The Hardness of Being Private

Ada, Anil; Chattopadhyay, Arkadev; Cook, Stephen A.; Fontes, Lila; Koucký, Michal; Pitassi, Toniann

doi:10.1145/2567671

Cited by 9 publications

(7 citation statements)

References 16 publications

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“…In the 1980s, the work of Ben-Or, Goldwasser and Wigderson [8] showed multiparty protocols in the message-passing model for computing any function in an information-theoretically private way, assuming that the corruption threshold t < k/2. 1 In addition, we know that information-theoretic perfect privacy is impossible to achieve if t ≥ k/2. That is, the adversary must learn some information about the honest players' inputs in this setting.…”

Section: Introductionmentioning

confidence: 99%

A Tight Bound for Set Disjointness in the Message-Passing Model

Braverman

Ellen

Oshman

et al. 2013

2013 IEEE 54th Annual Symposium on Foundations of Computer Science

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In a multiparty message-passing model of communication, there are k players. Each player has a private input, and they communicate by sending messages to one another over private channels. While this model has been used extensively in distributed computing and in multiparty computation, lower bounds on communication complexity in this model and related models have been somewhat scarce. In recent work [40,46,47], strong lower bounds of the form Ω(n · k) were obtained for several functions in the message-passing model; however, a lower bound on the classical Set Disjointness problem remained elusive.In this paper, we prove tight lower bounds of the form Ω(n · k) for the Set Disjointness problem in the message passing model. Our bounds are obtained by developing information complexity tools in the message-passing model, and then proving an information complexity lower bound for Set Disjointness. As a corollary, we show a tight lower bound for the task allocation problem [19] via a reduction from One of the most natural application domains for communication complexity is distributed computing: When we wish to study the cost of computing in a network spanning multiple cores or physical machines, it is very useful to understand how much communication is necessary, since communication between machines often dominates the cost of the computation. Accordingly, lower bounds in communication complexity have been used to obtain many negative results in distributed computing, from the round complexity of finding a minimum-weight spanning tree [42] to computing functions of distributed data [37,29] and distributed computation and verification of network graph structures and properties [42,23].To the best of our knowledge, however, all applications of communication complexity lower bounds in distributed computing to date have used only two-player lower bounds. The reason for this appears to be twofold: First, the models of multi-party communication favored by the communication complexity community, the number-on-forehead model and the number-in-hand broadcast model, do not correspond to most natural models of distributed computing. Second, two-party lower bounds are surprisingly powerful, even for networks with many players. A typical reduction from a two-player communication complexity problem to a distributed problem T finds a sparse cut in the network, and shows that, to solve T , the two sides of the cut must implicitly solve, say, Set Disjointness [30]. However, there are problems that cannot be addressed by reduction from a two-player problem, because such reductions must reveal almost the entire structure of the network to one of the two players. (One such example is described in [29].)In this paper, we study communication complexity in message-passing models, where each party has a private input, and the parties communicate by sending messages to each other over private channels. These models have been used extensively in distributed computing, for example, to study gossiping protocols [27], to compute various functions...

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Section: Introductionmentioning

confidence: 99%

A Tight Bound for Set Disjointness in the Message-Passing Model

Braverman

Ellen

Oshman

et al. 2013

2013 IEEE 54th Annual Symposium on Foundations of Computer Science

Self Cite

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“…This situation is similar to [19], which studies a different model of private two-party computation, and where the best upper and lower bounds are also exponential and linear. In a similar spirit, [2] proves that in a communication model of approximate privacy called PAR (based on [43]), privacy can come at an exponential cost.…”

Section: Results For Zammentioning

confidence: 88%

“…Lower bounds for models (2) and (3) can be proved using known techniques. In case of (2) it is not difficult to show that lower bounds follow from the classic corruption bound, which is known to characterize the complexity class SBP [24].…”

Section: New Models Uam and Zammentioning

confidence: 99%

Zero-Information Protocols and Unambiguity in Arthur-Merlin Communication

Göös

Pitassi

Watson

2015

Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science

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We study whether information complexity can be used to attack the long-standing open problem of proving lower bounds against Arthur-Merlin (AM) communication protocols. Our starting point is to show that-in contrast to plain randomized communication complexity-every boolean function admits an AM communication protocol where on each yesinput, the distribution of Merlin's proof leaks no information about the input and moreover, this proof is unique for each outcome of Arthur's randomness. We posit that these two properties of zero information leakage and unambiguity on yes-inputs are interesting in their own right and worthy of investigation as new avenues toward AM.• Zero-information protocols (ZAM). Our basic ZAM protocol uses exponential communication for some functions, and this raises the question of whether more efficient protocols exist. We prove that all functions in the classical space-bounded complexity classes NL and ⊕L have polynomial-communication ZAM protocols. We also prove that ZAM complexity is lower bounded by conondeterministic communication complexity.• Unambiguous protocols (UAM). Our most technically substantial result is a Ω(n) lower bound on the UAM complexity of the NP-complete set-intersection function; the proof uses information complexity arguments in a new, indirect way and overcomes the "zero-information barrier" described above. We also prove that in general, UAM complexity is lower bounded by the classic discrepancy bound, and we give evidence that it is not generally lower bounded by the classic corruption bound. * All proofs appear in the full version of this work [23].

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“…The "right" notion of computational privacy for use in ABE schemes is that of "doubly selective" security [3,34], where "doubly" refers to the two possibilities depending on whether x or y is chosen first. Unsurprisingly, proving 3 and using doubly selective security require substantially more 2 The easiest way to see this is via complexity leveraging: an adaptive distinguisher with advantage ε can be converted into a non-adaptive distinguisher with an exponential loss in ε via random guessing. Since any non-adaptive distinguisher has advantage 0, we must have ε = 0 to begin with.…”

Section: Implications For Dual System Abementioning

confidence: 99%

“…This question has been considered in several different models and settings [12,41,2,14]. In this work, we focus on a very simple and natural model where non-private computation requires very little communication (just a single bit), whereas the best upper bound for private computation is exponential.…”

Section: Introductionmentioning

confidence: 99%

Communication Complexity of Conditional Disclosure of Secrets and Attribute-Based Encryption

Gay

Kerenidis

Wee

2015

Lecture Notes in Computer Science

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Abstract. We initiate a systematic treatment of the communication complexity of conditional disclosure of secrets (CDS), where two parties want to disclose a secret to a third party if and only if their respective inputs satisfy some predicate. We present a general upper bound and the first non-trivial lower bounds for conditional disclosure of secrets. Moreover, we achieve tight lower bounds for many interesting setting of parameters for CDS with linear reconstruction, the latter being a requirement in the application to attribute-based encryption. In particular, our lower bounds explain the trade-off between ciphertext and secret key sizes of several existing attribute-based encryption schemes based on the dual system methodology.

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The Hardness of Being Private

Cited by 9 publications

References 16 publications

A Tight Bound for Set Disjointness in the Message-Passing Model

A Tight Bound for Set Disjointness in the Message-Passing Model

Zero-Information Protocols and Unambiguity in Arthur-Merlin Communication

Communication Complexity of Conditional Disclosure of Secrets and Attribute-Based Encryption

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