Title: Wave-Shaped Round Functions and Primitive Groups,
Abstract: Round functions used as building blocks for iterated block ciphers, both in
the case of Substitution-Permutation Networks and Feistel Networks, 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
represent a serious flaw for the cipher.