A Lower Bound of Fast Algebraic Immunity of a Class of 1-Resilient Boolean Functions

Boolean functions should possess high fast algebraic immunity when used in stream ciphers in order to stand up to fast algebraic attacks. However, in previous research, the fast algebraic immunity of Boolean functions was usually calculated by the computer. In 2017, Tang, Carlet, and Tang first mathematically proved that every function belonging to a class of 1-resilient Boolean functions has the fast algebraic immunity no less than n - 6. Inspired by the Tang's method, we also demonstrate that the fast algebraic immunity of another class of the 1-resilient Boolean functions is no less than n - 6. Meanwhile, we also prove some combinator facts originated from the Tu-Deng Conjecture.