The use of alternative operations in differential cryptanalysis, or alternative notions of differentials, are lately receiving increasing attention. Recently, Civino et al. managed to design a block cipher which is secure w.r.t. classical differential cryptanalysis performed using XOR-differentials, but weaker with respect to the attack based on an alternative difference operation acting on the first s-box of the block. We extend this result to parallel alternative operations, i.e. acting on each s-box of the block. First, we recall the mathematical framework needed to define and use such operations. After that, we perform some differential experiments against a toy cipher and compare the effectiveness of the attack w.r.t. the one that uses XOR-differentials.

In this paper we study the relationships between the elementary abelian regular subgroups and the Sylow 2-subgroups of their normalisers in the symmetric group Sym(F n 2 ), in view of the interest that they have recently raised for their applications in symmetric cryptography.2010 Mathematics Subject Classification. 20B35, 20D20, 94A60.

Round functions used as building blocks for iterated block ciphers, both in the case of Substitution-Permutation Networks (SPN) and Feistel Networks (FN), are often obtained as the composition of different layers which provide confusion and diffusion, and key additions. The bijectivity of any encryption function, crucial in order to make the decryption possible, is guaranteed by the use of invertible layers or by the Feistel structure. In this work a new family of ciphers, called wave ciphers, is introduced. In wave ciphers, round functions feature wave functions, which are vectorial Boolean functions obtained as the composition of non-invertible layers, where the confusion layer enlarges the message which returns to its original size after the diffusion layer is applied. This is motivated by the fact that relaxing the requirement that all the layers are invertible allows to consider more functions which are optimal with regard to non-linearity. In particular it allows to consider injective APN S-boxes. In order to guarantee efficient decryption we propose to use wave functions in Feistel Networks. With regard to security, the immunity from some group-theoretical attacks is investigated. In particular, it is shown how to avoid that the group generated by the round functions acts imprimitively, which represents a serious flaw for the cipher. The primitivity of this group is derived as a consequence of a more general result, which allows to reduce the problem of proving that a given FN generates a primitive group to the one of proving that an SPN, directly related to the given FN, generates a primitive group. Finally, a concrete instance of real-world size wave cipher is proposed as an example, and its resistance against differential and linear cryptanalysis is also established.

No abstract

No abstract