Modelling Opacity Using Petri Nets

Abstract

We consider opacity as a property of the local states of the secure (or high-level) part of the system, based on the observation of the local states of a low-level part of the system as well as actions. We propose a Petri net modelling technique which allows one to specify different information flow properties, using suitably defined observations of system behaviour. We then discuss expressiveness of the resulting framework and the decidability of the associated verification problems.

Opacity of discrete event systems and its applications

“…In the figure, we can see that from the initial state labeled by (1,2,3,4,5), it takes at most three transitions (N = 3) to reach states labeled by (2), (3), (4), or (5) at the bottom half of the figure. Therefore, take x = 2 for example, s ∈ θ(L >N x ) if and only if s ends in the state labeled by (2).…”

“…Secrecy has been studied before, for example, in [1] [5] [2] [6] [22]. In [2], for a finite state system with partial observers and for each observer, a secret is defined as a subset of trajectories.…”

Opacity generalised to transition systems

“…3 Note that this varies slightly from the one used in [4] where the step sequence semantics allowed multiple transitions to occur simultaneously. Here, transitions are clearly separated.…”

“…What now follows is a crucial result stating that initial opacity with an norwellian observation function is decidable provided that the LTS generated by a marked Petri net is finite 4 . In fact, this result could be generalised to any finite LTS; i.e., in the case of a finite LTS, initial opacity w.r.t.…”

“…Initial-opacity has been illustrated by the dining cryptographers example (in [4] with two cryptographers and [5] with three). It would appear that it is suited to modelling situations in which initialisation information such as crypto keys, etc., needs to be kept secret.…”