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We provide two sufficient conditions to guarantee that the round functions of a translation-based cipher generate a primitive group. Furthermore, under the same hypotheses, and assuming that a round of the cipher is strongly proper and consists of -bit S-Boxes, with or , we prove that such a group is the alternating group. As an immediate consequence, we deduce that the round functions of some lightweight translation-based ciphers, such as the PRESENT cipher, generate the alternating group. [ABSTRACT FROM AUTHOR]

A block cipher can be easily broken if its encryption functions can be seen as linear maps on a small vector space. Even more so, if its round functions can be seen as linear maps on a small vector space. We show that this cannot happen for the AES. More precisely, we prove that if the AES round transformations can be embedded into a linear cipher acting on a vector space, then this space is huge-dimensional and so this embedding is infeasible in practice. We present two elementary proofs. [ABSTRACT FROM AUTHOR]

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]