The GAC Property of a Class of 1-Resilient Functions with High Nonlinearity

The absolute and sum-of-squares indicators are used to evaluate the Global avalanche characteristics (GAC) of Boolean functions in a global manner. The GAC properties of a class of highly nonlinear 1-resilient Boolean functions are given. We derive new upper bounds of the absolute and sumof-squares indicators for a class of 1-resilient Boolean functions with high nonlinearity. Compared to the known 1-resilient Boolean functions, the constructed functions possess higher nonlinearity and better GAC properties.