evaluation on these approaches, which are enforced by chaotic cryptography and elliptic curve cryptography, are performed in this thesis. In this thesis, a hybrid cryptosystem is proposed. The new cryptosystem utilizes both private and public key cryptosystems. Chaotic cryptography is chosen as the private key cryptosystem while elliptic curve cryptography is utilized as the public key one. For private key cryptography, a new chaotic cryptographic scheme has been proposed. It is based on the observation that the properties of chaotic systems have some common features with those of cryptography. For example, sensitivity to initial condition in chaotic systems is similar to the fact that cryptography needs the exact encryption and decryption keys without tiny difference. One of the various chaotic cryptographic schemes is based on iterations over the logistic map, a simple chaotic discrete map, to reach the phase space corresponding to the plaintext. The ciphertext is then the number of iterations required. Some modifications of this chaotic cryptographic scheme are studied. Moreover, a new approach is proposed as part of the hybrid cryptosystem. Elliptic curve cryptography is one of the public key cryptosystems. It is based on the elliptic curve discrete logarithm problem which states that it is very time-consuming, if not impossible, to find out the number of times an elliptic curve point is added to itself if given the original and the resultant points only. In this public key cryptosystem, the number of additions of an elliptic curve point is the private key while the point itself and the resulting point is the public key pair. Elliptic curve cryptosystem runs under finite field arithmetic operation and elliptic curve point arithmetic operation. If the algorithm to compute finite field arithmetic operation is improved, the overall computational complexity is reduced as well. In this thesis, some fast algorithms are studied and implemented in the public key part of the hybrid cryptosystem. An implementation of the proposed hybrid cryptosystem has been tested on Personal Digital Assistant (PDA) running Microsoft Pocket PC. The hybrid cryptosystem is implemented in the form of client and server architecture. During the test, the PDA acts as client while a personal computer (PC) acts as server. The PDA utilizes wireless LAN to establish a TCP/IP connection with the wired network that the PC is connected. The major duty of the client is to digitally sign and encrypt a file before send it to the server side over the wireless network. In summary, a hybrid cryptosystem that combines both chaotic cryptography and elliptic curve cryptography has been designed and implemented. The methodology and system analysis, together with the testing results, are presented in this thesis.
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