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An Operational Approach to Information Leakage.

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Title: An Operational Approach to Information Leakage.
Authors: Issa, Ibrahim1 (AUTHOR) ii19@aub.edu.lb, Wagner, Aaron B.1 (AUTHOR) wagner@cornell.edu, Kamath, Sudeep2 (AUTHOR) sudeep.kamath@gmail.com
Source: IEEE Transactions on Information Theory. Mar2020, Vol. 66 Issue 3, p1625-1657. 33p.
Subjects: Leakage, Random variables, Definitions, Axiomatic design
Abstract: Given two random variables $X$ and $Y$ , an operational approach is undertaken to quantify the “leakage” of information from $X$ to $Y$. The resulting measure $\mathcal {L}\left ({X \!\! \to \!\! Y}\right)$ is called maximal leakage, and is defined as the multiplicative increase, upon observing $Y$ , of the probability of correctly guessing a randomized function of $X$ , maximized over all such randomized functions. A closed-form expression for $\mathcal {L}\left ({X \!\! \to \!\! Y}\right)$ is given for discrete $X$ and $Y$ , and it is subsequently generalized to handle a large class of random variables. The resulting properties are shown to be consistent with an axiomatic view of a leakage measure, and the definition is shown to be robust to variations in the setup. Moreover, a variant of the Shannon cipher system is studied, in which performance of an encryption scheme is measured using maximal leakage. A single-letter characterization of the optimal limit of (normalized) maximal leakage is derived and asymptotically-optimal encryption schemes are demonstrated. Furthermore, the sample complexity of estimating maximal leakage from data is characterized up to subpolynomial factors. Finally, the guessing framework used to define maximal leakage is used to give operational interpretations of commonly used leakage measures, such as Shannon capacity, maximal correlation, and local differential privacy. [ABSTRACT FROM AUTHOR]
Copyright of IEEE Transactions on Information Theory is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
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  Data: An Operational Approach to Information Leakage.
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  Data: <searchLink fieldCode="AR" term="%22Issa%2C+Ibrahim%22">Issa, Ibrahim</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ii19@aub.edu.lb</i><br /><searchLink fieldCode="AR" term="%22Wagner%2C+Aaron+B%2E%22">Wagner, Aaron B.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> wagner@cornell.edu</i><br /><searchLink fieldCode="AR" term="%22Kamath%2C+Sudeep%22">Kamath, Sudeep</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> sudeep.kamath@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22IEEE+Transactions+on+Information+Theory%22">IEEE Transactions on Information Theory</searchLink>. Mar2020, Vol. 66 Issue 3, p1625-1657. 33p.
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  Data: <searchLink fieldCode="DE" term="%22Leakage%22">Leakage</searchLink><br /><searchLink fieldCode="DE" term="%22Random+variables%22">Random variables</searchLink><br /><searchLink fieldCode="DE" term="%22Definitions%22">Definitions</searchLink><br /><searchLink fieldCode="DE" term="%22Axiomatic+design%22">Axiomatic design</searchLink>
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  Data: Given two random variables $X$ and $Y$ , an operational approach is undertaken to quantify the “leakage” of information from $X$ to $Y$. The resulting measure $\mathcal {L}\left ({X \!\! \to \!\! Y}\right)$ is called maximal leakage, and is defined as the multiplicative increase, upon observing $Y$ , of the probability of correctly guessing a randomized function of $X$ , maximized over all such randomized functions. A closed-form expression for $\mathcal {L}\left ({X \!\! \to \!\! Y}\right)$ is given for discrete $X$ and $Y$ , and it is subsequently generalized to handle a large class of random variables. The resulting properties are shown to be consistent with an axiomatic view of a leakage measure, and the definition is shown to be robust to variations in the setup. Moreover, a variant of the Shannon cipher system is studied, in which performance of an encryption scheme is measured using maximal leakage. A single-letter characterization of the optimal limit of (normalized) maximal leakage is derived and asymptotically-optimal encryption schemes are demonstrated. Furthermore, the sample complexity of estimating maximal leakage from data is characterized up to subpolynomial factors. Finally, the guessing framework used to define maximal leakage is used to give operational interpretations of commonly used leakage measures, such as Shannon capacity, maximal correlation, and local differential privacy. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IEEE Transactions on Information Theory is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1109/TIT.2019.2962804
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        Text: English
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        PageCount: 33
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      – SubjectFull: Leakage
        Type: general
      – SubjectFull: Random variables
        Type: general
      – SubjectFull: Definitions
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      – SubjectFull: Axiomatic design
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              Text: Mar2020
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