In this paper, we greatly increase the number of impossible differentials for SIMON and SIMECK by eliminating the 1-bit constraint in input/output difference, which is the precondition to ameliorate the complexity of attacks. We propose an algorithm which can greatly reduce the searching complexity to find such trails efficiently since the search space exponentially expands to find impossible differentials with multiple active bits. There is another situation leading to the contradiction in impossible differentials except for miss-in-the-middle. We show how the contradiction happens and conclude the precondition of it defined as miss-from-the-middle. It makes our results more comprehensive by applying these two approach simultaneously. This paper gives for the first time impossible differential characteristics with multiple active bits for SIMON and SIMECK, leading to a great increase in the number. The results can be verified not only by covering the state-of-art, but also by the MILP model.

在本文中，我们通过消除输入/输出差异中的 1 位约束，大大增加了 SIMON 和 SIMECK 的不可能差分的数量，这是改善攻击复杂性的前提。我们提出了一种算法，该算法可以大大降低搜索复杂度以有效地找到此类路径，因为搜索空间呈指数级扩展以找到具有多个活动位的不可能差异。除了中间错位之外，还有另一种情况会导致不可能微分的矛盾。我们展示了矛盾是如何发生的，并总结了它被定义为中间缺失的前提。通过同时应用这两种方法，它使我们的结果更加全面。本文首次给出了SIMON和SIMECK的多有效位的不可能差分特性，导致数量大幅增加。不仅可以通过覆盖最新技术，还可以通过 MILP 模型来验证结果。