Based On Global Optimization Search Good Password Properties Of Boolean Function Structure Strategy

Information security has been occupying an important position in information science. In today’s society, with the advent of the information age, particularly the growing popularity of the network environment, the security of the transmission and storage of information has received more and more attention. The importance of information security in the areas of military, scientific research, communications and computer science becomes more apparent. Cryptography, as the most important part of information security, has undergone dramatic development from Caesar Cipher to quantum computing, and has gradually become a comprehensive cutting-edge science with the wide application of computer and information technology. Also, cryptography has close link with mathematics, computer science, information science, acoustics, physics, linguistics and other disciplines. While the continuous integration of advanced theoretical results and experience of various disciplines has led to numerous results which contain human innovation. These results not only play important roles in the actions of nations to occupy information highland, but also constantly drive the development of information security forward. Cryptography is the one covering a broad range of disciplines, and this article mainly focused on the fields of cryptography which are popular in recent years such as algebraic attack and construction methods on Boolean functions.In recent years, algebraic attacks get more and more attention in the field of cryptography. A variety of effective algebraic attack modes have been proposed, and implemented on experiments attacking the cryptosystems which used to be considered safe with good results. Algebraic attacks have changed the traditional understanding of ciphers and make researchers begin to study many resistances of the cryptosystems with the tool named Boolean function. The algebraic immunity (AI) is the characteristic which measures the resistance to algebraic attacks. In this paper, we primarily analyze the AI of Boolean functions, and give some attention on that of symmetric Boolean functions. Moreover, we have also made some study on other cryptographic properties such as nonlinearity, resilience and so forth.Boolean functions with good cryptographic properties can be used as strong keys of cryptosystems to make them have resistances to many attacks. Consequently, constructing Boolean functions with good cryptographic properties is the focus of researches in this area. Traditional construction methods either put some limitations on the functions which restrict the performance of the Boolean functions under other evaluation criteria, or make some complicated operations to find Boolean functions in the subset of ones that already have some cryptographic properties. We analyze the relationship between different cryptographic properties of Boolean functions especially between AI and nonlineariy based on the study of existing construnction methods, and design a construction strategy of Boolean functions with good cryptographic properties based on global optimization search algorithms. Main works in this paper are as follows:We analyze and study important cryptographic properties of Boolean functions systematically with Walsh spectrum. Also algebraic attacks, AI and some existing construction methods of Boolean functions have been studied. We introduce some cryptographic characteristics of symmetric Boolean functions such as degree, nonlinearity and AI. Meanwhile we make a more detailed discussion on the construction methods of symmetric Boolean functions with maximum AI.We use the global optimization search algorithm to design a strategy for constructing Boolean functions with good cryptographic properties. Using genetic algorithm and combining nonlinearity with degree of Boolean functions as the selection criteria, the efficiency of the searching and selecting Boolean functions with good nonlinearity and high degree from the set of Boolean functions with high AI has been improved.From some experimental results analysis, this strategy can obtain Boolean functions with good cryptographic properties. Meanwhile, different adjustment with specific methods can be made to meet different requirments for cryptographic properties, and therefore this strategy can get greater freedom and wider scope of application.