On Higher-order Correlation Immunity and Higher Nonlinearity for a Class of Boolean Functions

Jinglian Huang, Zhuo Wang, Chunling Zhang
2016 DEStech Transactions on Engineering and Technology Research  
In this paper, we study the higher-order correlation immunity and the higher nonlinearity of Boolean functions, which is constructed by dividing the set of n-variable independent into two parts. With the propagation of a Boolean function, we construct a class of Boolean functions with 1-order algebraic immunity and higher-order correlation immunity, and reveal the relationship between the correlation immunity and 1-degree annihilator of Boolean functions. Meanwhile, with the lowest algebraic
more » ... ree annihilator of Boolean functions, we also derive the invariance of the nonlinearity of Boolean functions with higher correlation immunity, and prove the existence of a class of a Boolean function with higher nonlinearity.
doi:10.12783/dtetr/iect2016/3810 fatcat:u2zwwqijfffn3j2qgzbhe3aj4q