Research On Chaos-based Pseudo Random Number Generator And Its Application On Image Encryption

With the rapid development of computer science and communication technology, the need for more secure, high efficiency and reliable methods of protecting data is increasing. Chaotic systems have many good properties , such as the sensitive dependence on initial conditions and control parameters,the density of set of all periodic points and topological transitivity, which are related to some requirements such as confusion and diffusion in cryptography. Since 1980s, the idea of using digital chaotic systems to design new ciphers has attracted more and more attention. A great number of ciphers based on chaos have been proposed and a lot of promising progresses have been made. However, recent studies have shown that many chaotic ciphers which were considered to be practical and secure, are inefficient, insecure and unusable. How to design the practical and secure chaotic ciphers is becoming a key issue to be addressed. Based on the current status of chaotic cryptography, this thesis is dedicated to further more research on the design and analysis of chaos-based pseudo random number generator and its application on image encryption. The main work of this thesis includes:(1) Chaos theory and chaotic cryptography are introduced in brief. Then, the relationship between chaos theory and cryptography is compared. The detailed descriptions of various chaotic ciphers are given, including chaotic stream ciphers, chaotic block ciphers, chaotic public-key ciphers, other chaotic ciphers and chaotic image encryption and so on.(2)A new pseudo random number generator based on piecewise linear chaotic map (PWLCM) is proposed. The proposed scheme can overcome the defect of piecewise linear when using PWLCM to generate the pseudo random sequence. Theoretical analysis and computer simulation also indicate that the proposed pseudo random generator has good cryptographical properties. In addition, we propose a pseudo random number generator based on discrete two-dimension chaotic map. A LFSR is utilized to correct the degradation of the output of the discrete map. The experiment shows the scheme has good statistical properties.(3) A new image encryption scheme with diffusion-substitution architecture is designed by using the new pseudo random number generator. The proposed scheme consists of two diffusion processes: vertical diffusion and horizontal diffusion. In the scheme, two types of diffusion processes are applied in the diffusion stage in turn and the session key for the pseudo random number generator is dependent on the content of the image. The proposed scheme can efficiently resist known-plaintext and chosen-plaintext attacks. Theoretical analysis and computer simulation have also illustrated that our algorithm is effective and highly secure. In addition, a color image encryption scheme is proposed. In the scheme, the diffusion process which is carried out among all components to ensure a tiny change in one color component can spread out to all color components. Because the pixel at position (0,0) don't change its position during the permutation process based on discrete cat map, the session key for pseudo random generator and permutation process is the combination of the initial key and the pixel value at position (0,0). In this way, the proposed scheme can effectively resist known-plaintext and chosen-plaintext attacks.(4) Combined with the reversible data embedding technique, the authenticated encryption scheme for image is proposed. We propose two types of authenticated encryption scheme: message authentication code (MAC) then encryption and encryption then message authentication code (MAC). For the first type of authenticated encryption, the message authenticate code for plain image is embedded into the image by reversible data embedding technique first, then embedded image is masked by pseudo random sequence in CBC mode. For the second type of authenticated encryption, the image is first encrypted, and then the message authentication code for the encrypted image is embedded in the cipher image by reversible embedding technique. The proposed methods achieve not only privacy but also integrity. Based on the first method, we further propose an authenticated encryption scheme with tamper detection. The proposed scheme has the ability to detect the tampered region of the image.(5) We propose an encryption scheme for the compressed image. In the scheme, the image data is first encrypted in space domain and then is encrypted in frequency domain. The proposed scheme can not only achieve high security but also guarantee the efficiency of the compression algorithm.(6)Conclusions, as well as the future work, are given at the end of this thesis.