Composable Oblivious Extended Permutations

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8930)

Abstract

An extended permutation is a function \(f:\{1,\ldots ,m\}\rightarrow \{1,\ldots ,n\}\), used to map an \(n\)-element vector \(\varvec{a}\) to an \(m\)-element vector \(\varvec{b}\) by \(b_i=a_{f(i)}\). An oblivious extended permutation allows this mapping to be done while preserving the privacy of \(\varvec{a}\), \(\varvec{b}\) and \(f\) in a secure multiparty computation protocol. Oblivious extended permutations have several uses, with private function evaluation (PFE) being the theoretically most prominent one.

In this paper, we propose a new technique for oblivious evaluation of extended permutations. Our construction is at least as efficient as the existing techniques, conceptually simpler, and has wider applicability. Our technique allows the party providing the description of \(f\) to be absent during the computation phase of the protocol. Moreover, that party does not even have to exist — we show how to compute the private representation of \(f\) from private data that may itself be computed from the inputs of parties. In other words, our oblivious extended permutations can be freely composed with other privacy-preserving operations in a multiparty computation.

Keywords

Secure multiparty computation Private function evaluation Extended permutations 

References

  1. 1.
    SecureSCM. Technical report D9.1: Secure Computation Models and Frameworks, July 2008. http://www.securescm.org
  2. 2.
    Ben-David, A., Nisan, N., Pinkas, B.: FairplayMP: a system for secure multi-party computation. In: CCS 2008: Proceedings of the 15th ACM Conference on Computer and Communications Security, pp. 257–266. ACM, New York (2008)Google Scholar
  3. 3.
    Bogdanov, D., Kalu, A.: Pushing back the rain–how to create trustworthy services in the cloud. ISACA J. 3, 49–51 (2013)Google Scholar
  4. 4.
    Bogdanov, D., Kamm, L., Laur, S., Pruulmann-Vengerfeldt, P.: Secure multi-party data analysis: end user validation and practical experiments. Cryptology ePrint Archive, Report 2013/826 (2013). http://eprint.iacr.org/
  5. 5.
    Bogdanov, D., Laur, S., Willemson, J.: Sharemind: a framework for fast privacy-preserving computations. In: Jajodia, S., Lopez, J. (eds.) ESORICS 2008. LNCS, vol. 5283, pp. 192–206. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  6. 6.
    Bogdanov, D., Talviste, R., Willemson, J.: Deploying secure multi-party computation for financial data analysis. In: Keromytis, A.D. (ed.) FC 2012. LNCS, vol. 7397, pp. 57–64. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  7. 7.
    Bogetoft, P., et al.: Secure multiparty computation goes live. In: Dingledine, R., Golle, P. (eds.) FC 2009. LNCS, vol. 5628, pp. 325–343. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  8. 8.
    Burkhart, M., Strasser, M., Many, D., Dimitropoulos, X.: SEPIA: privacy-preserving aggregation of multi-domain network events and statistics. In: USENIX Security Symposium, Washington, DC, USA, pp. 223–239 (2010)Google Scholar
  9. 9.
    Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: FOCS, pp. 136–145. IEEE Computer Society (2001)Google Scholar
  10. 10.
    Damgård, I.B., 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
  11. 11.
    Damgård, I., Keller, M., Larraia, E., Pastro, V., Scholl, P., Smart, N.P.: Practical covertly secure MPC for dishonest majority – or: breaking the SPDZ limits. In: Crampton, J., Jajodia, S., Mayes, K. (eds.) ESORICS 2013. LNCS, vol. 8134, pp. 1–18. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  12. 12.
    Damgård, I., Meldgaard, S., Nielsen, J.B.: Perfectly secure oblivious RAM without random oracles. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 144–163. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  13. 13.
    Damgård, I.B., Nielsen, J.B.: Universally composable efficient multiparty computation from threshold homomorphic encryption. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 247–264. Springer, Heidelberg (2003) CrossRefGoogle Scholar
  14. 14.
    Geisler, M.: Cryptographic protocols: theory and implementation. Ph.D. thesis, Aarhus University, February 2010Google Scholar
  15. 15.
    Gennaro, R., Rabin, M.O., Rabin, T.: Simplified VSS and fast-track multiparty computations with applications to threshold cryptography. In: PODC, pp. 101–111 (1998)Google Scholar
  16. 16.
    Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Mitzenmacher, M. (ed.) STOC, pp. 169–178. ACM (2009)Google Scholar
  17. 17.
    Gentry, C., Goldman, K.A., Halevi, S., Julta, C., Raykova, M., Wichs, D.: Optimizing ORAM and using it efficiently for secure computation. In: De Cristofaro, E., Wright, M. (eds.) PETS 2013. LNCS, vol. 7981, pp. 1–18. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  18. 18.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC, pp. 218–229. ACM (1987)Google Scholar
  19. 19.
    Goldreich, O., Ostrovsky, R.: Software protection and simulation on oblivious RAMs. J. ACM 43(3), 431–473 (1996)CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    Guanciale, R., Gurov, D., Laud, P.: Private intersection of regular languages. In: Proceedings of the 12th Annual Conference on Privacy, Security and Trust, pp. 112–120. IEEE (2014)Google Scholar
  21. 21.
    Hamada, K., Ikarashi, D., Chida, K., Takahashi, K.: Oblivious radix sort: an efficient sorting algorithm for practical secure multi-party computation. Cryptology ePrint Archive, Report 2014/121 (2014). http://eprint.iacr.org/
  22. 22.
    Hamada, K., Kikuchi, R., Ikarashi, D., Chida, K., Takahashi, K.: Practically efficient multi-party sorting protocols from comparison sort algorithms. In: Kwon, T., Lee, M.-K., Kwon, D. (eds.) ICISC 2012. LNCS, vol. 7839, pp. 202–216. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  23. 23.
    Henecka, W., Kögl, S., Sadeghi, A.R., Schneider, T., Wehrenberg, I.: TASTY: tool for automating secure two-party computations. In: CCS 2010: Proceedings of the 17th ACM Conference on Computer and Communications Security, pp. 451–462. ACM, New York (2010)Google Scholar
  24. 24.
    Huang, Y., Evans, D., Katz, J.: Private set intersection: are garbled circuits better than custom protocols? In: NDSS. The Internet Society (2012)Google Scholar
  25. 25.
    Ikarashi, D., Kikuchi, R., Hamada, K., Chida, K.: Actively private and correct MPC scheme in \(t<n/2\) from passively secure schemes with small overhead. Cryptology ePrint Archive, Report 2014/304 (2014). http://eprint.iacr.org/
  26. 26.
    Ishai, Y., Paskin, A.: Evaluating branching programs on encrypted data. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 575–594. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  27. 27.
    Jónsson, K.V., Kreitz, G., Uddin, M.: Secure multi-party sorting and applications. Cryptology ePrint Archive, Report 2011/122 (2011). http://eprint.iacr.org/
  28. 28.
    Kamm, L., Bogdanov, D., Laur, S., Vilo, J.: A new way to protect privacy in large-scale genome-wide association studies. Bioinformatics 29(7), 886–893 (2013)CrossRefGoogle Scholar
  29. 29.
    Kolesnikov, V., Schneider, T.: A practical universal circuit construction and secure evaluation of private functions. In: Tsudik, G. (ed.) FC 2008. LNCS, vol. 5143, pp. 83–97. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  30. 30.
    Laud, P.: A private lookup protocol with low online complexity for secure multiparty computation. In: Shi, E., Yiu, S.M. (eds.) ICICS. LNCS. Springer, Heidelberg (2014, to appear)Google Scholar
  31. 31.
    Laud, P., Pankova, A.: Verifiable computation in multiparty protocols with honest majority. In: Chow, S.S.M., Liu, J.K., Hui, L.C.K., Yiu, S.M. (eds.) ProvSec 2014. LNCS, vol. 8782, pp. 146–161. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  32. 32.
    Laud, P., Willemson, J.: Composable oblivious extended permutations. Cryptology ePrint Archive, Report 2014/400 (2014). http://eprint.iacr.org/
  33. 33.
    Laur, S., Talviste, R., Willemson, J.: From oblivious AES to efficient and secure database join in the multiparty setting. In: Jacobson, M., Locasto, M., Mohassel, P., Safavi-Naini, R. (eds.) ACNS 2013. LNCS, vol. 7954, pp. 84–101. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  34. 34.
    Laur, S., Willemson, J., Zhang, B.: Round-efficient oblivious database manipulation. In: Lai, X., Zhou, J., Li, H. (eds.) ISC 2011. LNCS, vol. 7001, pp. 262–277. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  35. 35.
    Lejeune Dirichlet, J.P.G.: Über die Bestimmung der Mittleren Werthe in der Zahlentheorie. Abhandlungen der Köninglich Preussischen Akademie der Wissenschaften, pp. 69–83 (1849)Google Scholar
  36. 36.
    Lu, S., Ostrovsky, R.: Distributed oblivious RAM for secure two-party computation. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 377–396. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  37. 37.
    Malka, L., Katz, J.: VMCrypt - modular software architecture for scalable secure computation. Cryptology ePrint Archive, Report 2010/584 (2010). http://eprint.iacr.org/
  38. 38.
    Mohassel, P., Sadeghian, S., Smart, N.P.: Actively secure private function evaluation. Cryptology ePrint Archive, Report 2014/102 (2014). http://eprint.iacr.org/
  39. 39.
    Mohassel, P., Sadeghian, S.: How to hide circuits in MPC an efficient framework for private function evaluation. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 557–574. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  40. 40.
    Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)CrossRefMATHMathSciNetGoogle Scholar
  41. 41.
    Stefanov, E., van Dijk, M., Shi, E., Fletcher, C.W., Ren, L., Yu, X., Devadas, S.: Path ORAM: an extremely simple oblivious RAM protocol. In: Sadeghi, A.R., Gligor, V.D., Yung, M. (eds.) ACM Conference on Computer and Communications Security, pp. 299–310. ACM (2013)Google Scholar
  42. 42.
    Waksman, A.: A permutation network. J. ACM 15(1), 159–163 (1968)CrossRefMATHGoogle Scholar
  43. 43.
    Yao, A.C.C.: Protocols for secure computations (extended abstract). In: FOCS, pp. 160–164. IEEE (1982)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Cybernetica ASTallinnEstonia

Personalised recommendations