A novel chaotic, permutation-substitution architecture based, grayscale images’ encryption algorithm is introduced in this paper. To reduce the redundancies of Fridrich’s structure based image encryption scheme, a novel inter-intra bit-level permutation based confusion strategy is appealed. The confusion stage is developed with the aid of KenKen puzzles. Theoretical analysis and simulation resu...

I will build some standard resolutions for Mackey functors which are projective relative to p-subgroups. Those resolutions are closely related to the poset of p-subgroups. They lead to generalizations of known results on cohomology. They give a way to compute the Cartan matrix for Mackey functors, in terms of p-permutation modules, and to precise the structure of projective Mackey functors. The...

We prove that the set of growth rates of permutation classes includes an infinite sequence of intervals whose infimum is θB ≈ 2.35526, and that it also contains every value at least λB ≈ 2.35698. These results improve on a theorem of Vatter, who determined that there are permutation classes of every growth rate at least λA ≈ 2.48187. Thus, we also refute his conjecture that the set of growth ra...

Permutation modules are fundamental in the representation theory of symmetric groups Sn and their corresponding Iwahori–Hecke algebras H = H (Sn). We find an explicit combinatorial basis for the annihilator of a permutation module in the “integral” case — showing that it is a cell ideal in G.E. Murphy’s cell structure of H . The same result holds whenever H is semisimple, but may fail in the no...

There has been great interest in deciding whether a combinatorial structure satisfies some property, or in estimating the value of some numerical function associated with this combinatorial structure, by considering only a randomly chosen substructure of sufficiently large, but constant size. These problems are called property testing and parameter testing, where a property or parameter is said...

this paper presents a new audio encryption algorithm based on permutation and residue number system. in the current approach, signal samples are combined with residue number system through permutation; therefore, a specific noise is generated. then, the audio signal is combined with the noise, generated by the algorithm, to produce a silence signal. for this purpose, the algorithm uses a predef...

A permutation class is splittable if it is contained in the merge of two of its proper subclasses. We characterise the unsplittable subclasses of the class of separable permutations both structurally and in terms of their bases.

In this paper, we present some attacks on GAGE, InGAGE, and CiliPadi which are candidates of the first round of the NIST-LWC competition. GAGE and InGAGE are lightweight sponge based hash function and Authenticated Encryption with Associated Data (AEAD), respectively and support different sets of parameters. The length of hash, key, and tag are always 256, 128, and 128 bits, respec...

The lattice of flats of a matroid or combinatorial geometry can be regarded as a sublattice (with rank function) of the lattice of subsets of a set, having the property that, given an element of rank r of the lattice and a point outside it, a unique element of rank r+1 covers both. This paper develops a theory of permutation geometries, which are similarly defined objects in the semilattice of ...