Lower Bounds for Differentially Private RAMs

Persiano, Giuseppe; Yeo, Kyongmin

doi:10.1007/978-3-030-17653-2_14

Cited by 19 publications

(16 citation statements)

References 33 publications

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“…Given that the work of Goldreich and Ostrovsky [GO96] might serve as a primary reference for our community, we explain the issue in Section 5 to help preventing the use of the problematic definition in future works. Persiano and Yeo [PY19] recently adapted the chronogram technique [FS89] from the literature on data structure lower bounds to prove a lower bound for differentially private RAMs (a relaxation of ORAMs in the spirit of differential privacy [DMNS06] which ensures indistinguishability only for input sequences that differ in a single operation). Similarly to the work of Larsen and Nielsen [LN18], the proof in [PY19] exploits the fact that the distinguisher knows exactly which server accesses correspond to each input operation.…”

Section: Our Resultsmentioning

confidence: 99%

“…Persiano and Yeo [PY19] recently adapted the chronogram technique [FS89] from the literature on data structure lower bounds to prove a lower bound for differentially private RAMs (a relaxation of ORAMs in the spirit of differential privacy [DMNS06] which ensures indistinguishability only for input sequences that differ in a single operation). Similarly to the work of Larsen and Nielsen [LN18], the proof in [PY19] exploits the fact that the distinguisher knows exactly which server accesses correspond to each input operation. However, as the chronogram technique significantly differs from the information transfer approach, we do not think that our techniques would directly allow to strengthen the [PY19] lower bound for differentially private RAMs and prove it in the model with an unstructured access pattern.…”

Section: Our Resultsmentioning

confidence: 99%

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Stronger Lower Bounds for Online ORAM

Hubáček

Koucký

Král

et al. 2019

Lecture Notes in Computer Science

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Oblivious RAM (ORAM), introduced in the context of software protection by Goldreich and Ostrovsky [JACM'96], aims at obfuscating the memory access pattern induced by a RAM computation. Ideally, the memory access pattern of an ORAM should be independent of the data being processed. Since the work of Goldreich and Ostrovsky, it was believed that there is an inherent Ω(log n) bandwidth overhead in any ORAM working with memory of size n. Larsen and Nielsen [CRYPTO'18] were the first to give a general Ω(log n) lower bound for any online ORAM, i.e., an ORAM that must process its inputs in an online manner.In this work, we revisit the lower bound of Larsen and Nielsen, which was proved under the assumption that the adversarial server knows exactly which server accesses correspond to which input operation. We give an Ω(log n) lower bound for the bandwidth overhead of any online ORAM even when the adversary has no access to this information. For many known constructions of ORAM this information is provided implicitly as each input operation induces an access sequence of roughly the same length. Thus, they are subject to the lower bound of Larsen and Nielsen. Our results rule out a broader class of constructions and specifically, they imply that obfuscating the boundaries between the input operations does not help in building a more efficient ORAM.As our main technical contribution and to handle the lack of structure, we study the properties of access graphs induced naturally by the memory access pattern of an ORAM computation. We identify a particular graph property that can be efficiently tested and that all access graphs of ORAM computation must satisfy with high probability. This property is reminiscent of the Larsen-Nielsen property but it is substantially less structured; that is, it is more generic. * 1 Protecting the memory access of a computation is particularly relevant in the light of the recent Spectre [KGG + 18] and Meltdown [LSG + 18] attacks.

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Section: Our Resultsmentioning

confidence: 99%

Section: Our Resultsmentioning

confidence: 99%

Stronger Lower Bounds for Online ORAM

Hubáček

Koucký

Král

et al. 2019

Lecture Notes in Computer Science

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“…As a result, there has been a lot of work in ORAM [3,24,39,46,53] leading to logarithmic overhead constructions. Furthermore, ORAM lower bounds [41,48] have shown that these are the best possible constructions. A simple approach is to take any STE scheme and replace each access using an ORAM access to suppress leakage.…”

Section: Comparison To Previous Workmentioning

confidence: 99%

Mitigating Leakage in Secure Cloud-Hosted Data Structures

Patel

Persiano

Yeo

et al. 2019

Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security

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Volume leakage has recently been identified as a major threat to the security of cryptographic cloud-based data structures by Kellaris et al. [CCS'16] (see also the attacks in Grubbs et al. [CCS'18] and Lacharité et al. [S&P'18]). In this work, we focus on volume-hiding implementations of encrypted multi-maps as first considered by Kamara and Moataz [Eurocrypt'19]. Encrypted multi-maps consist of outsourcing the storage of a multi-map to an untrusted server, such as a cloud storage system, while maintaining the ability to perform private queries. Volume-hiding encrypted multi-maps ensure that the number of responses (volume) for any query remains hidden from the adversarial server. As a result, volume-hiding schemes can prevent leakage attacks that leverage the adversary's knowledge of the number of query responses to compromise privacy.We present both conceptual and algorithmic contributions towards volume-hiding encrypted multi-maps. We introduce the first formal definition of volume-hiding leakage functions. In terms of design, we present the first volume-hiding encrypted multi-map dprfMM whose storage and query complexity are both asymptotically optimal. Furthermore, we experimentally show that our construction is practically efficient. Our server storage is smaller than the best previous construction while we improve query complexity by a factor of 10-16x.In addition, we introduce the notion of differentially private volume-hiding leakage functions which strikes a better, tunable balance between privacy and efficiency. To accompany our new notion, we present a differentially private volume-hiding encrypted multimap dpMM whose query complexity is the volume of the queried key plus an additional logarithmic factor. This is a significant improvement compared to all previous volume-hiding schemes whose query overhead was the maximum volume of any key. In natural settings, our construction improves the average query overhead by a factor of 150-240x over the previous best volume-hiding construction even when considering small privacy budget of ϵ = 0.2.• Security and privacy → Management and querying of encrypted data;

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“…An intriguing question is whether the extra Θ(lg n) overhead for oblivious data structures over their nonoblivious counterparts is really necessary. For the problem of RAMs, it has been shown that the Θ(lg n) overhead is both necessary and sufficient [LN18,PY19]. Jacob et al [JLN19] also show that the Θ(lg n) overhead is necessary and sufficient for many fundamental data structures such as stacks and queues, but quite surprisingly, Jafargholi et al [JLS19] very recently showed that (comparison-based) priority queues can be made oblivious with no overhead at all.…”

Section: Introductionmentioning

confidence: 99%

“…This is also the first oblivious cell-probe lower bound exceeding ω(lg n) (for a problem where no super-logarithmic cell-probe lower bound is known). Previous works on oblivious cell-probe lower bounds have focused on data structures with O( √ lg n) or smaller complexity for their nonoblivious counterparts (such as RAMs [LN18,PY19] as well as stacks, queues, deques, priority queues and search trees [JLN19]) and peaked at Ω(lg n).…”

Section: Introductionmentioning

confidence: 99%

Lower Bounds for Oblivious Near-Neighbor Search

Larsen¹,

Malkin²,

Weinstein³

et al. 2020

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

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We prove an Ω(d lg n/(lg lg n) 2 ) lower bound on the dynamic cell-probe complexity of statistically oblivious approximate-near-neighbor search (ANN) over the ddimensional Hamming cube. For the natural setting of d = Θ(lg n), our result implies an Ω(lg 2 n) lower bound, which is a quadratic improvement over the highest (nonoblivious) cell-probe lower bound for ANN. This is the first super-logarithmic unconditional lower bound for ANN against general (non black-box) data structures. We also show that any oblivious static data structure for decomposable search problems (like ANN) can be obliviously dynamized with O(lg n) overhead in update and query time, strengthening a classic result of Bentley and Saxe (Algorithmica, 1980).

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Lower Bounds for Differentially Private RAMs

Cited by 19 publications

References 33 publications

Stronger Lower Bounds for Online ORAM

Stronger Lower Bounds for Online ORAM

Mitigating Leakage in Secure Cloud-Hosted Data Structures

Lower Bounds for Oblivious Near-Neighbor Search

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