  Denning's lattice model provided secure information flow analyses with an
intuitive mathematical foundation: the lattice ordering determines permitted
flows. We examine how this framework may be extended to support the flow of
information between autonomous organisations, each employing possibly quite
different security lattices and information flow policies. We propose a
connection framework that permits different organisations to exchange
information while maintaining both security of information flow as well as
their autonomy in formulating and maintaining security policies. Our
prescriptive framework is based on the rigorous mathematical framework of
Lagois connections proposed by Melton, together with a simple operational model
for transferring object data between domains. The merit of this formulation is
that it is simple, minimal, adaptable and intuitive. We show that our framework
is semantically sound, by proving that the connections proposed preserve
standard correctness notions such as non-interference. We then illustrate how
Lagois theory also provides a robust framework and methodology for negotiating
and maintaining secure agreements on information flow between autonomous
organisations, even when either or both organisations change their security
lattices. Composition and decomposition properties indicate support for a
modular approach to secure flow frameworks in complex organisations. We next
show that this framework extends naturally and conservatively to the
Decentralised Labels Model of Myers et al. - a Lagois connection between the
hierarchies of principals in two organisations naturally induces a Lagois
connection between the corresponding security label lattices, thus extending
the security guarantees ensured by the decentralised model to encompass
bidirectional inter-organisational flows.
