Yes, There is an Oblivious RAM Lower Bound!

Larsen, Kasper Green; Nielsen, Jesper Buus

doi:10.1007/978-3-319-96881-0_18

Cited by 78 publications

(34 citation statements)

References 23 publications

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“…The lower bound was proven in a model, where the ORAM construction is not allowed to read the data it is storing (the so-called "balls in bins" model) and where the adversary was allowed to have an unbounded running time. In [23] Larsen and Nielsen proved the same lower bound in a model where the encoding of the data can be arbitrary and where the adversary's running time is only allowed to be polynomial time. Notice that this is the more challenging model when proving a lower bound.…”

Section: Introductionmentioning

confidence: 77%

“…We prove our lower bounds in the oblivious cell probe model of Larsen and Nielsen [23]. In this model, a data structure consists of a server memory of w-bit cells, each having an integer address in [K] for some K ≤ 2 w .…”

Section: Lower Boundsmentioning

confidence: 95%

“…With these definitions, we are ready to proceed to our proofs. We refer readers interested in a more formal definition of oblivious cell probe data structures to [23].…”

Section: Lower Boundsmentioning

confidence: 99%

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Lower Bounds for Oblivious Data Structures

Jacob¹,

Larsen²,

Nielsen³

2019

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

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An oblivious data structure is a data structure where the memory access patterns reveals no information about the operations performed on it. Such data structures were introduced by Wang et al. [ACM SIGSAC'14] and are intended for situations where one wishes to store the data structure at an untrusted server. One way to obtain an oblivious data structure is simply to run a classic data structure on an oblivious RAM (ORAM). Until very recently, this resulted in an overhead of ω(lg n) for the most natural setting of parameters. Moreover, a recent lower bound for ORAMs by Larsen and Nielsen [CRYPTO'18] show that they always incur an overhead of at least Ω(lg n) if used in a black box manner. To circumvent the ω(lg n) overhead, researchers have instead studied classic data structure problems more directly and have obtained efficient solutions for many such problems such as stacks, queues, deques, priority queues and search trees. However, none of these data structures process operations faster than Θ(lg n), leaving open the question of whether even faster solutions exist. In this paper, we rule out this possibility by proving Ω(lg n) lower bounds for oblivious stacks, queues, deques, priority queues and search trees. * rikj@itu.dk. IT University Copenhagen. † larsen@cs.au.dk. Aarhus University.

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Section: Introductionmentioning

confidence: 77%

Section: Lower Boundsmentioning

confidence: 95%

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Lower Bounds for Oblivious Data Structures

Jacob¹,

Larsen²,

Nielsen³

2019

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…Oblivious RAM (ORAM) and private information retrieval (PIR) are two oblivious storage primitives that have been the objective of extensive research [12, 19, 25-28, 35, 36, 44, 48]. For ORAM, it has been shown that Ω(log n) overhead is necessary [37]. On the other hand, the best constructions for PIR require at least Ω(n) server computation over the entire outsourced database.…”

Section: Introductionmentioning

confidence: 99%

“…With this efficiency, the majority of ORAM schemes consider only simple upload and download operations and forego the use of expensive encryption schemes of PIR that require the server to perform untrusted computation, although some previous works consider ORAM with homomorphic encryption [20]. For a database with n records, it has been shown that ORAM requires overhead of Ω(log n) records [27,37] and that O(log n· log log n) communication suffices [44]. We also examine an extension to ORAM, which we denote as oblivious key-value storage (previously also denoted as oblivious storage), where database records are uniquely identified by keys from a large universe and clients might also attempt to retrieve a nonexistent key [29].…”

Section: Introductionmentioning

confidence: 99%

What Storage Access Privacy is Achievable with Small Overhead?

Patel

Persiano

Yeo

2019

Proceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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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 privacypreserving 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 storage access privacy that is achievable with only small overhead over plaintext access.To answer this question, we consider differential privacy access which is a generalization of the 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 ϵ = Ω(log n). We present asymptotically optimal constructions for differentially private variants of both ORAM and PIR with privacy budgets ϵ = Θ(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 ϵ = Θ(log n) and O(log log n) overhead. This construction uses a new oblivious, two-choice hashing scheme that may be of independent interest.

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Is There an Oblivious RAM Lower Bound for Online Reads?

Weiss

Wichs

2018

Theory of Cryptography

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Yes, There is an Oblivious RAM Lower Bound!

Cited by 78 publications

References 23 publications

Lower Bounds for Oblivious Data Structures

Lower Bounds for Oblivious Data Structures

What Storage Access Privacy is Achievable with Small Overhead?

Is There an Oblivious RAM Lower Bound for Online Reads?

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