A Study On Chaos Theory And Its Application In Information Security

With development of information technology and increasing frequency of information exchange, the research on information security engineering is becomming more and more important. As a novel technology in cryptography, digital chaotic cipher has been attracted researcher dense interest and widely studied.Chaos, as a kind of nonlinear phenomenon, have many remarkable characteristics: such as pseudo-random, unpredictability of evolution of its orbits, properties of mixing and sensitivity to initial conditions and system parameters. These characteristics are in accordance with the requirements of cryptography. Research shows that there are some relation between traditonal cipher and chaos. Challenges have been set with traditional cryptography because of the bulk data capacity and high redundancy of widely-used patterns and multi-media information, while chaotic cipher has great superiority over the encryption of multi-media information. This thesis is first to introduce the development, rudimentary and relevant knowledge of chaos theory. The relationship between chaos and cryptography from the piontview of chaotic stream cipher and chaotic block cipher is discussed in detail. We focus on chaos Hash algorithm, chaotic cipher based on searching and imaging encryption of chaos. The main contribution is as follows: 1) Research on the relationship between chaotic map and cryptological transformation, especially, the chaotic pseudo-random bit sequence and pseudo-random sequence. The detailed analysis on emerengy of four kinds of chaotic pseudo-random bit sequence is introduced and expatiated. 2) A new Hash function is constructed. The advantages of the proposed Hash function are analyzed when chaotic map is uesd in one-way hash function,the construction of one-way hash function is based on Logistic map, which fulfills 128bit Hash of original one-way Hash of free length, is proposed. Through detailed analysis, the construction illustrates uncomplicated, highly sensitive to initial conditions and has excellent property of one-way Hash function. 3) Chaotic cipher based on searching, proposed by M. S. Baptista and E. Alvarez, has been widely studied in the field of chaotic cipher. Many researchers have provided some revisions, and this thesis puts forward the new revision of K. W. Wong's and Li Shujun's scheme. Based on the analysis of the characteristic of Chinese character code and compared with the chaotic cipher scheme of M. S Baptista , the chaotic Chinese character encryption scheme, which is based on searching, is put forward. 4) With the superiority of chaotic cipher over imaging encryption, this thesis emphasizes on the research on chaotic imaging encryption technology and the method of imaging permutation matrix, produced by one dimensional chaotic map, two dimensional chaotic map and three dimensional chaotic map respectively. This method is capable of changing original images into unrecoganizable chaotic images, which offers to protect the real content of digital images. In the application of one dimensional chaos, the author puts forward a new method of producing imaging permutation matrix by using two one-dimensional chaotic system, which is of high speed and good permutation effects. In the application of two-dimensional chaos, the author puts forward and analyzes the scheme of image fulfillment by using chaotic system, which is based on the analysis of characteristic of Baker map in imaging encryption. In the application of three dimensional chaos, the author puts forward a three-dimensional chaotic system with parameter, and makes detailed security and statistical analysis. This three dimensional chaotic system, which has a large key space, has made great progress in the speed and security of image encryption, and it also proves its superiority over imaging encryption through computer simulation.