Research On The Correlation-immune Of H-Boolean Function

The information security is a comprehensive interdisciplinary studies, It involves mathematics, cryptography, computer science, communications and many other disciplines. In the recent 20 years, computer, communications and networks contribute significantly to the rapid development of information acquisition, processing, storage, transmission and other operational capabilities, but also broaden the scope of application of information. Cryptography is the basis of information security,it can be said that there is no information security and cryptography, would not be information security. Foreign experts had been a hot research on Boolean functions in cryptography because of its important applications in the domestic. Especially in the stream cipher system, Boolean functions as an important component of the password in key stream generator directly determine the nature of the cryptosystem security. Boolean functions used in cryptographic system must possess certain cryptographic properties,such as balanced state, correlation immunities, diffusibility and so on.And H-Boolean functions have inherently invasive and strict avalanche criterion for Boolean functions,which is a kind of great research value of the Boolean function. This paper studies the structure determination methods of the correlation-immune balanced H-Boolean function, based on the focus of study with a correlation-immune H-boolean function.In the article, we first introduced some basic concept of cryptography and H Boolean function, and then we discussed the cryptography characters and their relationships of Boolean function. Finally, we discussed the correlation-immunity and Generalized correlation-immunity of H Boolean function. The general H Boolean function don't have many cryptography characters, and can't be used in cryptography directly. We need some ways to construct H Boolean with many cryptography characters, for example, the H Boolean function with banlance and correlation-immune. In this regard, the research results at home and abroad are less.The main research results are as follows:On the basis of the research on the basic concept and in cryptology nature of H Boolean function, Took the derivative and e-derivative of Boolean function as a tool, research on the first-order correlation immune Boolean functions,and obtained the judgments and construct theorem of the first-order correlation-immune H-Boolean functions.Analyzed the inner structure of balanced H-Boolean functions, clearly obtained the conclusion that the second-order correlation-immune balanced H-Boolean function is not existent, solved the problem that whether there was a second-order correlation-immune balanced H-Boolean function which has not yet proper result, and derived the algorithms which reduced the balanced H-Boolean function correlation-measure, and while increased the order of correlation-measure.On the basis of the research on the differential coefficient of Boolean function, make the weigh scope of existing second-order correlation-immune Boolean functions, given the application of theorem for constructing a second-order correlation-immune Boolean functions.