GRAND : Graph Reconstruction from Potential Partial Adjacency and Neighborhood Data

摘要

Cryptographic approaches, such as secure multiparty computation, can be used to securely compute a function of a distributed graph without centralizing the data of each participant. However, the output of the protocol can leak sensitive information about the structure of the original graph. In particular, we propose an approach by which an adversary observing the result of a private protocol for the computation of the number of common neighbors between all pairs of vertices, can reconstruct the adjacency matrix of the graph. In fact, this can only be done up to co-squareness, a notion we introduce, as two different graphs can have the same matrix of common neighbors. To realize this, we consider two adversary models, one who observes the common neighbors matrix only and a more informed one that has partial knowledge of the original graph. Our results demonstrate that, from their common neighbors matrix, graphs can be reconstructed with high accuracy (up to co-squareness). The proposed reconstruction is also interesting in itself from the point of view of graph theory.