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With the rapid development of computer network technology, The human society has entered a new era—Information age. In the information age, people’s learning, living and working has undergone enormous changes, they can exchange a lot of information through the network. But the network bring people Security issue when it bring people convenience. Hash function is an important part of Cryptography, it is widely used in digital signatures, data integrity detection and authentication. The Hash functions MD5and SHA-1are used commonly in the international, however, with the continuous development of cryptographic techniques, MD5and SHA-1have been successfully deciphered by cryptologists, they are proved to be unsafe. In recent years, because chaos has pseudorandomness, aperiodic, unpredictability and initial value sensitivity, and so on, using chaotic systems to design the Hash function is becoming a research hotspot in the cryptography.The contents of this thesis include the following aspects:(1) The research basis of Hash function and chaos basic theory are introduced. First, the basic definitions, basic properties, the practical application, iterative structure and evaluation of Hash function are introduced. Then, chaos basic theory is presented. Finally, design methods of chaotic Hash function are presented.(2) Chaotic Hash function based on the Tandem-DM construction is proposed. Chaotic map of the proposed algorithm is discrete chaotic map which calculates in the integer domain, compared to floating-point Computing, it has faster computing speed. The proposed algorithm uses discrete chaotic map to construct discrete chaotic map network which is used in the Tandem-DM construction, and produce256-bit Hash value. Simulation results indicate that the algorithm has characteristics of one-way, confusion and diffusion, and collision-resistance, and it can satisfy all the performance requirements of Hash function.(3) Chaotic Hash function based on the tree structure is proposed. The algorithm is a keyed hash function, its iterative structure is tree structure, and its compression function adopt method of permutation-truncation. The core component of the compression function is the crossing coupled map lattice. Integer crossing coupled map lattice is used to extend the initial keys to get sub-keys which are applied to the iterative process of crossing coupled map lattice. Based on tree structure, the algorithm can produce128-bit,224-bit,256-bit,384-bit and512-bit Hash value with compression function processing. Simulation results show that the algorithm has good security and high parallelism, and satisfy all the performance requirements of Hash function.At last, to conclude the thesis, and to point out problems in the study of chaotic Hash function.
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