Hamming重量为k的布尔函数的全局特征和非线性度
doi: 10.3724/SP.J.1146.2007.01276
Global Avalanche Characteristics and Nonlinearity of Boolean Function with the Hamming Weight k
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摘要: 该文给出了布尔函数的自相关系数和互相关系数的一些性质，得到n元布尔函数f (x)满足t 阶扩散准则时，n，t 和Hamming重量wt(f)的制约关系，给出了任意Hamming重量为k的布尔函数的平方和指标下界表达式，推出了仅由布尔函数Hamming重量所确定的非线性度的上界表达式。这些结论推广了已有结果。Abstract: Some properties of autocorrelation coefficient and cross-correlation coefficient are given. The restricted relationship among n(n variables, wt(f) (the Hamming weight of Boolean function f (x) and t (t-th propagation criteria) was derived, then a lower bound on the sum-of-squares of any Boolean functions with Hamming weight k is concluded. Finally, the results generalized a upper bound on nonlinearity of Boolean function only depending on Hamming weight. This paper improved known results.
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