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MetaDORAM: Info-Theoretic Distributed ORAM with Less Communication

Authors Brett Hemenway Falk , Daniel Noble , Rafail Ostrovsky

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ACM Subject Classification
  • Security and privacy → Information-theoretic techniques
  • Theory of computation → Communication complexity
  • Theory of computation → Cryptographic primitives
  • Security and privacy → Management and querying of encrypted data
Keywords
  • ORAM
  • MPC
  • DORAM
  • multi-server ORAM
  • active ORAM

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Abstract

A Distributed Oblivious RAM is a multi-party protocol that securely implements a RAM functionality on secret-shared inputs and outputs. This paper presents two information-theoretically secure DORAMs whose communication costs are asymptotic improvements over the state of the art. Let n be the number of memory locations and let d be the bit-length of each location.
The first, MetaDORAM1, is statistically secure, with n^{-ω(1)} leakage. It has amortized O(log_b(n) d + b ω(1) log(n) + log³(n)/log(log(n))) bits of communication per memory access. Here, b ≥ 2 is a free parameter and ω(1) is any super-constant function (in n). The most communication-efficient prior statistically secure DORAM was that of Abraham et al (PKC 2017), which has cost O(log_b(n) d + b ω(1) log_b(n) log²(n)). MetaDORAM1 is a Θ(ω(1) log(log(n)))-factor improvement over the work of Abraham et al whenever d = O(log²(n)). 
The second protocol, MetaDORAM2, achieves perfect security. It has amortized communication cost O(log_b(n)d + b log(n) + log³(n)/log(log(n))) where, again, b ≥ 2 is a free parameter. The best prior perfectly secure DORAM is that of Chan et al (ASIACRYPT 2018) which has communication cost O(log(n) d + log³(n)). MetaDORAM2 is therefore a Ω(log(log(n)))-factor improvement over the DORAM of Chan et al under any parameter range (by setting b = log(n)) and is a Θ(log(n))-factor improvement for d = Ω(n^ε) for any constant ε > 0 (by setting b = d/log(n)). Our work is the first perfectly secure DORAM with sub-logarithmic communication overhead. MetaDORAM2 comes at the cost of a once-off (for any given n) setup phase which requires exponential (in n) computation.
Both DORAMs are in the 3-party setting with security against 1 semi-honest, static corruption. By a trivial transformation, these can be transformed, respectively, into statistically and perfectly secure active 3-server ORAM protocols secure against 1 corrupt server, with the same communication costs. These multi-server ORAM protocols are likewise asymptotic improvements over the state of the art.

Cite As Get BibTex

Brett Hemenway Falk, Daniel Noble, and Rafail Ostrovsky. MetaDORAM: Info-Theoretic Distributed ORAM with Less Communication. In 6th Conference on Information-Theoretic Cryptography (ITC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 343, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITC.2025.6

Author Details

Brett Hemenway Falk
  • University of Pennsylvania, Philadelphia, PA, USA
Daniel Noble
  • Silence Laboratories, Singapore
Rafail Ostrovsky
  • UCLA, CA, USA

Funding

This research was supported in part by DARPA under Cooperative Agreement HR0011-20-2-0025, the Algorand Centers of Excellence programme managed by Algorand Foundation, NSF grants CNS-2246355, CCF-2220450 and CNS-2001096, US-Israel BSF grant 2022370, Amazon Faculty Award, Cisco Research Award, Sunday Group, ONR grant (N00014-15-1-2750) “SynCrypt: Automated Synthesis of Cryptographic Constructions” and a gift from Ripple Labs, Inc. Any views, opinions, findings, conclusions or recommendations contained herein are those of the author(s) and should not be interpreted as necessarily representing the official policies, either expressed or implied, of DARPA, the Department of Defense, the Algorand Foundation, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes, notwithstanding any copyright annotation therein.

Acknowledgements

Daniel Noble would also like to acknowledge God for supporting him in this research.

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