Abstract: In this paper，the k-th order strict avalanche criterion of multi-output Boolean function is firstly researched.Two necessary and sufficient conditions of the multi-output Boolean functions satisfying k-th order strict avalanche criterion are presented，and the rule that a multi-output Boolean function fulfils the strict avalanche criterion of lower order if it fulfils the strict avalanche criterion of higher order is proved.By applying symmetric functions’ property and number theory，the necessary and sufficient conditions of the symmetric multi-output functions satisfying the strict avalanche criterion，propagation criterion，and k-th order strict avalanche criterion are presented.Especially，it gets two combination discriminants of the symmetric multi-output functions satisfying k-th order strict avalanche criterion.

摘要： 首次将k阶严格雪崩准则的概念扩展到多输出布尔函数上，首先研究了多输出函数的严格雪崩准则、扩散准则，给出了多输出函数满足k阶严格雪崩准则的两个充分必要条件，证明了多输出布尔函数满足高阶严格雪崩准则时一定满足低阶严格雪崩准则。然后根据对称函数的特性，应用数论的知识，研究了多输出对称布尔函数的严格雪崩准则、扩散准则和k阶严格雪崩性质，给出了相应准则的充分必要条件，特别给出了两个k阶严格雪崩准则的组合判别公式。