Hidden-Markov Program Algebra with iteration

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, 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

Quantifying Timing Leaks and Cost Optimisation

We develop a new notion of security against timing attacks where the attacker is able to simultaneously observe the execution time of a program and the probability of the values of low variables. We then show how to measure the security of a program with respect to this notion via a computable estimate of the timing leakage and use this estimate for cost optimisation.Comment: 16 pages, 2 figures, 4 tables. A shorter version is included in the proceedings of ICICS'08 - 10th International Conference on Information and Communications Security, 20-22 October, 2008 Birmingham, U

Compositional closure for Bayes Risk in probabilistic noninterference

We give a sequential model for noninterference security including probability (but not demonic choice), thus supporting reasoning about the likelihood that high-security values might be revealed by observations of low-security activity. Our novel methodological contribution is the definition of a refinement order and its use to compare security measures between specifications and (their supposed) implementations. This contrasts with the more common practice of evaluating the security of individual programs in isolation. The appropriateness of our model and order is supported by our showing that our refinement order is the greatest compositional relation --the compositional closure-- with respect to our semantics and an "elementary" order based on Bayes Risk --- a security measure already in widespread use. We also relate refinement to other measures such as Shannon Entropy. By applying the approach to a non-trivial example, the anonymous-majority Three-Judges protocol, we demonstrate by example that correctness arguments can be simplified by the sort of layered developments --through levels of increasing detail-- that are allowed and encouraged by compositional semantics

A static analysis for quantifying information flow in a simple imperative language

We propose an approach to quantify interference in a simple imperative language that includes a looping construct. In this paper we focus on a particular case of this definition of interference: leakage of information from private variables to public ones via a Trojan Horse attack. We quantify leakage in terms of Shannon's information theory and we motivate our definition by proving a result relating this definition of leakage and the classical notion of programming language interference. The major contribution of the paper is a quantitative static analysis based on this definition for such a language. The analysis uses some non-trivial information theory results like Fano's inequality and L1 inequalities to provide reasonable bounds for conditional statements. While-loops are handled by integrating a qualitative flow-sensitive dependency analysis into the quantitative analysis

Abstract Hidden Markov Models: a monadic account of quantitative information flow

Hidden Markov Models, HMM's, are mathematical models of Markov processes with state that is hidden, but from which information can leak. They are typically represented as 3-way joint-probability distributions. We use HMM's as denotations of probabilistic hidden-state sequential programs: for that, we recast them as `abstract' HMM's, computations in the Giry monad $\mathbb{D}$, and we equip them with a partial order of increasing security. However to encode the monadic type with hiding over some state $\mathcal{X}$ we use $\mathbb{D}\mathcal{X}\to \mathbb{D}^2\mathcal{X}$ rather than the conventional $\mathcal{X}{\to}\mathbb{D}\mathcal{X}$ that suffices for Markov models whose state is not hidden. We illustrate the $\mathbb{D}\mathcal{X}\to \mathbb{D}^2\mathcal{X}$ construction with a small Haskell prototype. We then present uncertainty measures as a generalisation of the extant diversity of probabilistic entropies, with characteristic analytic properties for them, and show how the new entropies interact with the order of increasing security. Furthermore, we give a `backwards' uncertainty-transformer semantics for HMM's that is dual to the `forwards' abstract HMM's - it is an analogue of the duality between forwards, relational semantics and backwards, predicate-transformer semantics for imperative programs with demonic choice. Finally, we argue that, from this new denotational-semantic viewpoint, one can see that the Dalenius desideratum for statistical databases is actually an issue in compositionality. We propose a means for taking it into account