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Perfectly Oblivious (Parallel) RAM Revisited, and Improved Constructions

Authors T-H. Hubert Chan, Elaine Shi, Wei-Kai Lin, Kartik Nayak

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  • Theory of computation → Cryptographic protocols
Keywords
  • perfect oblivious RAM
  • oblivious PRAM

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Abstract

Oblivious RAM (ORAM) is a technique for compiling any RAM program to an oblivious counterpart, i.e., one whose access patterns do not leak information about the secret inputs. Similarly, Oblivious Parallel RAM (OPRAM) compiles a parallel RAM program to an oblivious counterpart. In this paper, we care about ORAM/OPRAM with perfect security, i.e., the access patterns must be identically distributed no matter what the program’s memory request sequence is. In the past, two types of perfect ORAMs/OPRAMs have been considered: constructions whose performance bounds hold in expectation (but may occasionally run more slowly); and constructions whose performance bounds hold deterministically (even though the algorithms themselves are randomized).
In this paper, we revisit the performance metrics for perfect ORAM/OPRAM, and show novel constructions that achieve asymptotical improvements for all performance metrics. Our first result is a new perfectly secure OPRAM scheme with O(log³ N/log log N) expected overhead. In comparison, prior literature has been stuck at O(log³ N) for more than a decade. 
Next, we show how to construct a perfect ORAM with O(log³ N/log log N) deterministic simulation overhead. We further show how to make the scheme parallel, resulting in an perfect OPRAM with O(log⁴ N/log log N) deterministic simulation overhead. For perfect ORAMs/OPRAMs with deterministic performance bounds, our results achieve subexponential improvement over the state-of-the-art. Specifically, the best known prior scheme incurs more than √N deterministic simulation overhead (Raskin and Simkin, Asiacrypt'19); moreover, their scheme works only for the sequential setting and is not amenable to parallelization.
Finally, we additionally consider perfect ORAMs/OPRAMs whose performance bounds hold with high probability. For this new performance metric, we show new constructions whose simulation overhead is upper bounded by O(log³ /log log N) except with negligible in N probability, i.e., we prove high-probability performance bounds that match the expected bounds mentioned earlier.

Cite As Get BibTex

T-H. Hubert Chan, Elaine Shi, Wei-Kai Lin, and Kartik Nayak. Perfectly Oblivious (Parallel) RAM Revisited, and Improved Constructions. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 8:1-8:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ITC.2021.8

Author Details

T-H. Hubert Chan
  • Department of Computer Science, University of Hong Kong, Hong Kong
Elaine Shi
  • Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA
Wei-Kai Lin
  • Department of Computer Science, Cornell University, Ithaca, NY, USA
Kartik Nayak
  • Department of Computer Sciences, Duke University, Durham, NC, USA

Funding

  • Chan, T-H. Hubert: This work was partially supported by the Hong Kong RGC under the grants 17200418 and 17201220.
  • Shi, Elaine: This work was partially supported by NSF CNS-1601879, an ONR YIP award, and a Packard Fellowship.
  • Lin, Wei-Kai: This work was supported by a DARPA Brandeis award.
  • Nayak, Kartik: This work was partially supported by NSF Award 2016393.

Acknowledgements

Author ordering is randomized.

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