In this paper we present a collection of attacks based on generalisations of the complementation property of DES. We find symmetry relations in the key schedule and in the actual rounds, and we use these symmetries to build distinguishers for any number of rounds when the relation is deterministic. This can be seen as a generalisation of the complementation property of DES or of slide/related-k...

The most important tool for classifying recognizable languages is Eilenberg’s variety theorem [1], which gives a one-to-one correspondence between (pseudo)-varieties of finite semigroups and varieties of recognizable languages. Varieties of recognizable languages are classes of recognizable languages closed under union, intersection, complement, left and right quotients and inverse morphisms. R...

The Kreweras complementation map is an anti-isomorphism on the lattice of noncrossing partitions. We consider an analogous operation for plane trees motivated by the molecular biology problem of RNA folding. In this context, we explicitly count the orbits of Kreweras’ map according to their length as the number of appropriate symmetry classes of trees in the plane. These new enumeration results...