Abstract channels and their robust information-leakage ordering

Annabelle McIver, Carroll Morgan, Geoffrey Smith, Barbara Espinoza, Larissa Meinicke

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

34 Citations (Scopus)

Abstract

The observable output of a probabilistic system that processes a secret input might reveal some information about that input. The system can be modelled as an information-theoretic channel that specifies the probability of each output, given each input. Given a prior distribution on those inputs, entropy-like measures can then quantify the amount of information leakage caused by the channel. But it turns out that the conventional channel representation, as a matrix, contains structure that is redundant with respect to that leakage, such as the labeling of columns, and columns that are scalar multiples of each other. We therefore introduce abstract channels by quotienting over those redundancies. A fundamental question for channels is whether one is worse than another, from a leakage point of view. But it is difficult to answer this question robustly, given the multitude of possible prior distributions and leakage measures. Indeed, there is growing recognition that different leakage measures are appropriate in different circumstances, leading to the recently proposed g-leakage measures, which use gain functions g to model the operational scenario in which a channel operates: the strong g-leakage pre-order requires that channel A never leak more than channel B, for any prior and any gain function. Here we show that, on abstract channels, the strong g-leakage pre-order is antisymmetric, and therefore a partial order. It was previously shown [1] that the strong g-leakage ordering is implied by a structural ordering called composition refinement, which requires that A = BR, for some channel R; but the converse was not established in full generality, left open as the so-called Coriaceous Conjecture. Using ideas from [2], we here confirm the Coriaceous Conjecture. Hence the strong g-leakage ordering and composition refinement coincide, giving our partial order both structural- and leakage-testing significance.

Original languageEnglish
Title of host publicationPrinciples of Security and Trust - Third International Conference, POST 2014, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2014, Proceedings
EditorsMartín Abadi, Steve Kremer
Place of PublicationHeidelberg
PublisherSpringer, Springer Nature
Pages83-102
Number of pages20
ISBN (Print)9783642547911
DOIs
Publication statusPublished - 2014
Event3rd International Conference on Principles of Security and Trust, POST 2014 - Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2014 - Grenoble, France
Duration: 5 Apr 201413 Apr 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8414 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other3rd International Conference on Principles of Security and Trust, POST 2014 - Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2014
CountryFrance
CityGrenoble
Period5/04/1413/04/14

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  • Cite this

    McIver, A., Morgan, C., Smith, G., Espinoza, B., & Meinicke, L. (2014). Abstract channels and their robust information-leakage ordering. In M. Abadi, & S. Kremer (Eds.), Principles of Security and Trust - Third International Conference, POST 2014, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2014, Proceedings (pp. 83-102). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8414 LNCS). Heidelberg: Springer, Springer Nature. https://doi.org/10.1007/978-3-642-54792-8_5