Abstract
Oblivious RAM (ORAM), introduced by Goldreich and Ostrovsky (JACM 1996), can be used to read and write to memory in a way that hides which locations are being accessed. The best known ORAM schemes have an overhead per access, where is the data size. The work of Goldreich and Ostrovsky gave a lower bound showing that this is optimal for ORAM schemes that operate in a “balls and bins” model, where memory blocks can only be shuffled between different locations but not manipulated otherwise. The lower bound even extends to weaker settings such as offline ORAM, where all of the accesses to be performed need to be specified ahead of time, and read-only ORAM, which only allows reads but not writes. But can we get lower bounds for general ORAM, beyond “balls and bins”? The work of Boyle and Naor (ITCS ’16) shows that this is unlikely in the offline setting. In particular, they construct an offline ORAM with overhead assuming the existence of small sorting circuits. Although we do not have instantiations of the latter, ruling them out would require proving new circuit lower bounds. On the other hand, the recent work of Larsen and Nielsen (CRYPTO ’18) shows that there indeed is an lower bound for general online ORAM. This still leaves the question open for online read-only ORAM or for read/write ORAM where we want very small overhead for the read operations. In this work, we show that a lower bound in these settings is also unlikely. In particular, our main result is a construction of online ORAM where reads (but not writes) have an overhead, assuming the existence of small sorting circuits as well as very good locally decodable codes (LDCs). Although we do not have instantiations of either of these with the required parameters, ruling them out is beyond current lower bounds.
Original language | English |
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Title of host publication | Theory of Cryptography - 16th International Conference, TCC 2018, Proceedings |
Editors | Amos Beimel, Stefan Dziembowski |
Publisher | Springer Science and Business Media Deutschland GmbH |
Pages | 603-635 |
Number of pages | 33 |
ISBN (Print) | 9783030038090 |
DOIs | |
State | Published - 2018 |
Externally published | Yes |
Event | 16th International Conference on Theory of Cryptography, TCC 2018 - Panaji, India Duration: 11 Nov 2018 → 14 Nov 2018 |
Publication series
Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11240 LNCS |
ISSN (Print) | 0302-9743 |
ISSN (Electronic) | 1611-3349 |
Conference
Conference | 16th International Conference on Theory of Cryptography, TCC 2018 |
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Country/Territory | India |
City | Panaji |
Period | 11/11/18 → 14/11/18 |
Bibliographical note
Publisher Copyright:© 2018, International Association for Cryptologic Research.
Funding
Acknowledgements. Research supported by NSF grants CNS-1314722, CNS-1413964, CNS-1750795 and the Alfred P. Sloan Research Fellowship. The first author was supported in part by The Eric and Wendy Schmidt Postdoctoral Grant for Women in Mathematical and Computing Sciences.
Funders | Funder number |
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National Science Foundation | CNS-1750795, CNS-1413964, CNS-1314722 |
Alfred P. Sloan Foundation |