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Secure information flow and file movements: A topological theory of discretionary access controls

Achieving total information flow security is feasible through the use of formal mathematical models. A fundamental theorem of a topological theory of Discretionary Access Controls is presented: Let U be a set of UNIX users. The association from each data owner p to its data owners group F(p) defines a generalized topological space (U, F) and a binary relation BF. Thus, a DAC-system is information-flow-secure (via file movements): if and only if (U, F) is a finite topological space; if and only if (U, BF) is a reflexive and transitive graph. An important consequence is the following proved secure system in current UNIX: The information flow (via file movements) of UNIX generated by Read-access is information-flow-secure: if (U, F) is a finite topological space;if (U, BF) is a reflexive and transitive graph. This model is based on a modified security principle: Every data owner p has the discretionary authority (Individual Data Owner p's authority, or IDO(p)-authority) over who can access the data. The precise security policy is the integration of IDO(p)-security for All data owner p in All possible data states. Once granted access, information propagation can still be controlled by the topological structure.