We propose an efficient framework for enabling secure multi-party numerical computations in a Peer-to-Peer network. This problem arises in a range of applications such as collaborative filtering, distributed computation of trust and reputation, monitoring and numerous other tasks, where the computing nodes would like to preserve the privacy of their inputs while performing a joint computation of a certain function. Although there is a rich literature in the field of distributed systems security concerning secure multi-party computation, in practice it is hard to deploy those methods in very large scale Peer-to-Peer networks. In this work, we examine several possible approaches and discuss their feasibility. Among the possible approaches, we identify a single approach which is both scalable and theoretically secure. An additional novel contribution is that we show how to compute the neighborhood based collaborative filtering, a state-of-the-art collaborative filtering algorithm, winner of the Netflix progress prize of the year 2007. Our solution computes this algorithm in a Peer-to-Peer network, using a privacy preserving computation, without loss of accuracy. Using extensive large scale simulations on top of real Internet topologies, we demonstrate the applicability of our approach. As far as we know, we are the first to implement such a large scale secure multi-party simulation of networks of millions of nodes and hundreds of millions of edges.

10 pages, 2 figures, appeared in the 8th IEEE Peer-to-Peer Computing, Aachen, Germany, Sept. 2008