Trustworthy Systems

Hidden-markov program algebra with iteration


Annabelle McIver, Larissa Meinicke and Carroll Morgan

    School of Computer Science and Engineering
    Sydney 2052, Australia


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 work, having iteration but only qualitative (Morgan 2009), by making it quantitative; and we extend our earlier quantitative work (McIver et al. 2010) 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.

BibTeX Entry

    paperurl         = {},
    doi              = {10.1017/S0960129513000625},
    journal          = {Mathematical Structures in Computer Science},
    number           = {2},
    publisher        = {Cambridge University Press},
    author           = {{McIver}, Annabelle and Meinicke, Larissa and Morgan, Carroll},
    title            = {Hidden-Markov program algebra with iteration},
    volume           = {25},
    pages            = {320–360},
    year             = {2015}