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.
Similar content being viewed by others
References
Aggarwal CC, Yu PS (2008) A general survey of privacy-preserving data mining models and algorithms. In: Aggarwal CC, Yu PS, Elmagarmid AK (eds) Privacy-preserving data mining. The Kluwer International Series on Advances in Database Systems, vol 34, pp 11–52. Springer, New York. doi:10.1007/978-0-387-70992-5_2
Agrawal R, Srikant R (2000) Privacy-preserving data mining. SIGMOD Rec 29(2): 439–450. doi:10.1145/335191.335438
Bai, Z, Demmel, J, Dongarra, J, Ruhe, A, van der Vorst, H (eds) (2000) Templates for the solution of algebraic eigenvalue problems: a practical guide. SIAM, Philadelphia
Bianchini M, Gori M, Scarselli F (2005) Inside pagerank. ACM Trans Int Technol 5(1): 92–128. doi:10.1145/1052934.1052938
Bickson D, Dolev D, Bezman G, Pinkas B (2008) Peer-to-peer secure multi-party numerical computation. In: IEEE international conference on peer-to-peer computing. IEEE Computer Society, pp 257–266. doi:10.1109/P2P.2008.22
Bickson D, Malkhi D (2008) A unifying framework of rating users and data items in peer-to-peer and social networks. Peer-to-Peer Netw Appl 1(2): 93–103. doi:10.1007/s12083-008-0008-4
Bickson D, Reinman T, Dolev D, Pinkas B (2010) Peer-to-peer secure multi-party numerical computation facing malicious adversaries. Peer-to-Peer Netw Appl 3(2): 129–144. doi:10.1007/s12083-009-0051-9
Clifton C, Kantarcioglu M, Vaidya J, Lin X, Zhu MY (2002) Tools for privacy preserving distributed data mining. SIGKDD Explor Newsl 4(2): 28–34. doi:10.1145/772862.772867
Das K, Bhaduri K, Kargupta H (2011) Multi-objective optimization based privacy preserving distributed data mining in peer-to-peer networks. Peer-to-Peer Netw Appl 4(2): 192–209. doi:10.1007/s12083-010-0075-1
Datta S, Bhaduri K, Giannella C, Wolff R, Kargupta H (2006) Distributed data mining in peer-to-peer networks. IEEE Int Comput 10(4): 18–26. doi:10.1109/MIC.2006.74
Frommer A, Szyld DB (2000) On asynchronous iterations. J Comput Appl Math 123(1–2): 201–216. doi:10.1016/S0377-0427(00)00409-X
Goldreich O, Micali S, Wigderson A (1987) How to play any mental game. In: Proceedings of the nineteenth annual ACM symposium on theory of computing, STOC ’87. ACM, New York, pp 218–229. doi:10.1145/28395.28420
Golub GH, Van Loan CF (1996) Matrix computations, 3rd edn. The Johns Hopkins University Press
He W, Liu X, Nguyen HV, Nahrstedt K, Abdelzaher T (2011) PDA: privacy-preserving data aggregation for information collection. ACM Trans Sen Netw 8(1): 6:1–6:22. doi:10.1145/1993042.1993048
Jelasity M, Canright G, Engø-Monsen K (2007) Asynchronous distributed power iteration with gossip-based normalization. In: Kermarrec AM, Bougé L, Priol T (eds) Euro-Par 2007. Lecture notes in computer science, vol 4641. Springer, Berlin, pp 514–525. doi:10.1007/978-3-540-74466-5_55
Jelasity M, Montresor A, Babaoglu O (2005) Gossip-based aggregation in large dynamic networks. ACM Trans Comput Syst 23(3): 219–252. doi:10.1145/1082469.1082470
Kamvar SD, Schlosser MT, Garcia-Molina H (2003) The eigentrust algorithm for reputation management in p2p networks. In: Proceedings of the 12th international conference on World Wide Web (WWW’03). ACM, New York, pp 640–651. doi:10.1145/775152.775242
Kempe D, Dobra A, Gehrke J (2003) Gossip-based computation of aggregate information. In: Proceedings of the 44th annual IEEE symposium on Foundations of Computer Science (FOCS’03). IEEE Computer Society, pp 482–491. doi:10.1109/SFCS.2003.1238221
Kempe D, McSherry F (2004) A decentralized algorithm for spectral analysis. In: Proceedings of the 36th ACM symposium on theory of computing (STOC’04). ACM, New York, pp 561–568. doi:10.1145/1007352.1007438
Lindell Y, Pinkas B (2002) Privacy preserving data mining. J Cryptol 15(3): 177–206. doi:10.1007/s00145-001-0019-2
Lubachevsky B, Mitra D (1986) A chaotic asynchronous algorithm for computing the fixed point of a nonnegative matrix of unit radius. J ACM 33(1): 130–150. doi:10.1145/4904.4801
Maurer U (2006) Secure multi-party computation made simple. Discrete Appl Math 154(2): 370–381. doi:10.1016/j.dam.2005.03.020
Montresor A, Jelasity M (2009) Peersim: a scalable P2P simulator. In: Proceedings of the 9th IEEE international conference on Peer-to-Peer Computing (P2P 2009). IEEE, Seattle, pp 99–100. doi:10.1109/P2P.2009.5284506. Extended abstract
Mosk-Aoyama D, Shah D (2008) Fast distributed algorithms for computing separable functions. IEEE Trans Inf Theory 54(7): 2997–3007. doi:10.1109/TIT.2008.924648
Parreira JX, Donato D, Michel S, Weikum G (2006) Efficient and decentralized PageRank approximation in a peer-to-peer web search network. In: Proceedings of the 32nd international conference on Very large data bases (VLDB’2006). VLDB Endowment, pp 415–426
van Renesse R, Birman KP, Vogels W (2003) Astrolabe: a robust and scalable technology for distributed system monitoring, management, and data mining. ACM Trans Comput Syst 21(2): 164–206. doi:10.1145/762483.762485
Shamir A (1979) How to share a secret. Commun ACM 22(11): 612–613. doi:10.1145/359168.359176
Stutzbach D, Rejaie R (2006) Understanding churn in peer-to-peer networks. In: Proceedings of the 6th ACM SIGCOMM conference on Internet measurement (IMC’06). ACM, New York, pp 189–202. doi:10.1145/1177080.1177105
Yao AC (1982) Protocols for secure computations. In: Proceedings of the 23rd annual symposium on Foundations of Computer Science (FOCS), pp 160–164. doi:10.1109/SFCS.1982.38
Yao ACC (1986) How to generate and exchange secrets. In: Proceedings of 27th annual symposium on Foundations of Computer Science (FOCS), pp 162–167. doi:10.1109/SFCS.1986.25
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Naranjo, J.A.M., Casado, L.G. & Jelasity, M. Asynchronous privacy-preserving iterative computation on peer-to-peer networks. Computing 94, 763–782 (2012). https://doi.org/10.1007/s00607-012-0200-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00607-012-0200-5