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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Δf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Δf,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,Δf,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 The concept of the global avalanche characteristic of a single function f is proposed, and the upper and lower bounds of the squared sum indicator σf and the absolute indicator Δf of a single function avalanche characteristic are given. Zhou Yu et al. Promoted the above concept and proposed the concept of global avalanche characteristics of two functions f and g. They present the square sum indicator σf, g and the absolute indicator Δf, g of the global avalanche characteristics of the two functions. Then we define two new indices: λf (which means minimum value of σf, g when g traverses all n-ary Boolean functions) and βf (minimum value of Δf, g when g traverses all n-ary Boolean functions). The value of λf is obtained, giving the upper and lower bounds of λf and βf.