Multi-party Indirect Indexing and Applications

  • Matthew Franklin
  • Mark Gondree
  • Payman Mohassel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4833)


We develop a new multi-party generalization of Naor-Nissim indirect indexing, making it possible for many participants to simulate a RAM machine with only poly-logarithmic blow-up. Our most efficient instantiation (built from length-flexible additively homomorphic public key encryption) improves the communication complexity of secure multi-party computation for a number of problems in the literature. Underlying our approach is a new multi-party variant of oblivious transfer which may be of independent interest.


communication complexity oblivious RAM machine privacy-preserving protocols secure multiparty computation 


  1. 1.
    Aiello, B., Ishai, Y., Reingold, O.: Priced oblivious transfer: How to sell digital goods. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 119–135. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  2. 2.
    Barkol, O., Ishai, Y.: Secure computation of constant-depth circuits with application to database search problems. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, Springer, Heidelberg (2005)Google Scholar
  3. 3.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant disributed computation. In: Proc. of STOC 1988, pp. 1–10 (1988)Google Scholar
  4. 4.
    Brassard, G., Crépeau, C., Robert, J.-M.: Information theoretic reductions among disclosure problems. In: Proc. of FOCS, pp. 168–173 (1986)Google Scholar
  5. 5.
    Canetti, R.: Security and composition of multiparty cryptographic protocols. Journal of Cryptology 13, 143–202 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Crépeau, C., Kilian, J.: Achieving oblivious transfer using weakened security assumptions. In: Proc. of FOCS, pp. 42–52 (1988)Google Scholar
  7. 7.
    Damgård, I., Fitzi, M., Kiltz, E., Nielsen, J.B., Toft, T.: Unconditionally secure constant-rounds multi-party computation for equality, comparison, bits and exponentiation. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 285–304. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Damgård, I., Jurik, M.: A generalisation, a simplification and some applications of Paillier’s probabilistic public-key system. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. 9.
    Damgård, I., Jurik, M.: A length-flexible threshold cryptosystem with applications. In: Information Security and Privacy, pp. 350–364 (2003)Google Scholar
  10. 10.
    Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. Comm. of the ACM 28(6), 637–647 (1985)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Franklin, M., Gondree, M., Mohassel, P.: Improved efficiency for private stable matching. In: Proc. of CT-RSA (2007)Google Scholar
  12. 12.
    Franklin, M., Gondree, M., Mohassel, P.: Multi-party indirect indexing and applications. Cryptology ePrint Archive, Report 2007/341 (2007)Google Scholar
  13. 13.
    Freuder, E.C., Wallace, R.J.: Constraint-based multi-agent meeting scheduling: effects of agent heterogeneity on performance and privacy loss. In: Proc. of the 3rd Workshop on Distributed Constraint Reasoning (DCR 2002), pp. 176–182 (2002)Google Scholar
  14. 14.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: Proc. of STOC 1987, pp. 218–229 (1987)Google Scholar
  15. 15.
    Goldreich, O.: Foundations of Cryptography. Cambridge University Press, Cambridge (2001)zbMATHGoogle Scholar
  16. 16.
    Goldreich, O., Ostrovsky, R.: Software protection and simulation on oblivious rams. Journal of the ACM 43(3), 431–473 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Goldreich, O., Vainish, R.: How to solve any protocol problem - an efficiency improvement. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 73–86. Springer, Heidelberg (1988)Google Scholar
  18. 18.
    Golle, P.: A private stable matching algorithm. In: Di Crescenzo, G., Rubin, A. (eds.) FC 2006. LNCS, vol. 4107, Springer, Heidelberg (2006)CrossRefGoogle Scholar
  19. 19.
    Ishai, Y., Malkin, T., Strauss, M.J., Wright, R.N.: Private multiparty sampling and approximation of vector combinations. In: Proc. of International Colloquium on Automata, Languages and Programming (ICALP) (2007)Google Scholar
  20. 20.
    Kilian, J.: A general completeness theorem for 2-party games. In: Proc. of STOC 1991, pp. 553–560 (1991)Google Scholar
  21. 21.
    Kushilevitz, E., Ostrovsky, R.: Replication is not needed: Single database, computationally-private information retrieval. In: Proc. of FOCS, pp. 364–373 (1997)Google Scholar
  22. 22.
    Lipmaa, H.: Verifiable homomorphic oblivious transfer and private equality test. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 416–433. Springer, Heidelberg (2003)Google Scholar
  23. 23.
    Meisels, A., Lavee, O.: Using additional information in DisCSP search. In: Proc. of the 5th Workshop on Distributed Constraint Reasoning (DCR-04) (2004)Google Scholar
  24. 24.
    Naor, M., Nissim, K.: Communication preserving protocols for secure function evaluation. In: Proc. of STOC 2001, pp. 590–599 (2001)Google Scholar
  25. 25.
    Naor, M., Pinkas, B.: Oblivious transfer and polynomial evaluation. In: Proc. of STOC 1999, pp. 245–254 (1999)Google Scholar
  26. 26.
    Naor, M., Pinkas, B.: Distributed oblivious transfer. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 205–219. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  27. 27.
    Naor, M., Pinkas, B., Sumner, R.: Privacy preserving auctions and mechanism design. In: EC 1999. Proc. of the 1st ACM conference on Electronic Commerce, pp. 129–139. ACM Press, New York (1999)Google Scholar
  28. 28.
    Nikov, V., Nikova, S., Preneel, B., Vandewalle, J.: On unconditionally secure distributed oblivious transfer. In: Menezes, A.J., Sarkar, P. (eds.) INDOCRYPT 2002. LNCS, vol. 2551, pp. 395–408. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  29. 29.
    Nissim, K., Zivan, R.: Secure DisCSP protocols - from centralized towards distributed solutions. In: Proc. of the 6th Workshop on Distributed Constraint Reasoning (DCR-05) (2005)Google Scholar
  30. 30.
    Ostrovsky, R., Skeith III, W.E.: A survey of single database PIR: Techniques and applications. Cryptology ePrint Archive, Report 2007/059 (2007)Google Scholar
  31. 31.
    Ostrovsky, R., Shoup, V.: Private information storage (extended abstract). In: Proc of STOC 1997, pp. 294–303 (1997)Google Scholar
  32. 32.
    Pippenger, N., Fischer, M.J.: Relations among complexity measures. Journal of the ACM 26(2), 361–381 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  33. 33.
    Rabin, M.O.: How to exchange secrets with oblivious transfer. Technical Report TR-81, Harvard University, available as the Cryptology ePrint Archive Report 2005/187 (1981),
  34. 34.
    Silaghi, M.-C.: Solving a distributed CSP with cryptographic multi-party computations, without revealing constraints and without involving trusted servers. In: Proc. of the 4th Workshop on Distributed Constraint Reasoning (DCR-03) (2003)Google Scholar
  35. 35.
    Silaghi, M.-C., Mitra, D.: Distributed constraint satisfaction and optimization with privacy enforcement. In: Proc. of the 3rd International Conference on Intelligence Agent Technology, pp. 531–535 (2004)Google Scholar
  36. 36.
    Solotorevsky, G., Gudes, E., Meisels, A.: Modeling and solving distributed constraint satisfaction problems (DCSPs). In: Constraint Processing-96, pp. 561–562 (1996)Google Scholar
  37. 37.
    Stern, J.P.: A new and efficient all-or-nothing disclosure of secrets protocol. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 357–371. Springer, Heidelberg (1998)Google Scholar
  38. 38.
    Yokoo, M.: Algorithms for distributed satisfaction problems: A review. In: Autonomous Agents and Multi-Agent Sys., pp. 198–212 (2000)Google Scholar
  39. 39.
    Yokoo, M., Suzuki, K., Hirayama, K.: Secure distributed constraint satisfaction: Reaching agreement without revealing private information. In: Artificial Intelligence, pp. 229–246 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Matthew Franklin
    • 1
  • Mark Gondree
    • 1
  • Payman Mohassel
    • 1
  1. 1.Department of Computer Science, University of California, Davis 

Personalised recommendations