Locality-Preserving Oblivious RAM

Gilad Asharov*, T. H.Hubert Chan, Kartik Nayak, Rafael Pass, Ling Ren, Elaine Shi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Oblivious RAMs, introduced by Goldreich and Ostrovsky [JACM’96], compile any RAM program into one that is “memory oblivious,” i.e., the access pattern to the memory is independent of the input. All previous ORAM schemes, however, completely break the locality of data accesses (for instance, by shuffling the data to pseudorandom positions in memory). In this work, we initiate the study of locality-preserving ORAMs—ORAMs that preserve locality of the accessed memory regions, while leaking only the lengths of contiguous memory regions accessed. Our main results demonstrate the existence of a locality-preserving ORAM with polylogarithmic overhead both in terms of bandwidth and locality. We also study the trade-off between locality, bandwidth and leakage, and show that any scheme that preserves locality and does not leak the lengths of the contiguous memory regions accessed, suffers from prohibitive bandwidth. To further improve the parameters, we also consider a weaker notion of a File ORAM, which supports accesses to predefined non-overlapping regions. Assuming one-way functions, we present a computationally secure File ORAM that has a work overhead and locality of roughly O(log 2N) , while ignoring log log N factors. To the best of our knowledge, before our work, the only works combining locality and obliviousness were for symmetric searchable encryption [e.g., Cash and Tessaro (EUROCRYPT’14), Asharov et al. (STOC’16)]. Symmetric search encryption ensures obliviousness if each keyword is searched only once, whereas ORAM provides obliviousness to any input program. Thus, our work generalizes that line of work to the much more challenging task of preserving locality in ORAMs.

Original languageEnglish
Article number6
JournalJournal of Cryptology
Volume35
Issue number2
DOIs
StatePublished - Apr 2022
Externally publishedYes

Funding

FundersFunder number
Office of Naval Research
Marie Skłodowska-Curie
Microsoft
Simons Foundation
GoogleCNS-1314857, CNS-1617676, CNS-1544613, CNS-1514261, CNS-1601879
National Science FoundationCNS-1704788, CNS-1561209, 1601879, CNS-1217821
Horizon 2020 Framework Programme891234
Israel Science Foundation2439/20
RGC17200418, 17201220
Air Force Office of Scientific ResearchFA9550-15-1-0262

    Keywords

    • Locality
    • Oblivious RAM
    • Randomized algorithms

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