Study On Hash Function Based On Macro And Micro Chaotic Maps And Its Application In Image Encryption

As an important branch of modern cryptography, hash function is the key technology of data integrity verification, identity authentication and digital signature. However, with the development of information technology and the deepening of theoretical research, some defects of the traditional hash algorithms are exposed, such as low efficiency, poor performance of anti-collision, suffer from various forms of attack easily. Encryption systems based on these algorithms are being threatened for those reasons. It's the key problem to be solved by designing hash function which are more secure and efficient.The emergence of chaos theory has made a breakthrough in many fields of research. Hence, the hash function is constructed by taking into account the excellent inherent characteristics of chaos, which to make up for the shortcomings of traditional hash scheme.This paper deeply analyzed the quantum chaotic maps and several highdimensional chaotic maps from microscopic field and macroscopic field respectively, and designed different types of secure hash algorithms. In addition, the new hash functions are applied in the field of digital image encryption. Specific innovations are as follows:(1) This paper proposes a hash algorithm based on quantum chaotic map. Using the characteristic which the quantum system can return to the initial state accurately after the time-reversal, importing it to the design of hash function creatively. And it analyses the dynamics of the quantum system, calculates the max Lyapunov exponents by the Jacob matrix, and describes its trend in the changes of the parameters. Combined with the analysis of the bifurcation diagram, it shows that the quantum map has a stronger non periodicity than the classical chaotic maps, and it is more suitable for the hash algorithm. Compared with hash schemes based on classical chaotic systems, the scheme of quantum chaos has great advantages in plaintext sensitivity, confusion and diffusion properties and collision attack resistance.(2) This paper proposes a hash scheme based on multi-layer chaotic neural network(CNN) and high-dimention Arnold maps. First, it constructs a CNN model with hidden layer, and analyses the chaos characteristics to the proposed high-dimention Arnold maps, and uses them to generate the weight matrice, which are used to link the CNN layers, bias and the parameter vector of transfer functions. Dealing with brute force by using huge key space is one of this algorithm's advantages. Also it can generate the hash value with arbitrary multiple of 128-bit length, so that it reflects the extensible property of this algorithm. Simulation results and theoretical analysis show that the proposed scheme is superior to the existing hash schemes in terms of safety performance.(3) This paper proposes an image encryption and decryption scheme based on the chaotic hash function with keys. It transforms the external key into the chaotic encryption matrix of the image encryption algorithm by utilizing the one-way characteristic and the pseudo-random characteristic of the hash function skillfully. The internal keys of the encryption algorithm are obtained from the modulo operation to combining the chaotic encryption matrix and the original image, which makes the key of the different images are different. It significantly improves the ability of the encryption algorithm to resist attacks. This scheme has better safety performance and efficiency through the analysis and comparison of the correlation, the information entropy, the avalanche criterion and the encryption speed.