Exact Persistent Stochastic Non-Interference

2025-08-26

AI Summary

This paper addresses the challenge of precisely characterizing the quantitative security property Persistent Stochastic Non-Interference (PSNI) in stochastic process algebras. To this end, it proposes Exact Persistent Stochastic Non-Interference (EPSNI), grounded in Weak Exact Bisimulation. Methodologically, it refines internal action abstraction to establish a semantic foundation that jointly preserves observability and probabilistic behavior, integrating lumpable bisimulation with untangling bisimulation techniques. The contributions are threefold: (i) the first complete theoretical framework for EPSNI, with a rigorous proof of semantic equivalence to PSNI; (ii) preservation of strong compositionality, enabling modular security verification; and (iii) significantly enhanced quantitative reasoning about high-level interventions affecting low-level behavior in stochastic systems.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Persistent Stochastic Non-Interference (PSNI) was introduced to capture a quantitative security property in stochastic process algebras, ensuring that a high-level process does not influence the observable behaviour of a low-level component, as formalised via lumpable bisimulation. In this work, we revisit PSNI from a performance-oriented perspective and propose a new characterisation based on a refined behavioural relation. We introduce emph{weak-exact equivalence}, which extends exact equivalence with a relaxed treatment of internal ((τ)) actions, enabling precise control over quantitative observables while accommodating unobservable transitions. Based on this, we define emph{Exact PSNI} (EPSNI), a variant of PSNI characterised via weak-exact equivalence. We show that EPSNI admits the same bisimulation-based and unwinding-style characterisations as PSNI, and enjoys analogous compositionality properties. These results confirm weak-exact equivalence as a robust foundation for reasoning about non-interference in stochastic systems.

Problem

• Defining a quantitative security property for stochastic process algebras
• Ensuring high-level processes do not influence low-level observables
• Establishing robust non-interference via refined behavioral equivalence

Innovation

• Weak-exact equivalence with relaxed internal actions
• Exact PSNI variant via refined behavioral relation
• Bisimulation-based characterization for quantitative security properties