Advertisement

An ORAM Scheme with Improved Worst-Case Computational Overhead

  • Nairen Cao
  • Xiaoqi Yu
  • Yufang Yang
  • Linru Zhang
  • SiuMing YiuEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9543)

Abstract

We construct a statistically secure ORAM with computational overhead of \(O(\log ^2N\log \log N)\). Moreover, when accessing continuous blocks, our scheme can achieve an amortized complexity \(O(\log N\log \log N)\), which almost matches the theoretical lower bound of the ORAM problem. Our construction is based on a tree-based construction [16]. The technical novelty comes from the idea of combining \(O(\log N)\) blocks into a big block together with a more aggressive and efficient “flush” operation, which is the bottleneck of existing ORAM schemes. All in all, we can achieve better amortized overhead in our new scheme.

Notes

Acknowledgement

This work is supported in part by National High Technology Research and Development Program of China (No. 2015AA016008), NSFC/RGC Joint Research Scheme (N_HKU 729/13), and Seed Funding Programme for Basic Research of HKU (201411159142).

References

  1. 1.
    Arbitman, Y., Naor, M., Segev, G.: Backyard cuckoo hashing: Constant worst-case operations with a succinct representation. CoRR, abs/0912.5424 (2009)Google Scholar
  2. 2.
    Chung, K.-M., Liu, Z., Pass, R.: Statistically-secure ORAM with \(\tilde{O}(\log ^2 n)\) overhead. CoRR, abs/1307.3699 (2013)Google Scholar
  3. 3.
    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
  4. 4.
    Goldreich, O., Ostrovsky, R.: Software protection and simulation on oblivious rams. J. ACM 43(3), 431–473 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Goodrich, M.T.: Randomized shellsort: a simple data-oblivious sorting algorithm. J. ACM 58(6), 27: 1–27: 26 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    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
  7. 7.
    Goodrich, M.T., Mitzenmacher, M., Ohrimenko, O., Tamassia, R.: Oblivious ram simulation with efficient worst-case access overhead. In: Proceedings of the 3rd ACM Workshop on Cloud Computing Security Workshop, CCSW 2011, New York, pp. 95–100. ACM (2011)Google Scholar
  8. 8.
    Goodrich, M.T., Mitzenmacher, M., Ohrimenko, O., Tamassia, R.: Privacy-preserving group data access via stateless oblivious ram simulation. In: Proceedings of the Twenty-third Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012, pp. 157–167. SIAM (2012)Google Scholar
  9. 9.
    Liu, Z., Chung, K.M., Lam, H., Mitzenmacher, M.: Chernoff-hoeffding bounds for markov chains: generalized and simplified. In: ACM (1998)Google Scholar
  10. 10.
    Chung, K.-M., Pass, R.: A simple oram (2013)Google Scholar
  11. 11.
    Goldreich, M.T.: Towards a theory of software protection and simulation by oblivious rams. STOC (1987)Google Scholar
  12. 12.
    Pinkas, B., Reinman, T.: Oblivious RAM revisited. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 502–519. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Raab, M., Steger, A.: “Balls into bins" - a simple and tight analysis. In: Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 1998, London, pp. 159–170. Springer-Verlag (1998)Google Scholar
  14. 14.
    Ostrovsky, R.: Efficient computation on oblivious rams. STOC (1990)Google Scholar
  15. 15.
    Shi, Elaine, Chan, T-HHubert, Stefanov, Emil, Li, Mingfei: Oblivious RAM with o((logn)\(^\text{3}\)) worst-case cost. In: Lee, Dong Hoon, Wang, Xiaoyun (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 197–214. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  16. 16.
    Stefanov, E., van Dijk, M., Shi, E., Fletcher, C., Ren, L., Xiangyao, Y., Devadas, S., Path oram: An extremely simple oblivious ram protocol. In: Proceedings of the ACM SIGSAC Conference on Computer & Communications Security, CCS 2013, New York, pp. 299–310. ACM (2013)Google Scholar
  17. 17.
    Wang, X., Chan, H., Shi, E.: Circuit oram: On tightness of the goldreich-ostrovsky lower bound. Cryptology ePrint Archive, Report /672 (2014). http://eprint.iacr.org/
  18. 18.
    Williams, P., Sion, R., Carbunar, B.: Building castles out of mud: practical access pattern privacy and correctness on untrusted storage. In: Proceedings of the 15th ACM Conference on Computer and Communications Security, CCS 2008, New York, pp. 139–148. ACM (2008)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Nairen Cao
    • 1
  • Xiaoqi Yu
    • 1
  • Yufang Yang
    • 2
  • Linru Zhang
    • 3
  • SiuMing Yiu
    • 1
    Email author
  1. 1.The University of Hong KongHong KongChina
  2. 2.Tsinghua UniversityBeijingChina
  3. 3.Sun Yat-sen UniversityGuangzhouChina

Personalised recommendations