Civino et al. (2019) have shown how some diffusion layers can expose a Substitution-Permutation Network to vulnerability from differential cryptanalysis when employing alternative operations coming from groups isomorphic to the translation group on the message space. In this study, we present a classification of diffusion layers that exhibit linearity with respect to certain parallel alternative operations, enabling the possibility of an alternative differential attack simultaneously targeting all the s-boxes within the block. Furthermore, we investigate the differential behaviour with respect to alternative operations for all classes of optimal 4-bit s-boxes, as defined by Leander and Poschmann (2007). Our examination reveals that certain classes contain weak permutations w.r.t. alternative differential attacks. Finally, we leverage these vulnerabilities to execute a series of experiments showing the effectiveness of the cryptanalysis performed with a parallel alternative operation compared to the classical one.

翻译：Civino等人（2019）的研究表明，当采用源自与消息空间平移群同构的群的替代运算时，某些扩散层会使代换-置换网络面临差分密码分析的威胁。在本研究中，我们对表现出针对特定并行替代运算线性特性的扩散层进行了分类，这使得针对块内所有S盒的并行替代差分攻击成为可能。此外，我们依据Leander和Poschmann（2007）的定义，对所有类别的最优4位S盒在替代运算下的差分特性进行了研究。分析表明，某些类别的置换在替代差分攻击下存在脆弱性。最后，我们利用这些脆弱性开展了一系列实验，证明了采用并行替代运算的密码分析相较于传统方法的有效性。