%A HUANG Jing-lian, WANG Zhuo and LI Juan
%T H Boolean Functions with Divided into Two Parts and High Nonlinearity Boolean Functions
%0 Journal Article
%D 2016
%J Computer Science
%R 10.11896/j.issn.1002-137X.2016.07.030
%P 166-170
%V 43
%N 7
%U {https://www.jsjkx.com/CN/abstract/article_15876.shtml}
%8 2018-12-01
%X Using the derivative of the Boolean functions and the e-derivative defined by ourselves as research tools,we studied the cryptographic properties of a class of H Boolean function which satisfy one degree propagation and are divi-ded into the product of two subfunctions,including nonlinearity,correlation immunity and algebraic immunity and so on.We achieved the relationship between the correlation immunity of this kind of H Boolean function and the two subfunctions,and also arrived at a conclusion on the correlation immunity of this kind of H Boolean function which can reach n2 －1.Moreover,we obtained the relationship between the lowest algebraic degree annihilator of this kind of an H Boolean function and the two subfunctions.Further,using e-derivative and derivative of a Boolean function,we constructed a cluster of H Boolean function which has the nonlinearity 2n－2+2n－3,the correlation immunity and 2-order algebraic immunity from obtained H Boolean functions.In this way,we resolved the problem of improving the nonlinearity of a Boolean function,and the existence problem of a Boolean function having higher nonlinearity,propagation,correlation immunity and higher algebraic immunity.