Study On Chaos Based Pseudorandom Sequence Algorithm And Image Encryption Technique

Image, as a kind of special data form, exists widely in military, diplomacy, satellite communication and people’s daily lives. Image data have many particular characteristics. For example, the data are two-dimentional, the energy distribution is not uniform. Especially, the sizes of many high-resolution images and remote sensing images are very big. The security protection to these kind of images need especially higher efficiency. While the classical cryptographic techniques are not appropriate. The appearance of chaos based cryptographic technique provides a new way to protect the security of images. Meanwhile, for many good chaotic systems, the efficiency is high and the cost is small. So chaos based cryptography is very suited to protect big images. However, because of some questions such as theoretical basis and implementation efficiency, the practicability of chaos based image encryption is limited. Aiming at the theoretical basis and implementation efficiency, the further study on chaotic systems, the secure and efficient pseudorandom sequence generation and image encryption schemes and their practical application have been the prominent problems in the study of chaos cryptography.The relationship between chaos based pseudorandom sequence generation and image encryption is close while relatively independent. Commonly, the chaotic sequences are discretized to get pseudorandom sequences, and the pseudorandom sequences serve as key-streams to encrypt images. From the point of theory research and practicability, the complex variable based chaos cryptography and hyperchaos based chaos cryptography are studied in this paper. The main research contents of this paper are as follows:The theoretical study on chaotic system is the premise to protect the security of images. But at present, few searchers prove the chaotic systems according to the definitions. Then the theoretical basis of chaos is weak. Aiming at this defect, we think that the study on complex chaotic mapping can strengthen the theoretical basis and practical value. So from the point of theory, the chaotic mapping in the complex field is studied. A chaotic mapping in the complex field is constructed and proved. Based on the further study on the complex chaotic mapping, it is expanded to be a parameterized mapping family. This mapping family is proved to be chaotic in the complex field by a conformal mapping. Moreove, its properties are analyzed.At present, most studies on complex chaos are about synchronization. The studies on complex chaos cryptography are less. But the performance of the real chaotic mapping(especially the low-dimentional real mapping) is easy to degenerate. Then the practicability of chaos cryptography is affected. The behaviors of complex chaotic mapping are more complicated. Applying the complex chaotic mapping to cryptography can add the variable number and improve the security. So we apply the complex chaotic mapping to cryptographic algorithms. At first, the complex chaotic sequences are discretized to get binary pseudorandom sequences with its probability distribution characteristics. Then the pseudorandom sequences are used as key-streams to ecnrypt images. The security protection of images is implemented in the complex fiels. It is a new idea to study chaos based image encryption.In many practical applications, because of the characteristics of chaos such as random-like behavior and topological transitivity, people want some nonlinear systems to generate chaos. So generating chaos purposefully becomes an important subject. Aiming at this actual demand, this paper studys the generation and performance analysis of hyperchaotic systems. By adding the state feedback controller, two hyperchaotic systems are constructed and their dynamic behaviors are analyzed. They both have two positive Lyapunov exponents. Their maximum Lyapunov exponents are bigger than many classical hyperchaotic systems. Their chaotic behaviors are more classical.Hyperchaotic systems are more complex than ordinary low-dimentional systems. Then the randomness of the sequences grows. Moreover, its one iteration can generate multiple sequences. So it can help to improve the efficiency of generating pseudorandom sequence and encrypting images. But most of the current hyperchaotic encryption algorithms have some defects. For example, the Lyapunov exponent is small, the analysis of the sequences is inadequate or the theory basis is not clear. So aiming at these problems, this paper selects the proposed hyperchaotic system with bigger Lyapunov exponent to generate pseudorandom sequences. In the generating process, Geffe logic is combined with the hyperchaotic sequence to overcome the performance degeneration. Moreover, one iteration of the system can generate multiple bits. So the efficiency of the algorithm is improved. The performance of the sequence is analyzed sufficiently. The generated pseudorandom sequences are used as the key-streams to encrypt images. In the encryption algorithm, the most important component is the dynamic S-box of the finite field. Its theory basis is described and analyzed in detail.At last, the hyperchaos cipher is applied to digital watermarking. The pseudorandom sequence generated by the hyperchaotic system is used to scramble the pixels to get uniform distribuction. The scrambled image, as the watermarking information, is embedded into the original image. The information of an block is saved in three positions. The tampering detection and self-recovery performs well.