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Calculating Information Leakage in Continuous Domains

### Tom Chothia

Information theory provides a range of useful methods to analyse
probability distributions and these techniques have been successfully
applied to measure information flow and the loss of anonymity in
secure systems. However, previous work has tended to assume that the
exact probabilities of every action are known, or that the system is
non-deterministic. In this talk I will describe a result, developed
with Guha and Chatzikokolakis that makes it possible to calculate
measures of information leakage based on mutual information and
capacity from trial runs of a system alone. I will demonstrate the
calculation of information flow from a program with a small domain of
secrets but which uses the Java Random library, sockets and
multi-threading. When the observable actions of a system come from a
continuous domain (e.g. time or power measurements) but the secret
values are still discrete (e.g. bytes) it is necessary to use a hybrid
version of mutual information in order to calculate information
leakage. I will sketch some initial results on the convergence of
mutual information estimates for these hybrid processes and I will
illustrate these results by analysing an attack against e-passports.