Algebraic Immunity Of Boolean Functions

The development of cryptology is in struggle between cryptography and crptanalysis. There is no cipher in absolute safety,but be immune to all-known attacks.Boolean functions can be used to construct some cryptographic protocols widely.Their securities have close relation to the chosen Boolean functions.From the current references,many important results on Boolean functions have been achieved.But with the development of cryptology,many new problems need to solve.A new criterion—algebraic immunity is studied in this paper.According to the new requirement of Boolean functions on algebraic attack,the algebraic immunity is an important criteria for deciding the security of Boolean functions.In chapter 1,both the history and the new advance in cryptography and Boolean functions are mainly introduced,which include the applied background and the studying status in algebraic attack and so on.In chapter 2,some knowledge of cryptology based on algebra is briefly given,while the expression of Boolean functions and the fundamental nature of cryptography are focused on.In chapter 3,the algebraic attacks on block ciphers and stream cipher are investigated,the results of current research on are summarized and analyzed.In chapter 4, the algebraic immunity of Boolean functions is further studied.The main content is:(1)explain the principle of algebraic attack,and give the definition of annihilators of Boolean functions in existing articles;(2)discuss upper bound of minimal algebraic degree of annihilators for a random Boolean functions,meanwhile analyze the algorithm on deciding (non-)existence of low-degree annihilators;(3)the properties of annihilators of Boolean functions are introduced,the relations between the weight and the algebraic immunity of the Boolean functions are involved.