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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。
For the first time, the concept of strict avalanche criterion of order k is extended to multi-output Boolean functions. First, the strict avalanche criterion and diffusion criterion of multi-output function are studied. Two necessary and sufficient conditions for the multi-output function to satisfy the strict avalanche criterion of order k are given. It is proved that the multi-output Boolean function must satisfy the low-order strict avalanche criterion when satisfying the high-order strictly avalanche criterion. Then, based on the properties of symmetric functions and the knowledge of number theory, the strict avalanche criterion, the diffusion criterion and the strictly avalanche property of multi-output symmetric Boolean functions are studied. The necessary and sufficient conditions for the corresponding criteria are given. Two k Combined discriminant formula of strict avalanche criterion.