We use Hidden Markov Models to motivate a quantitative compositional semantics for noninterference-based security with iteration, including a refinement- or implements relation that compares two programs with respect to their information leakage; and we propose a program algebra for source-level reasoning about such programs, in particular as a means of establishing that an implementation program leaks no more than its specification program. <p>This joins two themes: we extend our earlier work, having iteration but only qualitative, by making it quantitative; and we extend our earlier quantitative work by including iteration. <p>We advocate stepwise refinement and source-level program algebra, both as conceptual reasoning tools and as targets for automated assistance. A selection of algebraic laws is given to support this view in the case of quantitative noninterference; and it is demonstrated on a simple iterated password-guessing attack.
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