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We study the relation among some security parameters for vectorial Boolean functions which prevent attacks on the related block cipher. We focus our study on a recently-introduced security criterion, called weak differential uniformity, which prevents the existence of an undetectable trapdoor based on imprimitive group action. We present some properties of functions with low weak differential uniformity, especially for the case of power functions and 4-bit S-Boxes. [ABSTRACT FROM AUTHOR]

Abstract: S-Boxes are important security components of block ciphers. We provide theoretical results on necessary or sufficient criteria for an (invertible) 4-bit S-Box to be weakly APN. Thanks to a classification of 4-bit invertible S-Boxes achieved independently by De Cannière and Leander–Poschmann, we can strengthen our results with a computer-aided proof. We also propose a class of 4-bit S-Boxes which are very strong from a security point of view. [Copyright &y& Elsevier]