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从研究全局雪崩准则的表达方式出发,提出了全局雪崩准则的矩阵表示方法,并证明了布尔函数f(x)与f(x+α)全局雪崩的绝对值指标和平方和指标相同。依据矩阵表示方法得到了全局雪崩准则与布尔函数Walsh谱值的关系,并给出了一个布尔函数同一个仿射函数的互相关全局雪崩准则绝对指标的上、下限。最后,分析了修改序列中的一位对布尔函数全局雪崩准则指标的影响,结合爬山算法设计了一种修改M-M型Bent函数的优化算法,得到的布尔序列在非线性度和全局雪崩准则指标上优于已有的构造。
Based on the study of the global avalanche criterion expression, a matrix representation method of global avalanche criterion is proposed, and the absolute value of the global avalanche of the Boolean functions f (x) and f (x + α) is the same as the square sum indicator. The relation between the global avalanche criterion and the Walsh spectral value of the Boolean function is obtained according to the matrix representation method. The upper and lower bounds of the absolute index of the cross-correlated global avalanche criterion for the same affine function of a Boolean function are given. Finally, the influence of one bit in the modified sequence on the global avalanche criterion of the Boolean function is analyzed. An optimization algorithm to modify the Bent function of the MM type is designed in combination with the hill-climbing algorithm. The Boolean sequence is obtained on the basis of nonlinearity and global avalanche criterion Better than the existing structure.