6,692 research outputs found
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 , and we equip them with a partial order of increasing
security. However to encode the monadic type with hiding over some state
we use rather
than the conventional that suffices for
Markov models whose state is not hidden. We illustrate the
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
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