OptORAMa: Optimal Oblivious RAM

Gilad Asharov, Ilan Komargodski, Wei Kai Lin, Kartik Nayak, Enoch Peserico, Elaine Shi

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Oblivious RAM (ORAM), first introduced in the ground-breaking work of Goldreich and Ostrovsky (STOC '87 and J. ACM '96) is a technique for provably obfuscating programs' access patterns, such that the access patterns leak no information about the programs' secret inputs. To compile a general program to an oblivious counterpart, it is well-known that ω (log N) amortized blowup in memory accesses is necessary, where N is the size of the logical memory. This was shown in Goldreich and Ostrovksy's original ORAM work for statistical security and in a somewhat restricted model (the so-called balls-and-bins model), and recently by Larsen and Nielsen (CRYPTO '18) for computational security.A long-standing open question is whether there exists an optimal ORAM construction that matches the aforementioned logarithmic lower bounds (without making large memory word assumptions, and assuming a constant number of CPU registers). In this article, we resolve this problem and present the first secure ORAM with O(log N) amortized blowup, assuming one-way functions. Our result is inspired by and non-trivially improves on the recent beautiful work of Patel et al. (FOCS '18) who gave a construction with O(log Ng log log N) amortized blowup, assuming one-way functions. One of our building blocks of independent interest is a linear-time deterministic oblivious algorithm for tight compaction: Given an array of n elements where some elements are marked, we permute the elements in the array so that all marked elements end up in the front of the array. Our O(n) algorithm improves the previously best-known deterministic or randomized algorithms whose running time is O(n g log n) or O(n g log log n), respectively.

Original languageAmerican English
Article number4
Pages (from-to)4:1-4:70
Number of pages70
JournalJournal of the ACM
Volume70
Issue number1
DOIs
StatePublished - 20 Dec 2022

Bibliographical note

Publisher Copyright:
© 2022 Association for Computing Machinery.

Keywords

  • Oblivious RAM
  • oblivious tight compaction

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