### On some applications of graphs to cryptography and turbocoding

*V. Ustimenko, T. Shaska*

#### Abstract

Families of simple graphs of high girth had been used for the development of algorithms in Cryptography and Turbocoding. Recent results in that directions show the interest of applied

researchers to "families of directed graphs of high girth", but the concept of the girth for the directed graphs is not well established. We discuss one of the possible definition. It agrees well with the classical definition in the case of simple graph and allows to create the analog of Extremal graph theory for simple graphs without small cycles for the class of balanced graphs i.e. directed graphs without multiple arrows such that each vertex has same number of inputs and outputs. Finally we discussed some explicit construction of simple and directed graphs which can be applicable to Turbocoding and Cryptography.

researchers to "families of directed graphs of high girth", but the concept of the girth for the directed graphs is not well established. We discuss one of the possible definition. It agrees well with the classical definition in the case of simple graph and allows to create the analog of Extremal graph theory for simple graphs without small cycles for the class of balanced graphs i.e. directed graphs without multiple arrows such that each vertex has same number of inputs and outputs. Finally we discussed some explicit construction of simple and directed graphs which can be applicable to Turbocoding and Cryptography.

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