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Dual Relationship Between Impossible Differentials and Zero Correlation Linear Hulls of SIMON-Like Ciphers

机译：SIMON类密码的不可能微分与零相关线性壳之间的对偶关系

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As far as we know, for impossible differentials and zero correlation linear hulls of SIMON-like ciphers (denoted as SIMON in our paper), the distinguishes previously constructed by the miss-in-the-middle technique are all based on bit-level contradictions. Under this condition, our results on the two kinds of distinguishers are presented as follows: Firstly, by introducing both the diffusion matrix and the dual cipher of SIMON, we establish some links between impossible differentials and zero correlation linear hulls for SIMON and its dual cipher. For SIMON, we prove that there is a one-to-one correspondence between impossible differentials and zero correlation linear hulls. Meanwhile, for SIMON and its dual cipher, we show that there is also a one-to-one correspondence between impossible differentials of one cipher and zero correlation linear hulls of the dual one. Secondly, we show that impossible differentials and zero correlation linear hulls of SIMON can be constructed by a matrix calculation approach. Finally, when applying our method to SIMON with some specific parameters, we show that SIMON with parameter (1,0,2) recommended at CRYPTO 2015 is worse than the original SIMON with respect to security against impossible differential and zero correlation linear cryptanalysis.
机译：据我们所知，对于SIMON类密码（在本文中称为SIMON）的不可能的微分和零相关线性外壳，以前由中间遗漏技术构造的区别都是基于位级矛盾的。在这种情况下，我们对两种区分器的研究结果如下：首先，通过引入SIMON的扩散矩阵和对偶密码，我们建立了SIMON及其对偶密码的不可能微分和零相关线性壳之间的一些联系。 。对于SIMON，我们证明了不可能的微分与零相关线性外壳之间存在一一对应的关系。同时，对于SIMON及其对偶密码，我们证明了一个密码的不可能微分与对偶密码的零相关线性外壳之间也存在一对一的对应关系。其次，我们表明可以通过矩阵计算方法构造出SIMON不可能的微分和零相关线性船体。最后，当将我们的方法应用于具有某些特定参数的SIMON时，我们表明CRYPTO 2015推荐的参数（1,0,2）的SIMON在针对不可能的差分和零相关线性密码分析的安全性方面比原始SIMON差。

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