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

A system of zero-knowledge proofs on graph signatures has been proposed, where a graph can be signed, and the owner of the graph signature can prove a graph relation such as the connectivity and isolation of any two vertexes on the graph without disclosing all information about the graph. The correctness of the graph information is guaranteed by the signature. One of the applications is a virtualized infrastructure, where an infrastructure provider manages a distributed system, and each tenant is allocated a specific portion of this infrastructure for use. Tenants need to check with the provider that their resources are properly connected (connectivity) and that their resources are properly separated from the resources of other tenants (isolation). On the other hand, the provider cannot simply disclose the entire infrastructure topology to each tenant. Using the zero-knowledge proof system on graph signatures, both requirements can be addressed. Previously, an efficient zero-knowledge proof system on 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 paper, 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 pairing library and evaluate it by measuring the processing times. Compared to the conference version of this paper, we show the formal definitions and the security proofs of our proposed system, and add implementation-based evaluations reflecting the application to the virtualized infrastructure.