The Criteria And Constructions Of High Nonlinear Resilient Boolean Functions

Resilient (balanced correlation immune) Boolean functions have important applications in nonlinear combiner model of a stream cipher systems. The main analysis content of this paper is about single output resilient Boolean functions. And this paper is concerned the criteria and constructions of high nonlinear resilient Boolean functions.About the criteria of high nonlinear resilient Boolean functions, first we study the security of it and analyze the divide and conquer attack and optimum affine approach attack. Then we study the criteria of high nonlinear resilient Boolean functions and the relation of this criteria each other.About the constructions of high nonlinear resilient Boolean functions, we study the in common use Boolean functions and base construction methods, which will supply some prepare for constructions of high nonlinear resilient Boolean functions in following text. Then we study the construction methods, which include two methods:The first method is about the concatenating of non common various functions. In the base of analyzing the concatenating of Bent function and linear function, we have concatenated the linear function and non-repeated homogeneous quadratic function. So we get the high nonlinear resilient Boolean functions.The second method is about a Maiorana-McFarland type construction in [13]. We have analyzed this construction and testified the conjecture that is about the relations of conditions which need be satisfied in the construction in [13].