Secure communication over Trellis: Graph theoretic approach

Abstract

Forney's representation of Trellis code received wide attention by researchers and engineers with its simplicity in representing codes and elegant nature to analyze codes with sys- tem theoretic properties, graph theoretic properties with efficient encoding and decoding procedures. In this paper, we consider the connected graph nature of trellis and propose security feature over Trellis using fundamental cut-set and fundamental circuits principle. We use the graph theoretic approach, by generating limited spanning trees of trellis, fundamental cut-sets and fundamental circuits, private key cryptosystem is defined in which fundamental cut-set acts as a key to encrypt and decrypt. We have used a class of group codes called Kernel codes and its trellis, to show that private key cryptosystem can be used over Trellis and fundamental cut-set acts as a key to encrypt and decrypt message at sender and receiver respectively.