Asymptotic Information Leakage under One-Try Attacks

Boreale, Michele; Pampaloni, Francesca; Paolini, Michela

doi:10.1007/978-3-642-19805-2_27

Cited by 25 publications

(19 citation statements)

References 26 publications

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“…This result extends to the general case |X | ≥ 2. Provided R is non-singular, it is enough to replace C (p 1 , p 2 ) by min x =x C (p x , p x ), thus (see [6,26]):…”

Section: Asymptotic Behaviormentioning

confidence: 99%

“…Randomization mechanisms are information-theoretic channels. The use of this concept in the field of qif has been in recent years promoted by, among others, Chatzikokolakis, Palamidessi and their collaborators [10,11,9]; the systems amenable to this form of representation are sometimes referred to as information hiding systems; 1 see also [6,7].…”

Section: Basic Terminologymentioning

confidence: 99%

“…Related work There is a large body of recent literature on qif [9,25,6,7] and dp [15,16]. The earliest proposal of a worst-case security notion is, to the best of our knowledge, found in [18].…”

Section: Introductionmentioning

confidence: 98%

“…Two major areas have by now clearly emerged: Quantitative Information Flow (qif) [9,25,6,7,10,11,33] and Differential Privacy (dp) [15,16,28,29,[19][20][21][22][23]. As discussed in [4], qif is mainly concerned with quantifying the degree of protection offered against an adversary trying to guess the whole secret; dp is rather concerned with protection of individual bits of the secret, possibly in the presence of background information, like knowledge of the remaining bits.…”

Section: Introductionmentioning

confidence: 99%

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Worst- and average-case privacy breaches in randomization mechanisms

Boreale

Paolini²

2015

Theoretical Computer Science

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In a variety of contexts, randomization is regarded as an effective technique to conceal sensitive information. Viewing randomization mechanisms as information-theoretic channels, we start from a semantic notion of security, which expresses absence of any privacy breach above a given level of seriousness , irrespective of any background information, represented as a prior probability on the secret inputs. We first examine this notion according to two dimensions: worst vs. average case, single vs. repeated observations. In each case, we characterize the security level achievable by a mechanism in a simple fashion that only depends on the channel matrix, and specifically on certain measures of "distance" between its rows, like norm-1 distance and Chernoff Information. We next clarify the relation between our worst-case security notion and differential privacy (dp): we show that, while the former is in general stronger, the two coincide if one confines to background information that can be factorized into the product of independent priors over individuals. We finally turn our attention to expected utility, in the sense of Ghosh et al., in the case of repeated independent observations. We characterize the exponential growth rate of any reasonable utility function. In the particular case the mechanism provides -dp, we study the relation of the utility rate with : we offer either exact expressions or upperbounds for utility rate that apply to practically interesting cases, such as the (truncated) geometric mechanism.

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“…This result extends to the general case |X | ≥ 2. Provided R is non-singular, it is enough to replace C (p 1 , p 2 ) by min x =x C (p x , p x ), thus (see [6,26]):…”

Section: Asymptotic Behaviormentioning

confidence: 99%

Section: Basic Terminologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Worst- and average-case privacy breaches in randomization mechanisms

Boreale

Paolini²

2015

Theoretical Computer Science

Self Cite

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“…These principles have been used to create ever more sophisticated QIF frameworks to model systems and reason about leakage. (See, for example, [1,2,3,4,5,6,7,8,9,10,11,12,13].) Traditional approaches to QIF represent the adversary's prior knowledge as a probability distribution on secret values.…”

Section: Introductionmentioning

confidence: 99%

Quantifying Vulnerability of Secret Generation Using Hyper-Distributions

Alvim

Mardziel

Hicks

2017

Lecture Notes in Computer Science

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Traditional approaches to Quantitative Information Flow (QIF) represent the adversary's prior knowledge of possible secret values as a single probability distribution. This representation may miss important structure. For instance, representing prior knowledge about passwords of a system's users in this way overlooks the fact that many users generate passwords using some strategy. Knowledge of such strategies can help the adversary in guessing a secret, so ignoring them may underestimate the secret's vulnerability. In this paper we explicitly model strategies as distributions on secrets, and generalize the representation of the adversary's prior knowledge from a distribution on secrets to an environment, which is a distribution on strategies (and, thus, a distribution on distributions on secrets, called a hyper-distribution). By applying information-theoretic techniques to environments we derive several meaningful generalizations of the traditional approach to QIF. In particular, we disentangle the vulnerability of a secret from the vulnerability of the strategies that generate secrets, and thereby distinguish security by aggregation-which relies on the uncertainty over strategies-from security by strategy-which relies on the intrinsic uncertainty within a strategy. We also demonstrate that, in a precise way, no further generalization of prior knowledge (e.g., by using distributions of even higher order) is needed to soundly quantify the vulnerability of the secret.is known to the adversary (e.g., when a cryptographic key is randomly generated according to a known algorithm). However, in some important situations secrets are generated according to a more complex structure. In these cases, representing the prior as a distribution loses important, security-relevant information.Consider the example of passwords. If an adversary gains access to a large collection of passwords (without the associated user identities), his prior knowledge can be modeled as the probability distribution over passwords corresponding to the relative frequency of passwords in the collection. It would be wrong to believe, however, that passwords are generated by a function exactly described by this distribution. This representation of prior knowledge aggregates a population of users into a single expected probabilistic behavior, whereas in fact it is more likely that individual users generate passwords according to some (not completely random) strategy. Some user born in 1983, for instance, may have a strategy of generally picking passwords containing the substring "1983". If an adversary knows this, he can guess relevant passwords more quickly. In addition, on a system that mandates password changes, he may have an advantage when guessing that a changed password by the same user contains "1983" as a substring. In short, if the adversary learns something about the secret-generating strategy, he may obtain additional information about the secret itself.Generally speaking, knowledge of strategies can be useful when multiple secrets are produce...

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Quantitative Evaluation of Systems

Norman¹,

Sanders²

2014

Lecture Notes in Computer Science

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In the min-entropy approach to quantitative information flow, the leakage is defined in terms of a minimization problem, which, in case of large systems, can be computationally rather heavy. The same happens for the recently proposed generalization called g-vulnerability. In this paper we study the case in which the channel associated to the system can be decomposed into simpler channels, which typically happens when the observables consist of several components. Our main contribution is the derivation of bounds on the g-leakage of the whole system in terms of the g-leakages of its components.

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Asymptotic Information Leakage under One-Try Attacks

Cited by 25 publications

References 26 publications

Worst- and average-case privacy breaches in randomization mechanisms

Worst- and average-case privacy breaches in randomization mechanisms

Quantifying Vulnerability of Secret Generation Using Hyper-Distributions

Quantitative Evaluation of Systems

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