Bounds on inference

Calmon, Flávio P.; Varia, Mayank; Médard, Muriel; Christiansen, Mark M.; Duffy, Ken R.; Tessaro, Stefano

doi:10.1109/allerton.2013.6736575

Cited by 33 publications

(46 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We prove that the smallest principal inertia component ( [3], [4]) of p S,X plays a central role for achieving perfect privacy: If |X | ≤ |S|, then perfect privacy is achievable with I(X; Y ) > 0 if and only if the smallest principal inertia component of p S,X is 0. Since I(S; Y ) = 0 (perfect privacy) if and only if S ⊥ ⊥ Y , this fundamental result holds for any privacy metric where statistical independence implies perfect privacy.…”

Section: Introductionmentioning

confidence: 99%

Fundamental limits of perfect privacy

Calmon

Makhdoumi

Médard

2015

2015 IEEE International Symposium on Information Theory (ISIT)

Self Cite

View full text Add to dashboard Cite

Abstract-"To be considered for an 2015 IEEE Jack Keil Wolf ISIT Student Paper Award." We investigate the problem of intentionally disclosing information about a set of measurement points X (useful information), while guaranteeing that little or no information is revealed about a private variable S (private information). Given that S and X are drawn from a finite set with joint distribution pS,X , we prove that a non-trivial amount of useful information can be disclosed while not disclosing any private information if and only if the smallest principal inertia component of the joint distribution of S and X is 0. This fundamental result characterizes when useful information can be privately disclosed for any privacy metric based on statistical dependence. We derive sharp bounds for the tradeoff between disclosure of useful and private information, and provide explicit constructions of privacy-assuring mappings that achieve these bounds.

show abstract

Section: Introductionmentioning

confidence: 99%

Fundamental limits of perfect privacy

Calmon

Makhdoumi

Médard

2015

2015 IEEE International Symposium on Information Theory (ISIT)

Self Cite

View full text Add to dashboard Cite

show abstract

“…If M is uniformly distributed and f is a one-bit function, e.g., one of the bits of the message, then the relationship between maximal correlation and the advantage follows readily by the work of Witsenhausen [8]. Applying the result by Calmon et al [9], the advantage for uniformly distributed M and general f is upper-bounded by ρ. A contribution of this paper is to extend this result on the relationship between maximal correlation and the advantage to scenarios in which the distribution of M is not fixed and Eve has access to some side information about the message.…”

Section: Introductionmentioning

confidence: 92%

“…Next we state a result relating maximal correlation and the χ 2 -divergence between the joint pmf and the product of the marginal pmfs, also known as χ 2 measure of correlation which follows directly from [9].…”

Section: A Properties Of Maximal Correlationmentioning

confidence: 99%

See 1 more Smart Citation

Maximal Correlation Secrecy

Gamal

2018

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

This paper shows that the Hirschfeld-Gebelein-Rényi maximal correlation between the message and the ciphertext provides good secrecy guarantees for cryptosystems that use short keys. We first establish a bound on the eavesdropper's advantage in guessing functions of the message in terms of maximal correlation and the Rényi entropy of the message. This result implies that maximal correlation is stronger than the notion of entropic security introduced by Russell and Wang. We then show that a small maximal correlation ρ can be achieved via a randomly generated cipher with key length ≈ 2 log(1/ρ), independent of the message length, and by a stream cipher with key length 2 log(1/ρ) + log n + 2 for a message of length n. We establish a converse showing that these ciphers are close to optimal. This is in contrast to entropic security for which there is a gap between the lower and upper bounds. Finally, we show that a small maximal correlation implies secrecy with respect to several mutual information based criteria but is not necessarily implied by them. Hence, maximal correlation is a stronger and more practically relevant measure of secrecy than mutual information.

show abstract

“…In this context, information-theoretic metrics for privacy are naturally well suited. In fact, the adversarial model determines the appropriate information metric: an estimating adversary that minimizes mean square error is captured by χ 2 -squared measures [40], a belief refining adversary is captured by MI [39], an adversary that can make a hard MAP decision for a specific set of private features is captured by the Arimoto MI of order ∞ [58,59], and an adversary that can guess any function of the private features is captured by the maximal (over all distributions of the dataset for a fixed support) Sibson information of order ∞ [55,57].…”

Section: Related Workmentioning

confidence: 99%

Context-Aware Generative Adversarial Privacy

Huang

Kairouz

Chen

et al. 2017

Entropy

131

120

View full text Add to dashboard Cite

Preserving the utility of published datasets while simultaneously providing provable privacy guarantees is a well-known challenge. On the one hand, context-free privacy solutions, such as differential privacy, provide strong privacy guarantees, but often lead to a significant reduction in utility. On the other hand, context-aware privacy solutions, such as information theoretic privacy, achieve an improved privacy-utility tradeoff, but assume that the data holder has access to dataset statistics. We circumvent these limitations by introducing a novel context-aware privacy framework called generative adversarial privacy (GAP). GAP leverages recent advancements in generative adversarial networks (GANs) to allow the data holder to learn privatization schemes from the dataset itself. Under GAP, learning the privacy mechanism is formulated as a constrained minimax game between two players: a privatizer that sanitizes the dataset in a way that limits the risk of inference attacks on the individuals' private variables, and an adversary that tries to infer the private variables from the sanitized dataset. To evaluate GAP's performance, we investigate two simple (yet canonical) statistical dataset models: (a) the binary data model; and (b) the binary Gaussian mixture model. For both models, we derive game-theoretically optimal minimax privacy mechanisms, and show that the privacy mechanisms learned from data (in a generative adversarial fashion) match the theoretically optimal ones. This demonstrates that our framework can be easily applied in practice, even in the absence of dataset statistics.

show abstract

Bounds on inference

Cited by 33 publications

References 30 publications

Fundamental limits of perfect privacy

Fundamental limits of perfect privacy

Maximal Correlation Secrecy

Context-Aware Generative Adversarial Privacy

Contact Info

Product

Resources

About