Study On Application Technology Of Chaotic Digital Encryption

With the speedy development of communication technology, informationization process has been impelled. It does not only bring facility for human's work and life, but also poses big potential risk. People are anxiously expecting new and more secure information technology with given the traditional encryption algorithms have been successful cracked. The chaos with its ergodicity, unpredictable orbit and extremely sensitivity to initial status has be widely applied in communication, control, test and cryptography fields, and achieved prosperous progress. The paper mainly studies chaotic sequence encryption and designs a series of image encryption algorithm, digital watermark algorithm and Hash function based on the chaotic pseudo-random sequence. The article comprises of the following 5 parts.Part one: Firstly, It describes its development of cryptography and information security in recent years, meanwhile, it mentions traditional encryption algorithm has been cracked or has potential risk with the speedy development of technology of computer and internet, and then we apply the chaotic systems to encryption. Chaotic encryption is a new direction of modern cryptography. We make detailed introduction of the behavior and study method of chaos, and use strict mathematics to define chaos according to Li-Yorke's definition. Furthermore, it describes the achievement and advancement in this field during recent years within chaos theory. The study of chaos encryption focuses on the chaotic block cipher and sequential cipher. The difference between them is the way of using secret key and the speed of the whole encryption process. Chaotic sequence encryption has been widely applied with high efficiency. Study and application of chaotic sequence encryption is the major subject of this thesis.Part two: Launched from the concept of pseudo-random sequence and its development. The random sequence is divided into real random sequence created by physical method and pseudo-random sequence with certain probability distribution caused by algorithm simulation. Pseudo-random sequence is made from definite algorithm or process, also easily managed and regenerated. It's applied widely because of its similar white noise characteristics, quick process and high efficiency. There exist many methods to construct pseudo-random sequence generators by applying chaotic systems. In this part we propose an innovative method by applying the generalized Henon map which can be infinite dimensional chaotic system in theory to build a pseudo-random sequence generator. By analyzing the statistical characteristics of the pseudo-random sequence which is generated by the generalized Henon map, we have realized that the randomicity of the sequence is not very ideal. So, a new algorithm is created to optimize the sequence, and then the improved sequence is transformed into binary one. After that the statistical test (such as frequency test, serial test, poker test, auto-correlation test, runs test) and the security analysis (such as key space, sensitivity and linear complexity properties) are conducted to testify the excellent random statistical characteristics of the chaotic binary sequence and set up better foundation for the following encryption algorithm based on chaotic sequence.Part three: Started from the digital image encryption. It describes the importance of digital image encryption and the achievement in the study of image encryption. Traditional digital image encryption algorithms adopt simple linear methods to confuse the arrangement of pixel position and replace the pixel value of the original image. But because of the huge data volume and the high correlation between the adjacent pixels of digital image, traditional image encryption method can't reach the ideal effect, and also very low in efficiency. Therefore, this part proposes to apply the chaotic system to encrypt digital image. The main idea is: To apply chaotic system to create chaotic pseudo-random sequence, and then build the confusion matrix and transform matrix by using the sequence to confuse the pixel position and change the pixel value of the image. And then verify its encryption effect by simulation. Finally, the excellent encryption performance and strong resistance of the algorithm can be testified by the analysis of key space, sensitivity, statistics and anti-interference capabilities.Part four: First of all, it briefs the basic model and its performance evaluation of image digital watermark. Digital watermark includes four parts, which are creation, embedding, extraction and detection. According to embedding position, image digital watermark is divided into space-time domain and transform domain watermark. Embedding method for space-time domain watermark is designed to directly modify the pixels and hide the digital watermark into the pixels of the original image. The advantage of space-time domain watermark is that it is easy to realize, and contains large amount of information and has high efficiency, but the disadvantage is not very robust. Normally, the study of embedding algorithm of image watermark is concentrated in the transform domain, especially based on DCT and DWT. The main purpose is to decompose the image signal into high and low frequency. The low-frequency coefficients typically represent the general shape, whereas outline and the high-frequency coefficients describe shape details and sharp corners. The low-frequency part gathers a greater amount of energy of image, which is an important part for vision. Therefore, the embedding of the image watermark is mostly located in low frequency part to ensure wartermark's robustness. The extraction of a watermark is the inverse process of embedding. The detection method is to calculate the similarity between the restored watermark and original watermark. We can define a threshold of the similarity to assess the existence of the watermark, if the similarity surpasses the threshold there will be a watermark in the image. The main idea on chaotic digital watermark is to confuse the watermark by applying chaotic sequence and embed it into the original image so as to prevent the watermark from being restored. Even though the confused watermark is successfully restored by attacker, if he does not understand the model and the key of the chaotic system he can never crack or forge it. Finally, the results of simulation can verify that the algorithm designed in this part has excellent visual effects and robustness with strong resistance to attack.Part five: This part mainly studies the construction of Hash function based on the chaotic systems. Firstly, introduce the basic characteristics of Hash function. It is imperative to design new and more secure Hash function in data integrity and information authentification because some classical Hash functions such as MD4, MD5 and SHA-1 have been cracked by some researchers. The ergodicity, unpredictable orbit and initial sensitivity characteristics on chaos match with the requirements on Hash function which has good diffusibility, forgery prevention capability, irreversibility and initial sensitivity. Therefore, to build Hash function by applying chaotic system has become the hot topic for current investigators. In this part, two kinds of instruction algorithms of Hash function are mainly designed, one is based on the generalized Henon map and the other one is based on the composed chaotic system combined from infinite collapse chaotic map and the generalized Henon map. The main intention of the algorithm is to divide the message into groups, create chaotic sequence by initial key and then make the XOR operation for each section by the chaotic sequence. The result will be used as the new key of the next loop to generate the new chaotic sequence. Repeat the procedure until the entire message has been processed, then the final sequence should be the Hash value. Finally, we use security analysis to testify the high confusion and diffusion capability, excellent statistical properties, strong collision resistance and great initial sensitivity of our Hash function and the comparison with other research can indicate that our scheme is better.