  Graphs are a widely used data structure for collecting and analyzing
relational data. However, when the graph structure is distributed across
several parties, its analysis is particularly challenging. In particular, due
to the sensitivity of the data each party might want to keep their partial
knowledge of the graph private, while still willing to collaborate with the
other parties for tasks of mutual benefit, such as data curation or the removal
of poisoned data. To address this challenge, we propose Crypto'Graph, an
efficient protocol for privacy-preserving link prediction on distributed
graphs. More precisely, it allows parties partially sharing a graph with
distributed links to infer the likelihood of formation of new links in the
future. Through the use of cryptographic primitives, Crypto'Graph is able to
compute the likelihood of these new links on the joint network without
revealing the structure of the private individual graph of each party, even
though they know the number of nodes they have, since they share the same graph
but not the same links. Crypto'Graph improves on previous works by enabling the
computation of a certain number of similarity metrics without any additional
cost. The use of Crypto'Graph is illustrated for defense against graph
poisoning attacks, in which it is possible to identify potential adversarial
links without compromising the privacy of the graphs of individual parties. The
effectiveness of Crypto'Graph in mitigating graph poisoning attacks and
achieving high prediction accuracy on a graph neural network node
classification task is demonstrated through extensive experimentation on a
real-world dataset.
