布尔函数全局雪崩特征的两个新指标

摘要

ZHANG Xian-Mo 和 ZHENG Yu-liang 提出单个函数 f 的全局雪崩特征的概念,并且给出单个函数雪崩特征的平方和指标σf 与绝对指标△f 的上下界。周宇等将上面的概念作了推广,提出了两个函数 f 和 g 全局雪崩特征的概念。他们给出了两个函数全局雪崩特征的平方和指标σf,g与绝对指标△f,g。进而定义两个新指标：λf(指 g 遍历所有 n 元布尔函数时,σf,g取得的最小值)和βf(指 g遍历所有 n 元布尔函数时,△f,g取得的最小值)。得到了λf 的值,给出了λf 和βf 的上界和下界。%ZHANG Xian-Mo and ZHENG Yu-liang suggested the notion of global avalanche characteristics of single Boolean function f,and introduced the sum of squares indicatorσf and the absolute indicator △f . ZHOU Yu et al. generalized the above notions. The notion of global avalanche characteristics of two Boole-an function f and g is proposed, and the sum of squares indicatorσf,g and absolute indicator △f,g of global avalanche characteristics of two Boolean function f and g are defined. Given n-variable function f,λf , which is minimum value of σf,g ,where g is any n-variable Boolean function ,is defined. βf ,which is mini-mum value of △f,g ,where g is any n-variable Boolean function ,is defined. These are two new indicators.λf is computed. The lower and the upper bounds of λf and βf are given.