Oblivious RAM with Worst-Case Logarithmic Overhead

Gilad Asharov, Ilan Komargodski*, Wei Kai Lin, Elaine Shi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We present the first Oblivious RAM (ORAM) construction that for N memory blocks supports accesses with worst-case O(log N) overhead for any block size Ω (log N) while requiring a client memory of only a constant number of memory blocks. We rely on the existence of one-way functions and guarantee computational security. Our result closes a long line of research on fundamental feasibility results for ORAM constructions as logarithmic overhead is necessary. The previous best logarithmic overhead construction only guarantees it in an amortized sense, i.e., logarithmic overhead is achieved only for long enough access sequences, where some of the individual accesses incur Θ (N) overhead. The previously best ORAM in terms of worst-case overhead achieves O(log 2N/ log log N) overhead. Technically, we design a novel de-amortization framework for modern ORAM constructions that use the “shuffled inputs” assumption. Our framework significantly departs from all previous de-amortization frameworks, originating from Ostrovsky and Shoup (STOC’97), that seem to be fundamentally too weak to be applied on modern ORAM constructions.

Original languageEnglish
Article number7
Pages (from-to)1-42
Number of pages42
JournalJournal of Cryptology
Volume36
Issue number2
DOIs
StatePublished - Apr 2023

Bibliographical note

Funding Information:
This work is supported in part by a DARPA Brandeis award, a DARPA SIEVE grant, NSF grants under the award numbers CNS-1601879, 2001026, 2044679, by Packard Fellowship, a JP Morgan Award, an ONR YIP award, by the Israel Science Foundation (grants No. 2439/20 and 1774/20), by an Alon Young Faculty Fellowship, and by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 891234. Ilan Komargodski is the incumbent of the Harry & Abe Sherman Senior Lectureship at the School of Computer Science and Engineering at the Hebrew University.

Funding Information:
This work is supported in part by a DARPA Brandeis award, a DARPA SIEVE grant, NSF grants under the award numbers CNS-1601879, 2001026, 2044679, by Packard Fellowship, a JP Morgan Award, an ONR YIP award, by the Israel Science Foundation (grants No. 2439/20 and 1774/20), by an Alon Young Faculty Fellowship, and by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 891234. Ilan Komargodski is the incumbent of the Harry & Abe Sherman Senior Lectureship at the School of Computer Science and Engineering at the Hebrew University.

Publisher Copyright:
© 2023, International Association for Cryptologic Research.

Keywords

  • Deamortization
  • Logarithmic overhead
  • Oblivious RAM

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