Preserving Secrecy Under Refinement

Abstract

We propose a general framework of secrecy and preservation of secrecy for labeled transition systems. Our definition of secrecy is parameterized by the distinguishing power of the observer, the properties to be kept secret, and the executions of interest, and captures a multitude of definitions in the literature. We define a notion of secrecy preserving refinement between systems by strengthening the classical trace-based refinement so that the implementation leaks a secret only when the specification also leaks it. We show that secrecy is in general not definable in µ-calculus, and thus not expressible in specification logics supported by standard model-checkers. However, we develop a simulation-based proof technique for establishing secrecy preserving refinement. This result shows how existing refinement checkers can be used to show correctness of an implementation with respect to a specification.Abstract. We propose a general framework of secrecy and preservation of secrecy for labeled transition systems. Our definition of secrecy is parameterized by the distinguishing power of the observer, the properties to be kept secret, and the executions of interest, and captures a multitude of definitions in the literature. We define a notion of secrecy preserving refinement between systems by strengthening the classical trace-based refinement so that the implementation leaks a secret only when the specification also leaks it. We show that secrecy is in general not definable in µ-calculus, and thus not expressible in specification logics supported by standard model-checkers. However, we develop a simulation-based proof technique for establishing secrecy preserving refinement. This result shows how existing refinement checkers can be used to show correctness of an implementation with respect to a specification.

Unifying Theories of Confidentiality

“…Our approach towards confidentiality-preserving refinement also has links to work by Alur et al [19]. In this work, the refinement of a labelled transition system is expected to preserve L's inability to deduce whether system runs satisfy a specified set of properties on secret variables.…”

Unifying Hyper and Epistemic Temporal Logics

“…For all observation maps Obs such that Obs(a) = ∅, (K, Obs) |= ϕ p means that there is some non-root level in the unwinding of K at which no node satisfies p. Property φ p is a well-known non-regular context-free branching-time property (see e.g. [2]). …”

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.…”