Information Security Research Based On Discrete Chaotic Theory

Under the rapid development of information technology, the security of information has attracted more and more attentions in recent years. Until now, a lot of research works have been made in depth and plentiful achievements have been obtained by the researchers in this field. However, there also exists much virgin field need to be dug up, and the information security technologies are not perfect and many of them have been attacked effectively. Because of the rapid development of the information technology, it is becoming increasingly difficult to maintain a satisfactory level of information security, and new information security theory and advanced technologies are required urgently. Chaotic dynamical system is a deterministic system and has random-like behavior. Since it is very sensitive to the initial conditions and control parameters, a large number of uncorrelated, random-like, yet deterministic and reproducible signals can be generated easily. These properties have natural affiliations with the information security technology. In these years, along with the development of the theory and application of chaos, many researchers are now focusing on the chaotic cryptography and information hiding based on chaotic theory. Nevertheless, considering the security and efficiency, there also exist some deficiencies in the presented information security schemes. In this thesis, we study the information security based on the discrete chaotic systems, including cryptography and information hiding. The main work and research results of this thesis lie in the following. (1) The main defects lying in feasibility and efficiency are pointed out through the study of M.S. Baptista's approach and a lot of modified methods presented by K.-W. Wong et al. In all these methods, the Logistic map is widely used. Since the output signal of the Logistic map is not uniformly distributed and there are infinite windows in its trajectory, the encrypted speed is not fast and the encryption algorithm would fail by chance if the control parameter of the Logistic map is not chosen properly. A new cryptosystem based on piecewise linear chaotic map (PLCM) which has a uniform distribution is presented. The experimental results demonstrate the efficiency of our new method. (2) A new class of dynamical cryptosystems based on discrete chaotic system are presented, which encrypt the ASCII coded plaintext directly. In our algorithms, the chaotic attractor region is divided into equal disjoint intervals, and every interval is associated with the plaintext unit to be encrypted which includes 0, 1 or a sequence composed of 0 and 1. Since a one-to-more mapping is created between the plaintext unit and the disjoint intervals, it is an efficient way to improve the encryption speed. Moreover, it is easy to avoid the defect existed in most of the chaotic systems that the output sequence has not a uniform distribution. The presented cryptosystem is generic and the secrecy resides entirely on the secret keys, which satisfy the Kerchoff's principle. (3) A new general key stream generator based on discrete chaotic maps is presented. The Hénon chaotic map and Logistic map are adopted in our generator. A matrix composed of 0's and 1's is generated by two Logistic maps, and a one-to-one mapping is created between the elements of the matrix and the intervals of the Hénon chaotic attractor. In order to avoid the finite precision effect existed in the discrete chaotic sequence, we apply a little permutation to the control parameters of the Logistic maps periodically. Thus the matrix is changed dynamically and the generated key stream has a long enough cycle length. The standard statistical tests demonstrate that the generated key stream has a random-like behavior, δ-like auto-correlation function and near-zero cross-correlation function. (4) A new image encryption scheme is presented, in which shuffling the positions of image pixels and changing the grey values of image pixels are combined. Firstly the Arnold map is used to shuffle the positions of the image pixels in the spatial-domain. Then the discrete output signal of the Chen's chaotic system is preprocessed to be suitable for the grayscale image encryption, and the disturbed image is encrypted by the processed signal pixel by pixel. The key space is large enough to resist the brute-force attack and the distribution of grey values of the encrypted image has a random-like behavior. Moreover, in order to improve the security of our algorithm, some possible attacks are considered and the corresponding modified methods are proposed in our algorithm. (5) A new generic transparency model for block-based watermarking method is presented. The transparency model is adopted as generic criteria to get highest robustness without losing transparency in our watermarking method. Two chaos-based watermarking methods using this model are proposed: A hybrid SVD-DCT watermarking method based on discrete chaotic system; a blind DCT watermarking method based on discrete chaotic system. In these two methods, a recognized pattern (a grayscale image or a binary image) is used as the watermark. In order to improve the security of our scheme, firstly the watermark is encrypted by chaos-based image encryption algorithm, and then another chaos-based encryption algorithm is used to choose the sub-blocks of the original image for watermark embedding.Finally, a summary has been done for all the proposed information security methods. And the research works in further study are presented.