The information security community has long debated the exact definition of the term ‘security’. Even if we focus on the more specific notion of confidentiality the precise definition remains controversial. In their seminal paper, Goguen and Meseguer took an important step towards a formalisation of the notion of absence of information flow with the concept of non-interference. This too was found to have problems and limitations, particularly when applied to systems displaying non-determinism which led to a proliferation of refinements of this notion and there is still no consensus as to which of these is ‘correct’.

We show that this central concept in information security is closely related to a central concept of computer science: that of the equivalence of systems. The notion of non-interference depends ultimately on our notion of process equivalence. However what constitutes the equivalence of two processes is itself a deep and controversial question in computer science with a number of distinct definitions proposed in the literature. We illustrate how several of the leading candidates for a definition of non-interference mirror notions of system equivalence. Casting these security concepts in a process algebraic framework clarifies the relationship between them and allows many results to be carried over regarding, for example, composition and the completeness of unwinding rules.

We also outline some generalisations of a CSP formulation of non-interference to handle partial and conditional information flows.