基于plateaued函数的平衡布尔函数构造

布尔函数在对称密码的设计和分析中起着重要的作用。通过对谱不相交函数集中子函数平衡性的问题的研究给出了包含4个plateaued函数的函数集中有3个为平衡函数的充分条件。在此基础上,基于3个平衡的谱不相交plateaued函数,一类特殊的布尔置换以及一个高非线性度平衡函数,提出了一个构造高非线性度平衡布尔函数的方法。通过分析可知,利用该方法可以构造代数次数达到最优、非线性度不小于2^2k-1-2^k-1-2^k/2-2^?(k-1)/2?的2k元平衡函数。

Construction of balanced Boolean functions using plateaued functions

Boolean function plays an important role in the design and analysis of symmetric cryptography. Firstly, by studying the balanced property of subfunctions of the disjoint spectra function set, some sufficient conditions were provided that there were three balanced Boolean functions in the set of four plateaued functions. Then, based on three balanced disjoint spectra plateaued functions, a special Boolean permutation and a balanced Boolean function with high nonlinearity, a method of constructing balanced Boolean functions with high nonlinearity was proposed on a small number of variables. The analysis results show that the proposed method can construct the 2k-variable balanced Boolean functions with the optimal algebraic number and the nonlinearity is not less than 2^2k-1-2^k-1-2^k/2-2^?(k-1)/2?.