#### Abstract

Privacy preserving algorithms allow several participants to compute a global function collaboratively without revealing local information to each other. Examples of applications include trust management, collaborative filtering, and ranking algorithms such as PageRank. Most solutions that can be proven to be privacy preserving theoretically are not appropriate for highly unreliable, large scale, distributed environments such as peer-to-peer (P2P) networks because they either require centralized components, or a high degree of synchronism among the participants. At the same time, in P2P networks privacy preservation is becoming a key requirement. Here, we propose an asynchronous privacy preserving communication layer for an important class of iterative computations in P2P networks, where each peer periodically computes a linear combination of data stored at its neighbors. Our algorithm tolerates realistic rates of message drop and delay, and node churn, and has a low communication overhead. We perform simulation experiments to compare our algorithm to related work. The problem we use as an example is power iteration (a method used to calculate the dominant eigenvector of a matrix), since eigenvector computation is at the core of several practical applications. We demonstrate that our novel algorithm also converges in the presence of realistic node churn, message drop rates and message delay, even when previous synchronized solutions are able to make almost no progress.