On Reductions from Multi-Domain Noninterference to the Two-Level Case
This work addresses foundational issues in information flow security for transitive policies, which is incremental but important for formal verification and security analysis.
The paper tackles the problem of reducing multi-domain information flow security policies to the two-domain case, showing that the commonly used Low-down reduction is weaker and that both Low-down and High-up reductions can be non-monotonic, while cut-based partitioning offers a more robust approach.
The literature on information flow security with respect to transitive policies has been concentrated largely on the case of policies with two security domains, High and Low, because of a presumption that more general policies can be reduced to this two-domain case. The details of the reduction have not been the subject of careful study, however. Many works in the literature use a reduction based on a quantification over "Low-down" partitionings of domains into those below and those not below a given domain in the information flow order. A few use "High-up" partitionings of domains into those above and those not above a given domain. Our paper argues that more general "cut" partitionings are also appropriate, and studies the relationships between the resulting multi-domain notions of security when the basic notion for the two-domain case to which we reduce is either Nondeducibility on Inputs or Generalized Noninterference. The Low-down reduction is shown to be weaker than the others, and while the High-up reduction is sometimes equivalent to the cut reduction, both it and the Low-down reduction may have an undesirable property of non-monotonicity with respect to a natural ordering on policies. These results suggest that the cut-based partitioning yields a more robust general approach for reduction to the two-domain case.