A New Construction Of Boolean Functions With Maximum Algebraic Immunity

In modern cryptography, attack and defense are two important subjects. At first we introduce LFSR-based stream cipher in cryptography has been threatened by the algebraic attacks, which means the LFSR-based generators’Boolean fuctions should have good cryptography properties to resist attacks effectively. Then we mainly introduce some basic knowledge of cryptography. They are necessary preparation knowledge in the process of constructing new Boolean functions. At last, we change the structure of a special kind of Boolean functions, then the thesis has got a class of new Boolean functions which can resist algebraic attacks well, and some relevant useful results.The paper is organized as follows:In the first chapter, we give a brief introduction about Boolean function and algebraic attacks, and the background of the article.In the second chapter, we recall some basic concepts and properties needed in this paper, and we discuss how to construct new Boolean functions.In the third chapter, we mainly study how to construct a new kind of Boolean functions with the property of resisting algebraic attacks. First of all, we change the structure of a special kind of Boolean functions. With the knowledge of matrix and rank, we can proof the new Boolean functions meet the requirements. Moreover, the exactly structure of a new form of Boolean functions is given.In the last chapter, by the conclusions of the third, a class of an odd number of Boolean functions with optimum algebraic immunity are obtained.