Differential cryptanalysis famously uses statistical biases in the propagation of differences in a block cipher to attack the cipher. In this paper, we investigate the existence of more general statistical biases in the differences. To this end, we discuss the $c$-differential uniformity of S-boxes, which is a concept that was recently introduced in Ellingsen et. al. to measure certain statistical biases that could potentially be used in attacks similar to differential attacks. Firstly, we prove that a large class of potential candidates for S-boxes necessarily has large $c$-differential uniformity for all but at most $B$ choices of $c$, where $B$ is a constant independent of the size of the finite field $q$. This result implies that for a large class of functions, certain statistical differential biases are inevitable. In a second part, we discuss the practical possibility of designing a differential attack based on weaknesses of S-boxes related to their $c$-differential uniformity.

翻译：不同的加密分析在传播一个区块密码中的差异以攻击密码时使用有名的统计偏见。 在本文中,我们调查在差异中是否存在更普遍的统计偏见。 为此,我们讨论S箱的美元差异性统一性,这是最近在Ellingsen等人公司采用的概念,以衡量某些统计偏见,这些偏见可能被用于类似不同攻击的攻击中。首先,我们证明一大批S箱的潜在候选者必然对所有人具有巨大的美元差异性统一性,但最多为美元,其中B美元是固定的,与有限字段的大小无关。这一结果意味着对于一大批功能而言,某些统计差异性偏见是不可避免的。 在第二部分,我们讨论根据S箱与美元差异性统一性有关的弱点设计差异性攻击的实际可能性。