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The affine general linear group acting on a vector space over a prime field is a well-understood mathematical object. Its elementary abelian regular subgroups have recently drawn attention in applied mathematics thanks to their use in cryptography as a way to hide or detect weaknesses inside block ciphers. This paper is focused on building a convenient representation of their elements which suits better the purposes of the cryptanalyst. Several combinatorial counting formulas and a classification of their conjugacy classes are given as well. [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]