Semiring-based Specification Approaches for Quantitative Security
This work addresses the need for quantitative security specification in systems with unknown malicious agents, representing an incremental extension of existing approaches like GNDC.
The paper tackles the problem of specifying quantitative security requirements by developing semiring-based formal tools, including an approximate behavioral equivalence and a weighted modal logic, to assess system security against malicious agents with respect to threshold values.
Our goal is to provide different semiring-based formal tools for the specification of security requirements: we quantitatively enhance the open-system approach, according to which a system is partially specified. Therefore, we suppose the existence of an unknown and possibly malicious agent that interacts in parallel with the system. Two specification frameworks are designed along two different (but still related) lines. First, by comparing the behaviour of a system with the expected one, or by checking if such system satisfies some security requirements: we investigate a novel approximate behavioural-equivalence for comparing processes behaviour, thus extending the Generalised Non Deducibility on Composition (GNDC) approach with scores. As a second result, we equip a modal logic with semiring values with the purpose to have a weight related to the satisfaction of a formula that specifies some requested property. Finally, we generalise the classical partial model-checking function, and we name it as quantitative partial model-checking in such a way to point out the necessary and sufficient conditions that a system has to satisfy in order to be considered as secure, with respect to a fixed security/functionality threshold-value.