Encryption using Network and Matrices through Signed Graphs

Security of a network is important to all organizations, personal computer users, and the military. With the invention of the Internet, major concern is about the security and the history of security allows a better understanding of the emergence of security technology. One of the ways to secure businesses from the Internet is through firewalls and encryption mechanisms. A network can be designed as a sigraph S where every sigraph will have its unique adjacency matrix associated with it. A signed graph (or sigraph in short) S is a graph G in which every edge x carries a value s(x) ∈ {-1, +1} called its sign denoted specially as S = (G, s). Given a sigraph S, H = L(S) called the line sigraph of S is that sigraph in which edges of S are represented as vertices, two of these vertices are adjacent whenever the corresponding edges in S have a vertex in common and any such edge ef is defined to be negative whenever both e and f are negative edges in S. Here S is called root sigraph of H. In this paper first we give an algorithm to obtain a line sigraph [1] and line root sigraph from a given sigraph [1], if it exists. This algorithm is an extension of an algorithm given by Lehot [2] in the realm of sigraphs. In the end we will propose a technique that will use adjacency matrix of S as a parameter to encrypt and forward the data in the form of adjacency matrix of L(S) and will decrypt it by applying inverse matrix operations.