Secure Information Flow Typing in LUSTRE

Synchronous reactive data flow is a paradigm that provides a high-level abstract programming model for embedded and cyber-physical systems, including the locally synchronous components of IoT systems. Security in such systems is severely compromised due to low-level programming, ill-defined interfaces and inattention to security classification of data. By incorporating a Denning-style lattice-based secure information flow framework into a synchronous reactive data flow language, we provide a framework in which correct-and-secure-by-construction implementations for such systems may be specified and derived. In particular, we propose an extension of the Lustre programming framework with a security type system. The novelty of our type system lies in a symbolic formulation of constraints over security type variables, in particular the treatment of node calls, which allows us to reason about secure flow with respect to any security class lattice. The main theorem is the soundness of our type system with respect to the co-inductive operational semantics of Lustre, which we prove by showing that well-typed programs exhibit non-interference. Rather than tackle the full language, we first prove the non-interference result for a well-behaved sub-language called "Normalised Lustre" (NLustre), for which our type system is far simpler. We then show that Bourke et al.'s semantics-preserving "normalisation" transformations from Lustre to NLustre are security-preserving as well. This preservation of security types by the normalisation transformations is a property akin to "subject reduction" but at the level of compiler transformations. The main result that well-security-typed Lustre programs are non-interfering follows from a reduction to our earlier result of non-interference for NLustre via the semantics-preservation (of Bourke et al.) and type preservation results.