We have been investigating the cryptographical properties of in nite families of simple
graphs of large girth with the special colouring of vertices during the last 10 years. Such …

The paper is devoted to the graph based cryptography. The girth of a directed graph (girth
indicator) is defined via its smallest commutative diagram. The analogue of Erdøos's Even …

Families of finite graphs of large girth were introduced in classical extremal graph theory.
One important theoretical result here is the upper bound on the maximal size of the graph …

The paper is devoted to the implementations of the public key algorithms based on simple
algebraic graphs A (n, K) and D (n, K) defined over the same finite commutative ring K. If K is …

Special family of non-bijective multivariate maps Fn of Zm n into itself is constructed for n= 2,
3,... and composite m. The map Fn is injective on Ωn={x| x1+ x2+... xn∈ Zm∗} and solution …

The paper is devoted to computer implementation of some graph based stream ciphers. We
compare the time performance of this new algorithm with fast, but no very secure RC4, and …

Algebraic Constructions of Extremal Graph Theory were efficiently used for the construction
of Low Density Parity Check Codes for satellite communication, constructions of stream …

The well known “real-life examples” of small world graphs, including the graph of binary
relation:“two persons on the earth know each other” contains cliques, so they have cycles of …

Certain families of graphs can be used to obtain multivariate polynomials for cryptographic
algorithms. In particular, in this paper, we introduce stream ciphers based on non-bijective …

In this paper we consider some properties of stream ciphers related to arithmetical
dynamical systems defined in [41] over commutative ring K. We modify the stream cipher …