A Bound of Fast Algebraic Immunity of Constructions With BPR Using a Four-Disjoint-Part Support

Boolean functions are used for stream cipher ought to be a high fast algebraic immunity (FAI) to effectively against fast algebraic attacks. In the previous research methods, there is no suitable method to gain the FAI of Boolean functions using mathematical proof. However, Tang’s research results in 2017 broke the trend. They first mathematically proved that a class of 1-resilient Boolean functions has FAI greater than or equal to
$n-6$
. Expanding on Tang’s research methods, we prove the bound of FAI of constructions with bivariate polynomial representation using a four-disjoint-part support.