Zero-Knowledge Proofs of Connectivity for Labeled Directed Graphs Using Bilinear-Map Accumulator.

Networked systems can be represented using graphs. Tenants who use the systems in which their resources are hosted need to check with the provider of the resources that their resources are properly connected (connectivity) and that their resources are properly separated from the resources of other tenants (isolation). Since providers manage systems for multiple tenants, a method to prove the connectivity and isolation without revealing the network topology is required. As a solution, an efficient zero-knowledge proof system of graph signatures using a bilinear-map accumulator has been proposed, where the verification time and the size of the proof data do not depend on the number of graph vertexes and edges. However, this system has two problems. First, since the proof does not include labels, it is not possible to prove the connectivity considering network bandwidth and cost. Second, since it assumes undirected graphs, it cannot handle applications on directed graphs such as network flows. In this study, we extend the previous system and propose a zero-knowledge proof system of the connectivity for directed graphs where each edge has labels. We implemented our system on a PC using a pairng library and evaluate it by measuring the processing times.