Access Control Matrix

In computer science, an Access Control Matrix or Access Matrix is an abstract, formal security model of protection state in computer systems, that characterizes the rights of each subject with respect to every object in the system. It was first introduced by Butler W. Lampson in 1971.

An access matrix can be envisioned as a rectangular array of cells, with one row per subject and one column per object. The entry in a cell – that is, the entry for a particular subject-object pair – indicates the access mode that the subject is permitted to exercise on the object. Each column is equivalent to an access control list for the object; and each row is equivalent to an access profile for the subject.

According to the model, the protection state of a computer system can be abstracted as a set of objects ${\displaystyle O}$, that is the set of entities that needs to be protected (e.g. processes, files, memory pages) and a set of subjects ${\displaystyle S}$, that consists of all active entities (e.g. users, processes). Further there exists a set of rights ${\displaystyle R}$ of the form ${\displaystyle r(s,o)}$, where ${\displaystyle s\in S}$, ${\displaystyle o\in O}$ and ${\displaystyle r(s,o)\subseteq R}$. A right thereby specifies the kind of access a subject is allowed to process object.

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