A Timed Logic for Modeling and Reasoning about Security Protocols

Many logical methods are usually considered suitable to express the static properties of security protocols while unsuitable to model dynamic processes or properties. However, a security protocol itself is in fact a dynamic process over time, and sometimes it is important to be able to express time-dependent security properties of protocols. In this paper, we present a new timed logic based on predicate modal logic, in which time is explicitly expressed in parameters of predicates or modal operators. This makes it possible to model an agent’s actions, knowledge and beliefs at different and exact time points, which enables us to model both protocols and their properties, especially time-dependent properties. We formalize semantics of the presented logic, and prove its soundness. We also present a modeling scheme for formalizing protocols and security properties of authentication and secrecy under the logic. The scheme provides a flexible and succinct framework to reason about security protocols, and essentially enhances the power of logical methods for protocol analysis. As a case study, we then analyze a timed-release protocol using this framework, and discover a new vulnerability that did not appear previously in the literature. We provide a further example to show additional advantages of the modeling scheme in the new logic.