We continue the study of asynchrony immunity in cellular automata (CA), which can be considered as a generalization of correlation immunity in the case of vectorial Boolean functions. The property could have applications as a countermeasure for side-channel attacks in CA-based cryptographic primitives, such as S-boxes and pseudorandom number generators. We first give some theoretical results on the properties that a CA rule must satisfy in order to meet asynchrony immunity, like central permutivity. Next, we perform an exhaustive search of all asynchrony immune CA rules of neighborhood size up to 5, leveraging on the discovered theoretical properties to greatly reduce the size of the search space.

中文翻译：

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异步免疫细胞自动机的搜索空间减少

我们继续研究细胞自动机（CA）中的异步免疫，在矢量布尔函数的情况下，可以将其视为相关免疫的一般化。该属性可以作为对基于CA的加密原语（例如S盒和伪随机数生成器）中的侧信道攻击的对策应用。首先，我们给出一些关于CA规则必须满足的属性的理论结果，以便满足异步抗扰性，例如中心置换。接下来，我们利用发现的理论属性对所有邻域大小最大为5的异步免疫CA规则进行详尽搜索，以大大减小搜索空间的大小。