Accuracy-Privacy Tradeoffs for Two-Party Differentially Private Protocols

Goyal, Vipul; Mironov, Ilya; Pandey, Omkant; Sahai, Amit

doi:10.1007/978-3-642-40041-4_17

Cited by 16 publications

(30 citation statements)

References 29 publications

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“…The above dependency between ε and α is tight since a Θ(ε 2 )-correct, ε-differential private, protocol for computing XOR can be constructed (with information theoretic security) using the socalled randomized response approach shown in Warner [37]. It improves, in the (ε, α) dependency aspect, upon Goyal et al [13] who showed that, for some constant c > 0, a cε-correct ε-differentially private XOR implies oblivious transfer, and upon Goyal et al [12] who showed that cε 2 -correct εdifferentially XOR implies one-way functions.…”

Section: Application To Differentially Private Xormentioning

confidence: 95%

“…A natural question is what assumptions are needed for such (symmetric) differentially private computation achieving certain level of accuracy. A sequence of work showed that for certain tasks, achieving high accuracy requires one-way functions [3,4,30,12]; some cannot even be instantiated in the random oracle model [16]; and some cannot be black-box reduced to key agreement [27]. See Section 1.4 for more details on these results.…”

Section: Application To Differentially Private Xormentioning

confidence: 99%

“…This is the best possible differential privacy that can be achieved for accuracy α. On the other extreme, an Θ(ε 2 )-accurate, ε-differential private, protocol for computing XOR can be constructed (with information theoretic security) using the so-called randomized response approach of Warner [37], as shown in [12]. Thus, it is natural to ask what are the minimal computational assumption that are needed for an α-accurate, ε-DP computation of XOR, for intermediate choices of ε 2 ≪ α ≪ ε.…”

Section: Non-trivial Differentially Private Xor Implies Key Agreementmentioning

confidence: 99%

See 2 more Smart Citations

Computational Two-Party Correlation: A Dichotomy for Key-Agreement Protocols

Haitner

Nissim

Omri

et al. 2018

2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)

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Let π be an efficient two-party protocol that given security parameter κ, both parties output single bits X κ and Y κ , respectively. We are interested in how (X κ , Y κ ) "appears" to an efficient adversary that only views the transcript T κ . We make the following contributions:• We develop new tools to argue about this loose notion and show (modulo some caveats)that for every such protocol π, there exists an efficient simulator such that the following holds: on input T κ , the simulator outputs a pair (

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Section: Application To Differentially Private Xormentioning

confidence: 95%

Section: Application To Differentially Private Xormentioning

confidence: 99%

Section: Non-trivial Differentially Private Xor Implies Key Agreementmentioning

confidence: 99%

See 1 more Smart Citation

Computational Two-Party Correlation: A Dichotomy for Key-Agreement Protocols

Haitner

Nissim

Omri

et al. 2018

2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)

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“…Considering multiplayer circumstance, multiparty differential privacy protocol can get the trade-off. Goyal et al [16] obtained general upper bounds on accuracy of two parties differential privacy protocol of computing any Boolean function. The major result was a new general geometric technique for obtaining non-trivial accuracy bounds for any Boolean functionality.…”

Section: Related Workmentioning

confidence: 99%

“…Multiparty differential privacy protocol can reach the trade-off. Goyal et al [16] obtained general upper bounds on accuracy of two parties' differential privacy protocol of computing any Boolean function. Kasiviswanathan et al [17] proposed local differential privacy that could also reach the trade-off by using random response mechanism.…”

Section: Introductionmentioning

confidence: 99%

Privacy-Preserving Monotonicity of Differential Privacy Mechanisms

Liu

Zhou

et al. 2018

Applied Sciences

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Differential privacy mechanisms can offer a trade-off between privacy and utility by using privacy metrics and utility metrics. The trade-off of differential privacy shows that one thing increases and another decreases in terms of privacy metrics and utility metrics. However, there is no unified trade-off measurement of differential privacy mechanisms. To this end, we proposed the definition of privacy-preserving monotonicity of differential privacy, which measured the trade-off between privacy and utility. First, to formulate the trade-off, we presented the definition of privacy-preserving monotonicity based on computational indistinguishability. Second, building on privacy metrics of the expected estimation error and entropy, we theoretically and numerically showed privacy-preserving monotonicity of Laplace mechanism, Gaussian mechanism, exponential mechanism, and randomized response mechanism. In addition, we also theoretically and numerically analyzed the utility monotonicity of these several differential privacy mechanisms based on utility metrics of modulus of characteristic function and variant of normalized entropy. Third, according to the privacy-preserving monotonicity of differential privacy, we presented a method to seek trade-off under a semi-honest model and analyzed a unilateral trade-off under a rational model. Therefore, privacy-preserving monotonicity can be used as a criterion to evaluate the trade-off between privacy and utility in differential privacy mechanisms under the semi-honest model. However, privacy-preserving monotonicity results in a unilateral trade-off of the rational model, which can lead to severe consequences.

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Channels of Small Log-Ratio Leakage and Characterization of Two-Party Differentially Private Computation

Haitner

Mazor

Shaltiel

et al. 2019

Theory of Cryptography

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Consider a ppt two-party protocol Π = (A, B) in which the parties get no private inputs and obtain outputs O A , O B ∈ {0, 1}, and let V A and V B denote the parties' individual views.The leakage of Π is the amount of information a party obtains about the event O A = O B ; that is, the leakage ǫ is the maximum, over P ∈ {A, B}, of the distance betweenTypically, this distance is measured in statistical distance, or, in the computational setting, in computational indistinguishability. For this choice, Wullschleger [TCC '09] showed that if ǫ ≪ α then the protocol can be transformed into an OT protocol.We consider measuring the protocol leakage by the log-ratio distance (which was popularized by its use in the differential privacy framework). The log-ratio distance between X, Y over domain Ω is the minimal ǫ ≥ 0 for which, for every v ∈ Ω, log Pr[X=v] PrIn the computational setting, we use computational indistinguishability from having log-ratio distance ǫ. We show that a protocol with (noticeable) accuracy α ∈ Ω(ǫ 2 ) can be transformed into an OT protocol (note that this allows ǫ ≫ α). We complete the picture, in this respect, showing that a protocol with α ∈ o(ǫ 2 ) does not necessarily imply OT. Our results hold for both the information theoretic and the computational settings, and can be viewed as a "fine grained" approach to "weak OT amplification".We then use the above result to fully characterize the complexity of differentially private twoparty computation for the XOR function, answering the open question put by Goyal, Khurana, Mironov, Pandey, and Sahai [ICALP '16] and Haitner, Nissim, Omri, Shaltiel, and Silbak [FOCS '18]. Specifically, we show that for any (noticeable) α ∈ Ω(ǫ 2 ), a two-party protocol that computes the XOR function with α-accuracy and ǫ-differential privacy can be transformed into an OT protocol. This improves upon Goyal et al. that only handle α ∈ Ω(ǫ), and upon Haitner et al. who showed that such a protocol implies (infinitely-often) key agreement (and not OT). Our characterization is tight since OT does not follow from protocols in which α ∈ o(ǫ 2 ), and extends to functions (over many bits) that "contain" an "embedded copy" of the XOR function.

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Accuracy-Privacy Tradeoffs for Two-Party Differentially Private Protocols

Cited by 16 publications

References 29 publications

Computational Two-Party Correlation: A Dichotomy for Key-Agreement Protocols

Computational Two-Party Correlation: A Dichotomy for Key-Agreement Protocols

Privacy-Preserving Monotonicity of Differential Privacy Mechanisms

Channels of Small Log-Ratio Leakage and Characterization of Two-Party Differentially Private Computation

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