Constructions Of Resilient Boolean Functions

Boolean functions are important components of block ciphers, stream ciphers and Hash functions. The cryptographic criteria of Boolean functions are crucial to the security of cryptographic algorithms. Correlation immune of Boolean functions is to prevent correlation attacks on the cryptographic systems and suggested that the concept was put forth, it caused widespread attention, especially Xiao Guozhen and Massey proposed the spectral characteristics related to correlation immunity function theorem (Xiao-Massey theorem), correlation immunity function and resilient functions are more profound understanding by people. To prevent algebraic attacks, the research on Boolean functions to be used in the cryptographic systems provides a new cryptographic criteria: algebraic immunity. Possessing optimum algebraic immunity is a necessary criteria for Boolean functions used in the cryptographic systems against algebraic attacks. The study of the cryptographic criteria of Boolean functions is important in the design and analysis of cryptographic algorithms.In this thesis, the recent constructions of resilient Boolean functions are reviewed at first. Based on the system summary of the existing constructions of resilient Boolean functions, by developing the idea of the 1-resilient functions given by Tang X.H. et al., we present two classes of even and odd variables resilient Boolean Function with almost optimal nonlinearity respectively, and analysis the nonlinearity of constructed functions. Then the construction based on plane theoretical of Boolean functions with maximum algebraic immunity (MAI) have been studied, given a class of n-variables 1-resilient Boolean functions with MAI, and their nonlinearities are also determined, which is higher than the Boolean functions of the existing structure.