Probabilistic Polynomial-Time Process Calculus and Security Protocol Analysis

John C. Mitchell

Abstract: We propose a formal framework for analyzing security protocols. This framework, which differs from previous logical methods based on the Dolev-Yao model, is based on a process calculus that captures probabilistic polynomial time. Protocols are written in a restricted form of π-calculus and security is expressed as a form or observational equivalence, a standard relation from programming language theory that involves quantifying over possible additional processes that might interact with the protocol. Using an asymptotic notion of probabilistic equivalence, we may relate observational equivalence to polynomial-time statistical tests. Several example protocols have been analyzed. We believe that this framework offers the potential to codify and automate realistic forms of protocol analysis. In addition, our work raises some foundational problems for reasoning about probabilistic programs and systems.