3-Party Secure Computation for RAMs: Optimal and Concretely Efficient

Atsunori Ichikawa*, Ilan Komargodski, Koki Hamada, Ryo Kikuchi, Dai Ikarashi

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A distributed oblivious RAM (DORAM) is a method for accessing a secret-shared memory while hiding the accessed locations. DORAMs are the key tool for secure multiparty computation (MPC) for RAM programs that avoids expensive RAM-to-circuit transformations. We present new and improved 3-party DORAM protocols. For a logical memory of size N and for each logical operation, our DORAM requires O(log N) local CPU computation steps. This is known to be asymptotically optimal. Our DORAM satisfies passive security in the honest majority setting. Our technique results with concretely-efficient protocols and does not use expensive cryptography (such as re-randomizable or homomorphic encryption). Specifically, our DORAM is 25X faster than the known most efficient DORAM in the same setting. Lastly, we extend our technique to handle malicious attackers at the expense of using slightly larger blocks (i.e., ω((λ+ b) log N) vs. λ+ b where b= Ω(log N) is original block size). To the best of our knowledge, this is the first concretely-efficient maliciously secure DORAM. Technically, our construction relies on a novel concretely-efficient 3-party oblivious permutation protocol. We combine it with efficient non-oblivious hashing techniques (i.e., Cuckoo hashing) to get a distributed oblivious hash table. From this, we build a full-fledged DORAM using a distributed variant of the hierarchical approach of Goldreich and Ostrovsky (J. ACM ’96). These ideas, and especially the permutation protocol, are of independent interest.

Original languageAmerican English
Title of host publicationTheory of Cryptography - 21st International Conference, TCC 2023, Proceedings
EditorsGuy Rothblum, Hoeteck Wee
PublisherSpringer Science and Business Media Deutschland GmbH
Pages471-502
Number of pages32
ISBN (Print)9783031486142
DOIs
StatePublished - 2023
Event21st International conference on Theory of Cryptography Conference, TCC 2023 - Taipei, Taiwan, Province of China
Duration: 29 Nov 20232 Dec 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14369 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference21st International conference on Theory of Cryptography Conference, TCC 2023
Country/TerritoryTaiwan, Province of China
CityTaipei
Period29/11/232/12/23

Bibliographical note

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

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