Peer-to-Peer Networking and Applications

, Volume 3, Issue 2, pp 129–144 | Cite as

Peer-to-peer secure multi-party numerical computation facing malicious adversaries

  • Danny BicksonEmail author
  • Tzachy Reinman
  • Danny Dolev
  • Benny Pinkas


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 other tasks, where the computing nodes are expected 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 try to bridge the gap between theoretical algorithms in the security domain, and a practical Peer-to-Peer deployment. We consider two security models. The first is the semi-honest model where peers correctly follow the protocol, but try to reveal private information. We provide three possible schemes for secure multi-party numerical computation for this model and identify a single light-weight scheme which outperforms the others. Using extensive simulation results over real Internet topologies, we demonstrate that our scheme is scalable to very large networks, with up to millions of nodes. The second model we consider is the malicious peers model, where peers can behave arbitrarily, deliberately trying to affect the results of the computation as well as compromising the privacy of other peers. For this model we provide a fourth scheme to defend the execution of the computation against the malicious peers. The proposed scheme has a higher complexity relative to the semi-honest model. Overall, we provide the Peer-to-Peer network designer a set of tools to choose from, based on the desired level of security.


Peer-to-Peer Secure multi-party computation Byzantine agreement Jacobi algorithm Numerical iterative methods 



We would like to thank Dr. Adam Wierzbicki for useful discussions and his helpful comments, especially regarding realistic models of privacy, where some of the nodes do not care about exposing their inputs.


  1. 1.
    GMP (2009) The GNU MP Bignum library.
  2. 2.
    Netflix (2009) Netflix homepage.
  3. 3.
    Advanced Crypto Software Collection (2006) Paillier C implementation by John Bethencourt.
  4. 4.
    Agrawal R, Srikant R (2000) Privacy-preserving data mining. In: Proceedings of the 2000 ACM SIGMOD international conference on management of data, ACM, Dallas, 16–18 May 2000, pp 439–450Google Scholar
  5. 5.
    Anker T, Bickson D, Dolev D, Hod B (2008) Efficient clustering for improving network performance in wireless sensor networks. In: European conference on wireless sensor networks (EWSN’08)Google Scholar
  6. 6.
    Bell RM, Koren Y (2007) Scalable collaborative filtering with jointly derived neighborhood interpolation weights. In: IEEE international conference on data mining (ICDM’07)Google Scholar
  7. 7.
    Ben-David A, Nisan N, Pinkas B (2008) Fairplaymp–a system for secure multi-party computation. ManuscriptGoogle Scholar
  8. 8.
    Ben-Or M (1983) Another advantage of free choice (extended abstract): completely asynchronous agreement protocols. In: PODC ’83: Proceedings of the second annual ACM symposium on principles of distributed computing, pp 27–30Google Scholar
  9. 9.
    Ben-Or M, Goldwasser S, Wigderson A (1988) Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: 20th STOC, pp 1–10Google Scholar
  10. 10.
    Bertsekas DP, Tsitsiklis JN (1989) Parallel and distributed calculation. Numerical Methods. Prentice Hall, Englewood CliffsGoogle Scholar
  11. 11.
    Bickson D, Shental O, Siegel PH, Wolf JK, Dolev D (2008) Gaussian belief propagation based multiuser detection. In: IEEE Int Symp on Inform Theory (ISIT), TorontoGoogle Scholar
  12. 12.
    Bickson D, Malkhi D, Zhou L (2007) Peer to peer rating. In: The 7th IEEE Peer-to-peer computing, p 9Google Scholar
  13. 13.
    Canetti R, Rabin T (1993) Fast asynchronous byzantine agreement with optimal resilience. In: 25th STOC, proceedings of the twenty-fifth annual ACM symposium on theory of computingGoogle Scholar
  14. 14.
    Canny J (2002) Collaborative filtering with privacy via factor analysis. In: SIGIR ’02: Proceedings of the 25th annual international ACM SIGIR conference on research and development in information retrieval, ACM, New York, pp 238–245CrossRefGoogle Scholar
  15. 15.
    Dinur I, Nissim K (2003) Revealing information while preserving privacy. In: PODS ’03: Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on principles of database systems, ACM, New York, pp 202–210CrossRefGoogle Scholar
  16. 16.
    Dolev D (1982) The byzantine generals strike again. J Algorithms 3:14–30zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Dolev D, Strong RH (1982) Polynomial algorithms for multiple processor agreement. In: 14th STOC, proceedings of the twenty-fifth annual ACM symposium on theory of computingGoogle Scholar
  18. 18.
    Dutta H, Kargupta H, Datta S, Sivakumar K (2003) Analysis of privacy preserving random perturbation techniques: further explorations. In: WPES ’03: Proceedings of the 2003 ACM workshop on privacy in the electronic society, ACM, New York, pp 31–38CrossRefGoogle Scholar
  19. 19.
    Feldman P, Micali S (1989) An optimal probabilistic algorithm for synchronous byzantine agreement. In: ICALP ’89: Proceedings of the 16th international colloquium on automata, languages and programming, pp 341–378Google Scholar
  20. 20.
    Fouque P-A, Poupard G, Stern J (2001) Sharing decryption in the context of voting or lotteries. In: Financial cryptography. Lecture notes in computer science, vol 1962. Springer, New York, pp 90–104CrossRefGoogle Scholar
  21. 21.
    Goldreich O, Micali S, Wigderson A (1987) How to play any mental game or A completeness theorem for protocols with honest majority. In: Proceedings of the 19th annual symposium on theory of computing (STOC), ACM, New York, pp 218–229Google Scholar
  22. 22.
    Kamvar SD, Schlosser MT, Molina HG (2003) The eigentrust algorithm for reputation management in p2p networks. In: Proceedings of the twelfth international world wide web conferenceGoogle Scholar
  23. 23.
    Lamport L, Shostak R, Pease M (1980) Reaching agreement in the presence of faults. J ACM 27(2):228–234zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Lamport L, Shostak R, Pease M (1982) The byzantine generals problem. ACM Trans Program Lang Syst 4(3):382–301CrossRefGoogle Scholar
  25. 25.
    Malkhi D, Nisan N, Pinkas B, Sella Y (2004) Fairplay—a secure two-party computation system. In: Proc usenix security symposiumGoogle Scholar
  26. 26.
    Mosk-Aoyama D, Shah D (2006) Computing separable functions via gossip. In: PODC ’06: Proceedings of the twenty-fifth annual ACM symposium on principles of distributed computing, ACM, New York, pp 113–122CrossRefGoogle Scholar
  27. 27.
    Paillier P (1999) Public-key cryptosystems based on composite degree residuosity classes. In: EUROCRYPT ’99, Springer-Verlag (LNCS 1592). Springer, New York, pp 223–238Google Scholar
  28. 28.
    Pearl J (1988) Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann, San FranciscoGoogle Scholar
  29. 29.
    Pedersen TP (1991) Non-interactive and information-theoretic secure verifiable secret sharing. In: Proc of CRYPTO 1991, the 11th Ann Intl Cryptology Conf, Springer-Verlag (LNCS 576). Springer, New York, pp 129–140Google Scholar
  30. 30.
    Shamir A (1979) How to share a secret. In communications of the ACM, vol 22. pp 612–613Google Scholar
  31. 31.
    Shavitt Y, Shir E (2005) Dimes: Let the internet measure itself. ACM SIGCOMM Comput Commun Rev 35(5):71–74CrossRefGoogle Scholar
  32. 32.
    Toueg S, Perry KJ, Srikanth TK (1987) Fast distributed agreement. SIAM J Comput 16(3):445–457zbMATHCrossRefMathSciNetGoogle Scholar
  33. 33.
    Wan L, Ng WK, Han S, Lee VCS (2007) Privacy-preservation for gradient descent methods. In: KDD ’07: Proceedings of the 13th ACM SIGKDD international conference on knowledge discovery and data mining, ACM, New York, pp 775–783CrossRefGoogle Scholar
  34. 34.
    Yao A (1982) Protocols for secure computations. In: Proceedings of the 23rd symposium on foundations of computer science (FOCS), IEEE Computer Society Press, pp 160–164Google Scholar
  35. 35.
    Zhang S, Ford J, Makedon F (2006) A privacy-preserving collaborative filtering scheme with two-way communication. In: EC ’06: Proceedings of the 7th ACM conference on electronic commerce, ACM, New York, pp 316–323CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, LLC 2009

Authors and Affiliations

  • Danny Bickson
    • 1
    Email author
  • Tzachy Reinman
    • 2
  • Danny Dolev
    • 2
  • Benny Pinkas
    • 3
  1. 1.IBM Haifa Research Lab, Mount CarmelHaifaIsrael
  2. 2.School of Computer Science and EngineeringThe Hebrew University of JerusalemJerusalemIsrael
  3. 3.Dept. of Computer ScienceUniversity of Haifa, Mount CarmelHaifaIsrael

Personalised recommendations