Agda Formalization of a Security-preserving Translation from Flow-sensitive to Flow-insensitive Security Types

The analysis of information flow is a popular technique for ensuring the confidentiality of data. It is in this context that confidentiality policies arise for giving guarantees that private data cannot be inferred by the inspection of public data. One of those policies is non-interference, a semantic condition that ensures the absence of illicit information flow during program execution by not allowing to distinguish the results of two computations when they only vary in their confidential inputs. A remarkable feature of non-interference is that it can be enforced statically by the definition of information flow type systems. In those type systems, if a program type-checks, then it means that it meets the security policy.

In this paper we focus on the preservation of non-interference through program translation. Concretely, we formalize the proof of security preservation of Hunt and Sands' translation that transforms high-level While programs typable in a flow-sensitive type system into equivalent high-level programs typable in a flow-insensitive type system. Our formalization is performed in the dependently-typed language Agda. We use the expressive power of Agda's type system to encode the security type systems at the type level. A particular aspect of our formalization is that it follows a fully internalist approach where we decorate the type of the abstract syntax with security type information in order to obtain the representation of well-typed (i.e secure) programs. A benefit of this approach is that it allows us to directly express the property of security preservation in the type of the translation relation. In this manner, apart from inherently expressing the transformation of programs, the translation relation also stands for an inductive proof of security preservation.