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Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms

On the (In)security of Hash-based Oblivious RAM and a New Balancing Scheme

Abstract

With the gaining popularity of remote storage (e.g. in the Cloud), we consider the setting where a small, protected local machine wishes to access data on a large, untrusted remote machine. This setting was introduced in the RAM model in the context of software protection by Goldreich and Ostrovsky. A secure Oblivious RAM simulation allows for a client, with small (e.g., constant size) protected memory, to hide not only the data but also the sequence of locations it accesses (both reads and writes) in the unprotected memory of size n.
Our main results are as follows:
We analyze several schemes from the literature, observing a repeated design flaw that leaks information on the memory access pattern. For some of these schemes, the leakage is actually non-negligible, while for others it is negligible.
On the positive side, we present a new secure oblivious RAM scheme, extending a recent scheme by Goodrich and Mitzenmacher. Our scheme uses only O(1) local memory, and its (amortized) overhead is O(log2 n/log log n), outperforming the previously-best O(log2 n) overhead (among schemes where the client only uses O(1) additional local memory).
We also present a transformation of our scheme above (whose amortized overhead is O(log2 n/log log n)) into a scheme with worst-case overhead of O(log2 n/log log n).

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Published In

cover image Proceedings
Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms
Pages: 143 - 156
Editor: Yuval Rabani, The Hebrew Institute of Jerusalem, Jerusalem, Israel
ISBN (Print): 978-1-61197-210-8
ISBN (Online): 978-1-61197-309-9

History

Published online: 18 December 2013

Keywords

  1. Oblivious RAM
  2. Cuckoo Hashing
  3. Secure Computation

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Notes

*
Supported by ISF grant 1361/10 and BSF grant 2008411. E-mail: [email protected]
This material is based upon work supported in part by NSF grants 0830803, 09165174, 1065276, 1118126 and 1136174, US-Israel BSF grant 2008411, grants from OKAWA Foundation, IBM, Lockheed-Martin Corporation and the Defense Advanced Research Projects Agency through the U.S. Office of Naval Research under Contract N00014-11-1-0392. The views expressed are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. E-mail: [email protected]

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