论文标题
差异偏见，$ c $差异均匀性及其与差分攻击的关系
Differential biases, $c$-differential uniformity, and their relation to differential attacks
论文作者
论文摘要
差分密码分析著名地使用统计偏见在块密码中的差异传播中攻击密码。在本文中，我们研究了差异中更一般的统计偏见的存在。为此，我们讨论了S-boxes的$ C $不同的均匀性，这是Ellingsen等人最近引入的概念。 al。测量某些统计偏差，这些统计偏见可能可能用于类似于差异攻击的攻击。首先，我们证明，S-box的大量潜在候选者必然具有$ c $ - 不同的均匀性，但最多只能使用$ c $的$ b $选择，其中$ b $是与有限field $ q $的大小独立的常数。该结果意味着，对于大量功能，某些统计差异偏差是不可避免的。 在第二部分中，我们讨论了基于与$ c $差异均匀性相关的S盒弱点设计差异攻击的实际可能性。
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.
