A graph G is said to be d-distinguishable if there is a d-coloring of G which no non-trivial automorphism preserves. That is, 9χ : G !f1; : : : ;dg; 8φ 2 Aut(G)nfidg;9v;χ(v) 6= χ(φ(v)): It was conjectured that if jGj> jAut(G)j and the Aut(G) action on G has no singleton orbits, then G is 2-distinguishable. We give an example where this fails. We partially repair the conjecture by showing that w...

We give interpretations of some known key agreement protocols in the framework of category theory and in this way we give a method of constructing of many new key agreement protocols.

In this paper we will provide two linear approximating for the stream cipher Salsa20, the both are probable to form distinguishing attack with about 64 2 blocks of keystream.

We consider infinite graphs. The distinguishing number D(G) of a graph G is the minimum number of colours in a vertex colouring of G that is preserved only by the trivial automorphism. An analogous invariant for edge colourings is called the distinguishing index, denoted by D′(G). We prove that D′(G) 6 D(G) + 1. For proper colourings, we study relevant invariants called the distinguishing chrom...

Let Σ be a surface. We prove that rigidity indices of graphs which admit a polyhedral embedding in Σ and 5-connected graphs admitting an embedding in Σ are bounded by a constant depending on Σ. Moreover if the Euler characteristic of Σ is negative, then the separation index of graphs admitting a polyhedral embedding in Σ is also bounded. As a side result we show that distinguishing number of bo...

Let G be a graph. A vertex labeling of G is distinguishing if the only label-preserving automorphism of G is the identity map. The distinguishing number of G, D(G), is the minimum number of labels needed so that G has a distinguishing labeling. In this paper, we present O(n log n)-time algorithms that compute the distinguishing numbers of trees and forests. Unlike most of the previous work in t...

The paper here presented was motivated by a case study involving high-dimensional and high-frequency tidal volume traces measured during induced panic attacks. The focus was to develop a procedure to determine the significance of whether a mean curve dominates another one. The key idea of the suggested method relies on preserving the order in mean while reducing the dimension of the data. The o...

Abstract Cryptanalysis is the development and study of attacks against cryptographic primitives protocols. Many properties rely on difficulty generating an adversary who, given object sampled from one two classes, correctly distinguishes class used to generate that object. In case cipher suite distinguishing problem, classes are different primitives. this paper, we propose a methodology based m...