Graph based private key crypto-system

Our symmetric key crypto-system is based on walks on a bipartite graph. The general idea is to treat vertices of a graph as messages and arcs of a certain length as an encryption tool. Starting from the plain text (vertex v1 of graph), we consider a one-step walk as an arc that connect vi to the next vertex vi+1 and which uses one character of the password. The adjacency matrix of this graph consists of a simple system of equations. A plain data is seen as an n-tuple in a Galois finite field GF(2⁸). We show that using this special family of graphs, for any password of length m, m<(n+5)/2, any cipher data (vertex in the graph) will have a unique path (walk) in the graph. Furthermore, our crypto-system has a linear complexity and it resists to different type of adversary attacks.