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Is it possible that a block cipher apparently immune to classical differential cryptanalysis can be attacked considering a different operation on the message space? Recently Calderini and Sala showed how to effectively compute alternative operations on a vector space which can serve as message space for a block cipher such that the resulting structure is still a vector space. The latter were used to mount a linearisation attack against a toy cipher. Here we investigate how alternative operations interact with the layers of a substitution-permutation network and show how they influence the differential probabilities, when the difference taken into consideration is different from the usual bit-wise addition modulo two. Furthermore, we design a block cipher which appears to be secure with respect to classical differential cryptanalysis, but weaker with respect to our attack which makes use of alternative operations. [ABSTRACT FROM AUTHOR]

We present an application of Hilbert quasi-polynomials to order domains, allowing the effective check of the second order-domain condition in a direct way. We also provide an improved algorithm for the computation of the related Hilbert quasi-polynomials. This allows to identify order domain codes more easily [ABSTRACT FROM AUTHOR]

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]