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Hidden-Markov program algebra with iteration

Published online by Cambridge University Press:  10 November 2014

ANNABELLE MCIVER ,
LARISSA MEINICKE  and
CARROLL MORGAN
ANNABELLE MCIVER
Affiliation:
Dept Comp Sci, Macquarie University, NSW, Australia Email: annabelle.mciver@mq.edu.au
LARISSA MEINICKE
Affiliation:
Dept Comp Sci, Univ Queensland, Qld, Australia Email: l.meinicke@uq.edu.au
CARROLL MORGAN
Affiliation:
School Comp Sci and Eng, Univ NSW, NSW, Australia Email: carrollm@cse.unsw.edu.au
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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.

Type
Special Issue: Quantitative Information Flow
Information
Mathematical Structures in Computer Science , Volume 25 , Issue 2: Quantitative Information Flow , February 2015 , pp. 320 - 360
Copyright
Copyright © Cambridge University Press 2014 

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