Generalized Feistel structures are widely used in the design of block ciphers. In this paper, we focused on retrieving impossible differentials for two kinds of generalized Feistel structures: CAST256-like structure with Substitution-Permutation (SP) or Substitution-Permutation-Substitution (SPS) round functions (named and , respectively) and MARS-like structure with SP/SPS round function (named and , respectively). Known results show that for bijective round function, CAST256-like structures and MARS-like structures have () and () rounds impossible differentials, respectively. By our observation, there existed () rounds impossible differentials in and () rounds impossible differentials in (this result does not require the P layer to be invertible). When the diffusion layer satisfied some special conditions, had () rounds impossible differentials and had () rounds impossible differentials.

中文翻译：

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两个广义Feistel结构的不可能微分判别器

广义Feistel结构广泛用于分组密码的设计中。在本文中，我们将重点放在检索不可能差为两类广义Feistel结构的：CAST256状可替代产品的置换（SP）或替代的置换-换人（SPS）的循环函数（命名结构和，分别地）和MARS状结构与SP / SPS循环函数（命名和，分别地）。已知结果表明，对于双射回合函数，CAST256类结构和MARS类结构分别具有（）和（）个回合不可能的微分。根据我们的观察，）舍入不可能的微分，而（）舍入不可能的微分（此结果不需要P层是可逆的）。当扩散层满足某些特殊条件时，具有）舍入不可能的差异，并（）舍入不可能的差异。