CRYPTIM: Graphs as tools for symmetric encryption

Abstract

A combinatorial method of encryption is presented. The general idea is to treat vertices of a graph as messages and walks of a certain length as encryption tools. We study the quality of such an encryption in case of graphs of high girth by comparing the probability to guess the message (vertex) at random with the probability to break the key, i. e. to guess the encoding walk. In fact the quality is good for graphs which are close to the Erdös bound, defined by the Even Cycle Theorem. We construct special linguistic graphs of affine type whose vertices (messages) and walks (encoding tools) could be both naturally identified with vectors over GF(q), and neighbors of the vertex defined by a system of linear equations. For them the computation of walks has a strong similarity with the classical scheme of linear coding. The algorithm has been implemented and tested.