Trustworthy Systems

Hidden-markov program algebra with iteration

Authors

Annabelle McIver, Larissa Meinicke and Carroll Morgan

    School of Computer Science and Engineering
    UNSW,
    Sydney 2052, Australia

Abstract

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

  @article{McIver_Meinicke_Morgan_15,
    paperurl         = {https://trustworthy.systems/publications/papers/McIver_Meinicke_Morgan_15.pdf},
    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}
  }

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