Probonite

Abstract

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.

Oblivious Turing Machine

“…An important element of our construction, which may be of independent interest, is what we call Blind Matrix Access (BMA). It is the extension of Blind Array Access (BAA) introduced in [3] which enables a server to obliviously access a one-dimensional encrypted array represented as a RLWE ciphertext. The access consists in performing a PBS on the array with the input index to be accessed.…”

“…This counter, by the end of Algorithm 2, will be utilized to restore the head to its first position. The initial phase of each step involves blindly reading the cell under the head, employing the Blind Array Access algorithm outlined in [3]. Subsequently, the resulting ciphertext, combined with the current state, is utilized to access the three matrices: Iw, Im, and Is.…”