Hidden-Markov program algebra with iteration

ANNABELLE MCIVER, LARISSA MEINICKE, CARROLL MORGAN
2014 Mathematical Structures in Computer Science  
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. This joins two themes: we extend our earlier
more » ... k, having iteration but only qualitative, by making it quantitative; and we extend our earlier quantitative work by including iteration. 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.
doi:10.1017/s0960129513000625 fatcat:si5oy4w2w5gjzmd4m543c27ajm