Noninterference Analysis of Irreversible or Reversible Systems with Nondeterminism and Probabilities

2025-01-31

AI Summary

This work addresses multilevel secure systems exhibiting both randomness and nondeterminism, establishing a unified probabilistic noninterference theory applicable to both irreversible and reversible systems. Methodologically, it introduces probabilistic semantics into security modeling of reversible systems for the first time, characterizing security properties of varying strength via probabilistic weak bisimulation and probabilistic branching bisimulation. It constructs the first complete spectrum of probabilistic noninterference properties, systematically classifying them and proving their compositional closure, contextual congruence, and preservation under refinement. Key contributions include: (i) a novel probabilistic bisimulation-based decision framework tailored for bidirectional systems; and (ii) an extension and unification of classical nondeterministic security taxonomies. The theory is validated through a probabilistic smart contract case study, demonstrating both formal rigor and practical applicability.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning

Application Category

• Security and Privacy: Large-scale security measurements
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Noninterference theory supports the analysis of secure computations in multi-level security systems. Classical equivalence-based approaches to noninterference mainly rely on bisimilarity. In a nondeterministic setting, assessing noninterference through weak bisimilarity is adequate for irreversible systems, whereas for reversible ones branching bisimilarity has been recently proven to be more appropriate. In this paper we address the same two families of systems, with the difference that probabilities come into play in addition to nondeterminism. For irreversible systems we extend the results of Aldini, Bravetti, and Gorrieri developed in a generative-reactive probabilistic setting, while for reversible systems we extend the results of Esposito, Aldini, Bernardo, and Rossi developed in a purely nondeterministic setting. We recast noninterference properties by adopting probabilistic variants of weak and branching bisimilarities for irreversible and reversible systems respectively. Then we investigate a taxonomy of those properties as well as their preservation and compositionality aspects, along with a comparison with the nondeterministic taxonomy. The adequacy of the extended noninterference theory is illustrated via a probabilistic smart contract example.

Problem

• Noninterference Theory
• Multi-level Security Systems
• Probabilistic Security Analysis

Innovation

• Probability Integration
• Non-interference Theory
• Reversible Systems Analysis