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ZHANG Xian-Mo和ZHENG Yu-liang提出单输出布尔函数f的全局雪崩特征的概念,并且给出单输出布尔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,提出了两个单输出布尔函数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。将GF(2)变为剩余类环Zq和将单输出变为多输出,可以进一步推广上述两个指标。设f和g是Znq到Zmq的函数,定义指标ξf,g和ρf,g,给出了ξf,g和ρf,g的上界和下界。
ZHANG Xian-Mo and ZHENG Yu-liang The concept of global avalanche characteristics of single-output Boolean function f is proposed. The upper and lower bounds of the square-sum indicator σf and the absolute indicator Δf of the avalanche characteristics of the single-output Boolean function are given. Zhou Yu et al. Promoted the above concept and put forward the concept of global avalanche characteristics of two single-output Boolean 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. Converting GF (2) to the residual class ring Zq and turning the single output into multiple outputs can further promote both of these metrics. Let f and g be functions of Znq to Zmq, define the indices ξf, g and ρf, g and give the upper and lower bounds of ξf, g and ρf, g.