Efficient zero-knowledge proofs for some practical graph problems

Abstract

From a cryptographic aspect zero-knowledge protocols for graph isomorphisms, graph non-isomorphisms, and graph-coloring are artificial problems, that received lots of attention. Due to recent work in network security in a broadcast setting, it seems important to design efficient zero-knowledge protocols for the following graph problems: independent set problem, neighbor independent set problem, and disjoint broadcast lines problem. In this paper, we will introduce a new concept of k-independent set problem which is a generalization of independent set and neighbor independent set problems, and we will present efficient zero-knowledge protocols for these problems. In the end of the paper we will give some cryptographic applications of k-independent set. Especially, we will point out the applications to the concept of "threshold" and appropriate access structures. Note that k-independent set also has applications outside cryptography, such as biology, methodology of scientific research, ethics, etc., which are beyond the scope of this paper. © Springer-Verlag Berlin Heidelberg 2003.