The cryptographic property of normality for cubic Boolean functions is studied in this paper. This property is highly relevant for the analysis and design of important building blocks in cryptosystems. We develop a novel greedy algorithm to find whether a given function is normal and the affine subspace where this property occurs. Our algorithm exploits the fact that cubic functions admit a matrix representation to work with tools having fast implementations. Thus, the proposed algorithm achieves a much lower complexity than other well known general techniques in the literature.
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