Abstract
We demonstrate a simple, statistically secure, ORAM with computational overhead \(\tilde{O}(\log^2 n)\); previous ORAM protocols achieve only computational security (under computational assumptions) or require \(\tilde{\Omega}(\log^3 n)\) overheard. An additional benefit of our ORAM is its conceptual simplicity, which makes it easy to implement in both software and (commercially available) hardware.
Our construction is based on recent ORAM constructions due to Shi, Chan, Stefanov, and Li (Asiacrypt 2011) and Stefanov and Shi (ArXiv 2012), but with some crucial modifications in the algorithm that simplifies the ORAM and enable our analysis. A central component in our analysis is reducing the analysis of our algorithm to a “supermarket” problem; of independent interest (and of importance to our analysis,) we provide an upper bound on the rate of “upset” customers in the “supermarket” problem.
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References
Ajtai, M.: Oblivious RAMs without cryptogrpahic assumptions. In: STOC, pp. 181–190 (2010)
Boneh, D., Mazieres, D., Popa, R.A.: Remote oblivious storage: Making oblivious RAM practical. CSAIL Technical Report: MIT-CSAIL-TR-2011-018 (2012)
Chung, K.M., Lam, H., Liu, Z., Mitzenmacher, M.: Chernoff-Hoeffding bounds for Markov chains: Generalized and simplified. In: Proceedings of the 29th International Symposium on Theoretical Aspects of Computer Science, STACS (2012)
Chung, K.-M., Liu, Z., Pass, R.: Statistically-secure ORAM with \tilde{O}(\log^2 n overhead. CoRR, abs/1307.3699 (2013)
Chung, K.-M., Pass, R.: A simple ORAM. Cryptology ePrint Archive, Report 2013/243 (2013)
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)
Eager, D.L., Lazowska, E.D., Zahorjan, J.: Lazowska, and John Zahorjan. Adaptive load sharing in homogeneous distributed systems. IEEE Trans. Software Eng. 12(5), 662–675 (1986)
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)
Gillman, D.: A Chernoff bound for random walks on expander graphs. SIAM Journal on Computing 27(4) (1997)
Goldreich, O.: Towards a theory of software protection and simulation by oblivious RAMs. In: STOC, pp. 182–194 (1987)
Goldreich, O., Ostrovsky, R.: Software protection and simulation on oblivious RAMs. J. ACM 43(3), 431–473 (1996)
Goodrich, M.T., Mitzenmacher, M.: Privacy-preserving access of outsourced data via oblivious RAM simulation. In: ICALP, vol. (2), pp. 576–587 (2011)
Goodrich, M.T., Mitzenmacher, M., Ohrimenko, O., Tamassia, R.: Privacy-preserving group data access via stateless oblivious RAM simulation. In: SODA, pp. 157–167 (2012)
Kahale, N.: Large deviation bounds for Markov chains. Combinatorics, Probability, and Computing 6(4) (1997)
Kushilevitz, E., Lu, S., Ostrovsky, R.: On the (in)security of hash-based oblivious RAM and a new balancing scheme. In: SODA, pp. 143–156 (2012)
Lezaud, P.: Chernoff-type bound for finite Markov chains. Annals of Applied Probability 8(3), 849–867 (1998)
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)
Maas, M., Love, E., Stefanov, E., Tiwari, M., Shi, E., Asanovic, K., Kubiatowicz, J., Song, D.: Phantom: Practical oblivious computation in a secure processor. In: CCS 2013, pp. 311–324. ACM Press, New York (2013)
Mitzenmacher, M., Upfal, E.: Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press (2005)
Mitzenmacher, M.: The power of two choices in randomized load balancing. IEEE Trans. Parallel Distrib. Syst. 12(10), 1094–1104 (2001)
Mitzenmacher, M., Prabhakar, B., Shah, D.: Load balancing with memory. In: FOCS, pp. 799–808 (2002)
Mitzenmacher, M., Vadhan, S.: Why simple hash functions work: exploiting the entropy in a data stream. In: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2008, pp. 746–755 (2008)
Mitzenmacher, M., Vocking, B.: The asymptotics of selecting the shortest of two, improved. Proceedings of the Annual Allerton Conference on Communication Control and Computing 37, 326–327 (1999)
Ostrovsky, R., Shoup, V.: Private information storage (extended abstract). In: STOC, pp. 294–303 (1997)
Pinkas, B., Reinman, T.: Oblivious RAM revisited. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 502–519. Springer, Heidelberg (2010)
Shah, D., Prabhakar, B.: The use of memory in randomized load balancing. Proceedingsof the 2002 IEEE International Symposium on Information Theory, p. 125. IEEE (2002)
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)
Stefanov, E., Shi, E.: Path O-RAM: An extremely simple oblivious RAM protocol. CoRR, abs/1202.5150v1 (2012)
Stefanov, E., Shi, E., Song, D.: Towards practical oblivious RAM. In: NDSS (2012)
Stefanov, E., Van Dijk, M., Shi, E., Fletcher, C., Ren, L., Yu, X., Devadas, S.: Path O-RAM: An extremely simple oblivious RAM protocol. In: CCS (2013)
Vvedenskaya, N.D., Dobrushin, R.L., Karpelevich, F.I.: Queueing system with selection of the shortest of two queues: An asymptotic approach. Problemy Peredachi Informatsii 32(1), 20–34 (1996)
Williams, P., Sion, R.: Usable PIR. In: NDSS (2008)
Williams, P., Sion, R., Carbunar, B.: Building castles out of mud: practical access pattern privacy and correctness on untrusted storage. In: ACM Conference on Computer and Communications Security, pp. 139–148 (2008)
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Chung, KM., Liu, Z., Pass, R. (2014). Statistically-secure ORAM with \(\tilde{O}(\log^2 n)\) Overhead. In: Sarkar, P., Iwata, T. (eds) Advances in Cryptology – ASIACRYPT 2014. ASIACRYPT 2014. Lecture Notes in Computer Science, vol 8874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45608-8_4
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