Abstract
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.
Highlights
In the last years, research about cryptographic applications of cellular automata (CA) focused on the properties of the underlying local rules (Martin 2006; Leporati and Mariot 2014; Formenti et al 2014)
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
We first give some theoretical results on the properties that a CA rule must satisfy in order to meet asynchrony immunity, like central permutivity
Summary
Research about cryptographic applications of cellular automata (CA) focused on the properties of the underlying local rules (Martin 2006; Leporati and Mariot 2014; Formenti et al 2014). The aim of this paper is to investigate a new property related to asynchronous CA called asynchrony immunity (AI), which could be of interest in the context of sidechannel attacks. This property can be described by a three-. If the CA is not (t, n)-AI, the attacker could gain some information on the internal state of the cipher by analyzing the differences of the output distributions in the original CA and the asynchronous CA. From the empirical point of view, we employ this new theoretical result to consistently extend the experimental search of asynchrony immune rules, by considering larger neighborhood sizes. We provide some possible ways to generalize the notion of asynchrony immunity and how this property can be linked to existing CA models in Sect. 5, as well as pointing out other avenues for future research on the subject
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