Enforcement and validation (at runtime) of various notions of opacity

Abstract

We are interested in the validation of opacity. Opacity models the impossibility for an attacker to retrieve the value of a secret in a system of interest. Roughly speaking, ensuring opacity provides confidentiality of a secret on the system that must not leak to an attacker. More specifically, we study how we can model-check, verify and enforce at system runtime, several levels of opacity. Besides existing notions of opacity, we also introduce K-step strong opacity, a more practical notion of opacity that provides a stronger level of confidentiality.

Opacity of Discrete Event Systems: models, validation and quantification

“…This definition can be reformulate as in Falcone et al (2014). The system is (X S , P, K)-opaque if for every execution t of G and for every secret execution t prefix of t with an observable difference inferior to K, there exist two executions s and s observationally equivalent respectively to t and t such that s is not a secret execution (i.e., which does not bring the system in a secret state).…”

“…Remark 5. In Falcone et al (2014), Definition 6 is referred to as K-step weak opacity. The property of K-step strong opacity holds if the system is K-step weakly opaque and there exists a trace of the system (observably equivalent to the actual execution) which does not cross any secret state over the last K steps.…”

“…In the sequel of the paper, only control and enforcement approached will be further developed. For more details about verification of: (i) LBO, refers to Lin (2011); (ii) SBO, refers to Falcone et al (2014) and Hadjicostis and Keroglou (2014).…”

“…Opacity enforcement at run-time was recently surveyed in Falcone et al (2014). Enforcement does not restrict the system behavior anymore.…”

“…More recently, Saboori and Hadjicostis investigated state-based opacity properties using finite-state automata (FSA) models (Saboori and Hadjicostis (2007), Saboori (2011)). Many researchers have considered the validation of opacity properties which spans from system's opacity verification (Hadjicostis and Keroglou (2014)) to the synthesis of a controller/scheduler which assures opacity, either through supervision (Dubreil (2010)) or enforcement (Falcone et al (2014)). Recent work has been conducted on quantifying a system's opacity (Bérard et al (2010)).…”