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Snapshot-Oblivious RAMs: Sub-logarithmic Efficiency for Short Transcripts

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Advances in Cryptology – CRYPTO 2022 (CRYPTO 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13510))

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Abstract

Oblivious RAM (ORAM) is a powerful technique to prevent harmful data breaches. Despite tremendous progress in improving the concrete performance of ORAM, it remains too slow for use in many practical settings; recent breakthroughs in lower bounds indicate this inefficiency is inherent for ORAM and even some natural relaxations.

This work introduces snapshot-oblivious RAMs, a new secure memory access primitive. Snapshot-oblivious RAMs bypass lower bounds by providing security only for transcripts whose length (call it \(c\)) is fixed and known ahead of time. Intuitively, snapshot-oblivious RAMs provide strong security for attacks of short duration, such as the snapshot attacks targeted by many encrypted databases.

We give an ORAM-style definition of this new primitive, and present several constructions. The underlying design principle of our constructions is to store the history of recent operations in a data structure that can be accessed obliviously. We instantiate this paradigm with data structures that remain on the client, giving a snapshot-oblivious RAM with constant bandwidth overhead. We also show how these data structures can be stored on the server and accessed using oblivious memory primitives. Our most efficient instantiation achieves \(\mathcal{O}(\log c)\) bandwidth overhead. By extending recent ORAM lower bounds, we show this performance is asymptotically optimal. Along the way, we define a new hash queue data structure—essentially, a dictionary whose elements can be modified in a first-in-first-out fashion—which may be of independent interest.

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Acknowledgments

The authors thank their shepherd Mark Simkin and the anonymous reviewers at CRYPTO 2022 for their helpful comments and suggestions. This work was partially supported by the Air Force Office of Scientific Research (AFOSR) under award number FA9550-20–1-0425; the National Science Foundation under grant CNS-1954712 and by a gift from Qualcomm.

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Authors and Affiliations

  1. University of Michigan, Ann Arbor, USA

    Yang Du & Paul Grubbs

  2. Georgia Tech, Atlanta, USA

    Daniel Genkin

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  1. Yang Du
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  2. Daniel Genkin
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  3. Paul Grubbs
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Correspondence to Paul Grubbs .

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Editors and Affiliations

  1. New York University, New York, NY, USA

    Yevgeniy Dodis

  2. University of Florida, Gainesville, FL, USA

    Thomas Shrimpton

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© 2022 International Association for Cryptologic Research

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Du, Y., Genkin, D., Grubbs, P. (2022). Snapshot-Oblivious RAMs: Sub-logarithmic Efficiency for Short Transcripts. In: Dodis, Y., Shrimpton, T. (eds) Advances in Cryptology – CRYPTO 2022. CRYPTO 2022. Lecture Notes in Computer Science, vol 13510. Springer, Cham. https://doi.org/10.1007/978-3-031-15985-5_6

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  • DOI: https://doi.org/10.1007/978-3-031-15985-5_6

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  • Online ISBN: 978-3-031-15985-5

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