Paper 2019/384

What Storage Access Privacy is Achievable with Small Overhead?

Sarvar Patel, Giuseppe Persiano, and Kevin Yeo

Abstract

Oblivious RAM (ORAM) and private information retrieval (PIR) are classic cryptographic primitives used to hide the access pattern to data whose storage has been outsourced to an untrusted server. Unfortunately, both primitives require considerable overhead compared to plaintext access. For large-scale storage infrastructure with highly frequent access requests, the degradation in response time and the exorbitant increase in resource costs incurred by either ORAM or PIR prevent their usage. In an ideal scenario, a privacy-preserving storage protocols with small overhead would be implemented for these heavily trafficked storage systems to avoid negatively impacting either performance and/or costs. In this work, we study the problem of the best $\mathit{storage\ access\ privacy}$ that is achievable with only $\mathit{small\ overhead}$ over plaintext access. To answer this question, we consider $\mathit{differential\ privacy\ access}$ which is a generalization of the $\mathit{oblivious\ access}$ security notion that are considered by ORAM and PIR. Quite surprisingly, we present strong evidence that constant overhead storage schemes may only be achieved with privacy budgets of $\epsilon = \Omega(\log n)$. We present asymptotically optimal constructions for differentially private variants of both ORAM and PIR with privacy budgets $\epsilon = \Theta(\log n)$ with only $O(1)$ overhead. In addition, we consider a more complex storage primitive called key-value storage in which data is indexed by keys from a large universe (as opposed to consecutive integers in ORAM and PIR). We present a differentially private key-value storage scheme with $\epsilon = \Theta(\log n)$ and $O(\log\log n)$ overhead. This construction uses a new oblivious, two-choice hashing scheme that may be of independent interest.

Metadata
Available format(s)
PDF
Category
Cryptographic protocols
Publication info
Published elsewhere. MINOR revision.ACM-PODS-2019
Keywords
oblivious RAMdifferential privacylower boundsoblivious hashing
Contact author(s)
kwlyeo @ google com
History
2019-04-16: received
Short URL
https://ia.cr/2019/384
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2019/384,
      author = {Sarvar Patel and Giuseppe Persiano and Kevin Yeo},
      title = {What Storage Access Privacy is Achievable with Small Overhead?},
      howpublished = {Cryptology ePrint Archive, Paper 2019/384},
      year = {2019},
      note = {\url{https://eprint.iacr.org/2019/384}},
      url = {https://eprint.iacr.org/2019/384}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.