Calculating bounds on information leakage using two-bit patterns

Theories of quantitative information flow have seen growing interest recently, in view of the fundamental importance of controlling the leakage of confidential information, together with the pragmatic necessity of tolerating intuitively "small" leaks. Given such a theory, it is crucial to develop automated techniques for calculating the leakage in a system. In this paper, we address this question in the context of deterministic imperative programs and under the recently-proposed min-entropy measure of information leakage, which measures leakage in terms of the confidential information's vulnerability to being guessed in one try by an adversary. In this context, calculating the maximum leakage of a program reduces to counting the number of feasible outputs that it can produce. We approach this task by determining patterns among pairs of bits in the output, for instance by determining that two bits must be unequal. By counting the number of solutions to the two-bit patterns, we obtain an upper bound on the number of feasible outputs and hence on the leakage. We explore the effectiveness of our approach on a number of case studies, in terms of both efficiency and accuracy.