Building Correlation Immune Functions from Sets of Mutually Orthogonal Cellular Automata

TL;DR

This paper presents a novel method to construct correlation immune Boolean functions using families of mutually orthogonal cellular automata, expanding the associated orthogonal arrays and demonstrating higher immunity orders through computational experiments.

Contribution

It introduces a new construction technique for correlation immune functions via MOCA and binary orthogonal arrays, with empirical validation up to 12 variables.

Findings

Orthogonal arrays from MOCA can be expanded to binary arrays of strength ≥ 2.

Constructed correlation immune functions exhibit immunity order ≥ 3 for up to 12 variables.

New perspectives for designing correlation-immune functions and orthogonal arrays are discussed.

Abstract

Correlation immune Boolean functions play an important role in the implementation of efficient masking countermeasures for side-channel attacks in cryptography. In this paper, we investigate a method to construct correlation immune functions through families of mutually orthogonal cellular automata (MOCA). First, we show that the orthogonal array (OA) associated to a family of MOCA can be expanded to a binary OA of strength at least 2. To prove this result, we exploit the characterization of MOCA in terms of orthogonal labelings on de Bruijn graphs. Then, we use the resulting binary OA to define the support of a second-order correlation immune function. Next, we perform some computational experiments to construct all such functions up to $n=12$ variables, and observe that their correlation immunity order is actually greater, always at least 3. We conclude by discussing how these results open up interesting perspectives for future research, with respect to the search of new correlation-immune functions and binary orthogonal arrays.