2012 IEEE 25th Computer Security Foundations Symposium (2007)

Venice, Italy

July 6, 2007 to July 8, 2007

ISBN: 0-7695-2819-8

pp: 341-354

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CSF.2007.27

Prakash Panangaden , McGill University, Canada

Konstantinos Chatzikokolakis , Ecole Polytechnique, France

Catuscia Palamidessi , Ecole Polytechnique, France

ABSTRACT

Randomized protocols for hiding private information can fruitfully be regarded as noisy channels in the information-theoretic sense, and the inference of the concealed information can be regarded as a hypothesis-testing problem. We consider the Bayesian approach to the problem, and investigate the probability of error associated to the inference when the MAP (Maximum Aposteriori Probability) decision rule is adopted. Our main result is a constructive characterization of a convex base of the probability of error, which allows us to compute its maximum value (over all possible input distributions), and to identify upper bounds for it in terms of simple functions. As a side result, we are able to improve substantially the Hellman-Raviv and the Santhi-Vardy bounds expressed in terms of conditional entropy. We then discuss an application of our methodology to the Crowds protocol, and in particular we show how to compute the bounds on the probability that an adversary breaks anonymity.

INDEX TERMS

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CITATION

Prakash Panangaden,
Konstantinos Chatzikokolakis,
Catuscia Palamidessi,
"Probability of Error in Information-Hiding Protocols",

*2012 IEEE 25th Computer Security Foundations Symposium*, vol. 00, no. , pp. 341-354, 2007, doi:10.1109/CSF.2007.27