 
Summary: MEFISTO 2003 Preliminary Version
A Quantitative Approach to Noninterference
for Probabilistic Systems
Alessandro Aldini 2,1
Istituto STI, Universit`a Carlo Bo, Urbino, Italy
Alessandra Di Pierro 3,1
Dipartimento di Informatica, Universit`a di Pisa, Italy
Abstract
We present a technique for measuring the security of a system which relies on a probabilistic process
algebraic formalisation of noninterference. We define a mathematical model for this technique which
consists of a linear space of processes and linear transformations on them. In this model the measured
quantity corresponds to the norm of a suitably defined linear operator associated to the system. The
probabilistic model we adopt is reactive in the sense that processes can react to the environment with
a probabilistic choice on a set of inputs; it is also generative in the sense that outputs autonomously
chosen by the system are governed by a probability distribution. In this setting, noninterference is
formulated in terms of a probabilistic notion of weak bisimulation. We show how the probabilistic
information in this notion can be used to estimate the maximal information leakage, i.e. the security
degree of a system against a most powerful attacker.
Key words: Probabilistic Noninterference, Process Algebra, Similarity Relation,
Weak Bisimulation
