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DORAM Revisited: Maliciously Secure RAM-MPC with Logarithmic Overhead

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Theory of Cryptography (TCC 2023)

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Abstract

Distributed Oblivious Random Access Memory (DORAM) is a secure multiparty protocol that allows a group of participants holding a secret-shared array to read and write to secret-shared locations within the array. The efficiency of a DORAM protocol is measured by the amount of communication required per read/write query into the array. DORAM protocols are a necessary ingredient for executing Secure Multiparty Computation (MPC) in the RAM model.

Although DORAM has been widely studied, all existing DORAM protocols have focused on the setting where the DORAM servers are semi-honest. Generic techniques for upgrading a semi-honest DORAM protocol to the malicious model typically increase the asymptotic communication complexity of the DORAM scheme.

In this work, we present a 3-party DORAM protocol which requires \(O((\kappa + D)\log N)\) communication per query, for a database of size N with D-bit values, where \(\kappa \) is the security parameter. Our hidden constants in the big-O nation are small. We show that our protocol is UC-secure in the presence of a malicious, static adversary. This matches the communication complexity of the best semi-honest DORAM protocols, and is the first malicious DORAM protocol with this complexity.

M. Shtepel–Work done while at UCLA.

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Notes

  1. 1.

    Most ORAM works assume \(D = \varOmega (\log N)\), so \(O((D + \log N)\log N) = O(D \log N)\) which is described as a logarithmic “overhead” or a logarithmic “blowup” over O(D) communication needed to make a query in the insecure setting.

  2. 2.

    Recall that we need to recurse on OMaps rather than ORAMs, since the smaller levels in the hierarchy need to be able to hold indices from the full space.

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Acknowledgments

Supported in part by ONR under grant N00014-15-1-2750, Ripple Labs Inc., DARPA under Cooperative Agreement HR0011-20-2-0025, the Algorand Centers of Excellence programme managed by Algorand Foundation, NSF grants CNS-2001096 and CCF-2220450, US-Israel BSF grant 2015782, Amazon Faculty Award, Cisco Research Award and Sunday Group. 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 ONR, Ripple Labs Inc., 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 not withstanding any copyright annotation therein.

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  1. University of Pennsylvania, Philadelphia, USA

    Brett Falk, Daniel Noble & Matan Shtepel

  2. UCLA, Los Angeles, USA

    Rafail Ostrovsky & Jacob Zhang

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Falk, B., Noble, D., Ostrovsky, R., Shtepel, M., Zhang, J. (2023). DORAM Revisited: Maliciously Secure RAM-MPC with Logarithmic Overhead. In: Rothblum, G., Wee, H. (eds) Theory of Cryptography. TCC 2023. Lecture Notes in Computer Science, vol 14369. Springer, Cham. https://doi.org/10.1007/978-3-031-48615-9_16

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