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Linearly equivalent S-boxes and the division property

机译：线性等效的S箱和分区属性

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Division property is a cryptanalysis method that proves to be very efficient on block ciphers. Computer-aided techniques such as MILP have been widely and successfully used to study various cryptanalysis techniques, and it especially led to many new results for the division property. Nonetheless, we claim that the previous techniques do not consider the full search space. We show that even if the previous techniques fail to find a distinguisher based on the division property over a given function, we can potentially find a relevant distinguisher over a linearly equivalent function. We show that the representation of the block cipher heavily influences the propagation of the division property, and exploiting this, we give an algorithm to efficiently search for such linear mappings. As a result, we exhibit a new distinguisher over 10 rounds of RECTANGLE, while the previous best was over 9 rounds, and rule out such a distinguisher over more than 9 rounds of PRESENT. We also give some insight about the construction of an S-box to strengthen a block cipher against our technique. We prove that using an S-box satisfying a certain criterion is optimal in term of resistance against classical division property. Accordingly, we exhibit stronger variants of RECTANGLE and PRESENT, improving the resistance against division property based distinguishers by 2 rounds.
机译：司属性是一种密码分析方法，证明在块密码上非常有效。计算机辅助技术，如MILP已被广泛且成功地研究了各种密码分析技术，特别是对该分区属性的许多新结果导致了许多新的结果。尽管如此，我们声称以前的技术不考虑完整的搜索空间。我们表明即使以前的技术未能基于给定函数的划分属性找到频道区，我们也可以通过线性等效功能找到相关的频道。我们表明，块密码的表示大量影响了分区属性的传播，并利用这一点，我们提供了一种有效地搜索此类线性映射的算法。因此，我们在10轮矩形中展示了一个新的聊天区，而以前最好的是超过9轮，并排除了超过9轮目前的区分机。我们还对S-Box的构建进行了一些洞察力，以加强对我们技术的块密码。我们证明，使用满足某种标准的S盒在抵抗古典分区属性的抵抗期间是最佳的。因此，我们表现出较强的矩形变体和存在，提高了2轮的分裂性区分区分的阻力。

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