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., \(\omega ((\lambda + b)\log N)\) vs. \(\lambda +b\) where \(b=\varOmega (\log N)\) 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.
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Notes
- 1.
We model parties as RAM machines that can perform word-level addition and standard Boolean operations at unit cost.
- 2.
- 3.
- 4.
Here, we emphasize again that the DORAM of Falk et al. [19] requires \(O(\log ^2 N)\) computational cost in addition to the communication cost. We only have \(O(\log N)\) computational cost.
- 5.
- 6.
Note that if \(p\le \log \log N\), the obtained PRF key is single, \([\![s_p]\!] \).
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Acknowledgements
We thank Brett Hemenway Falk, Daniel Noble, Rafail Ostrovsky, Matan Shtepel, and Jacob Zhang for observing a gap in a previous version of this work. Ilan Komargodski is the incumbent of the Harry & Abe Sherman Senior Lectureship at the School of Computer Science and Engineering at the Hebrew University. Research supported in part by an Alon Young Faculty Fellowship, by a grant from the Israel Science Foundation (ISF Grant No. 1774/20), and by a grant from the US-Israel Binational Science Foundation and the US National Science Foundation (BSF-NSF Grant No. 2020643).
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Ichikawa, A., Komargodski, I., Hamada, K., Kikuchi, R., Ikarashi, D. (2023). 3-Party Secure Computation for RAMs: Optimal and Concretely Efficient. 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_17
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