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Optimizing ORAM and Using It Efficiently for Secure Computation

  • Craig Gentry
  • Kenny A. Goldman
  • Shai Halevi
  • Charanjit Julta
  • Mariana Raykova
  • Daniel Wichs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7981)

Abstract

Oblivious RAM (ORAM) allows a client to access her data on a remote server while hiding the access pattern (which locations she is accessing) from the server. Beyond its immediate utility in allowing private computation over a client’s outsourced data, ORAM also allows mutually distrustful parties to run secure-computations over their joint data with sublinear on-line complexity. In this work we revisit the tree-based ORAM of Shi et al. [20] and show how to optimize its performance as a stand-alone scheme, as well as its performance within higher level constructions. More specifically, we make several contributions:

  • We describe two optimizations to the tree-based ORAM protocol of Shi et al., one reducing the storage overhead of that protocol by an O(k) multiplicative factor, and another reducing its time complexity by an O(logk) multiplicative factor, where k is the security parameter. Our scheme also enjoys a much simpler and tighter analysis than the original protocol.

  • We describe a protocol for binary search over this ORAM construction, where the entire binary search operation is done in the same complexity as a single ORAM access (as opposed to logn accesses for the naive protocol). We then describe simple uses of this binary-search protocol for things like range queries and keyword search.

  • We show how the ORAM protocol itself and our binary-search protocol can be implemented efficiently as secure computation, using somewhat-homomorphic encryption.

Since memory accesses by address (ORAM access) or by value (binary search) are basic and prevalent operations, we believe that these optimizations can be used to significantly speed-up many higher-level protocols for secure computation.

Keywords

Binary Search Range Query Secure Computation Security Parameter Homomorphic Encryption 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Alon, N., Spencer, J.: The Probabilistic Method. John Wiley (1992)Google Scholar
  2. 2.
    Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical gapsvp. In: Safavi-Naini, Canetti (eds.) [19], pp. 868–886Google Scholar
  3. 3.
    Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (leveled) fully homomorphic encryption without bootstrapping. In: Goldwasser, S. (ed.) ITCS, pp. 309–325. ACM (2012)Google Scholar
  4. 4.
    Brakerski, Z., Vaikuntanathan, V.: Efficient fully fomomorphic encryption from (standard) lwe. In: Ostrovsky, R. (ed.) FOCS, pp. 97–106. IEEE (2011)Google Scholar
  5. 5.
    Brakerski, Z., Vaikuntanathan, V.: Fully homomorphic encryption from ring-lwe and security for key dependent messages. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 505–524. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  6. 6.
    Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC, pp. 169–178 (2009)Google Scholar
  7. 7.
    Gentry, C., Halevi, S., Smart, N.P.: Fully homomorphic encryption with polylog overhead. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 465–482. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    Gentry, C., Halevi, S., Smart, N.P.: Homomorphic evaluation of the aes circuit. In: Safavi-Naini, Canetti (eds.) [19], pp. 850–867Google Scholar
  9. 9.
    Goldreich, O.: Towards a theory of software protection and simulation by oblivious rams. In: Aho, A.V. (ed.) STOC, pp. 182–194. ACM (1987)Google Scholar
  10. 10.
    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 (1987)Google Scholar
  11. 11.
    Goldreich, O., Ostrovsky, R.: Software protection and simulation on oblivious rams. J. ACM 43(3), 431–473 (1996)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Goodrich, M.T., Mitzenmacher, M.: Privacy-Preserving Access of Outsourced Data via Oblivious RAM Simulation. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 576–587. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  13. 13.
    Goodrich, M.T., Mitzenmacher, M., Ohrimenko, O., Tamassia, R.: Privacy-preserving group data access via stateless oblivious RAM simulation. In: Rabani, Y. (ed.) SODA, pp. 157–167. SIAM (2012)Google Scholar
  14. 14.
    Gordon, S.D., Katz, J., Kolesnikov, V., Krell, F., Malkin, T., Raykova, M., Vahlis, Y.: Secure two-party computation in sublinear (amortized) time. In: CCS (2012)Google Scholar
  15. 15.
    Ishai, Y., Kushilevitz, E.: Randomizing polynomials: A new representation with applications to round-efficient secure computation. In: FOCS, pp. 294–304. IEEE Computer Society (2000)Google Scholar
  16. 16.
    Ostrovsky, R.: Efficient computation on oblivious rams. In: Ortiz, H. (ed.) STOC, pp. 514–523. ACM (1990)Google Scholar
  17. 17.
    Ostrovsky, R., Shoup, V.: Private information storage. In: STOC (1997)Google Scholar
  18. 18.
    Pinkas, B., Reinman, T.: Oblivious RAM Revisited. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 502–519. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  19. 19.
    Safavi-Naini, R., Canetti, R. (eds.): CRYPTO 2012. LNCS, vol. 7417. Springer, Heidelberg (2012)MATHGoogle Scholar
  20. 20.
    Shi, E., Chan, T.-H.H., Stefanov, E., Li, M.: Oblivious RAM with O((logN)3) worst-case cost. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 197–214. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  21. 21.
    Yao, A.C.-C.: Protocols for secure computations (extended abstract). In: FOCS, pp. 160–164 (1982)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Craig Gentry
    • 1
  • Kenny A. Goldman
    • 1
  • Shai Halevi
    • 1
  • Charanjit Julta
    • 1
  • Mariana Raykova
    • 1
  • Daniel Wichs
    • 2
  1. 1.IBM ResearchUSA
  2. 2.Northeastern UniversityUSA

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