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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Access control matrix</span></span>
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<p>In <a href="Computer_science" title="Computer science">computer science</a>, an <b>access control matrix</b> or <b>access matrix</b> is an abstract, formal <a href="Computer_security_model" title="Computer security model">security model</a> 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 <a href="Butler_W._Lampson" class="mw-redirect" title="Butler W. Lampson">Butler W. Lampson</a> in 1971.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>
</p><p>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 <a href="Access_control_list" class="mw-redirect" title="Access control list">access control list</a> for the object; and each row is equivalent to an <i>access profile</i> for the subject.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>
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<div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2></div>
<p>According to the model, the protection state of a computer system can be abstracted as a set of objects <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>O</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle O}</annotation>
</semantics>
</math></span><img src="./9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}" loading="lazy"></span>, that is the set of entities that needs to be protected (e.g. processes, files, memory pages) and a set of subjects <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>S</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle S}</annotation>
</semantics>
</math></span><img src="./4611d85173cd3b508e67077d4a1252c9c05abca2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}" loading="lazy"></span>, that consists of all active entities (e.g. users, processes). Further there exists a set of rights <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>R</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle R}</annotation>
</semantics>
</math></span><img src="./4b0bfb3769bf24d80e15374dc37b0441e2616e33.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}" loading="lazy"></span> of the form <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r(s,o)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>r</mi>
<mo stretchy="false">(</mo>
<mi>s</mi>
<mo>,</mo>
<mi>o</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle r(s,o)}</annotation>
</semantics>
</math></span><img src="./8245df707f8b244dd8dd9a228812ce6e78e44b06.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.11ex; height:2.843ex;" alt="{\displaystyle r(s,o)}" loading="lazy"></span>, where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s\in S}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>s</mi>
<mo>∈<!-- ∈ --></mo>
<mi>S</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle s\in S}</annotation>
</semantics>
</math></span><img src="./acce52dffd84d073a24f4606a175da60148fd0c6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.43ex; height:2.176ex;" alt="{\displaystyle s\in S}" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle o\in O}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>o</mi>
<mo>∈<!-- ∈ --></mo>
<mi>O</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle o\in O}</annotation>
</semantics>
</math></span><img src="./50225e35975224ed009077e81e82a9b2a60a742c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.742ex; height:2.176ex;" alt="{\displaystyle o\in O}" loading="lazy"></span> and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r(s,o)\subseteq R}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>r</mi>
<mo stretchy="false">(</mo>
<mi>s</mi>
<mo>,</mo>
<mi>o</mi>
<mo stretchy="false">)</mo>
<mo>⊆<!-- ⊆ --></mo>
<mi>R</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle r(s,o)\subseteq R}</annotation>
</semantics>
</math></span><img src="./796a04baafa5efcbe5e5f88bd4df5ece513ddfcc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.972ex; height:2.843ex;" alt="{\displaystyle r(s,o)\subseteq R}" loading="lazy"></span>. A right thereby specifies the kind of access a subject is allowed to process object.
</p>
<div class="mw-heading mw-heading2"><h2 id="Example">Example</h2></div>
<p>In this matrix example there exist two processes, two assets, a file, and a device. The first process is the owner of asset 1, has the ability to execute asset 2, read the file, and write some information to the device, while the second process is the owner of asset 2 and can read asset 1.
</p>
<table class="wikitable" style="margin:1em auto;">
<tbody><tr>
<th>
</th>
<th>Asset 1
</th>
<th>Asset 2
</th>
<th>File
</th>
<th>Device
</th></tr>
<tr>
<th>Role 1
</th>
<td>read, write, execute, own
</td>
<td>execute
</td>
<td>read
</td>
<td>write
</td></tr>
<tr>
<th>Role 2
</th>
<td>read
</td>
<td>read, write, execute, own
</td>
<td>
</td>
<td>
</td></tr></tbody></table>
<div class="mw-heading mw-heading2"><h2 id="Utility">Utility</h2></div>
<p>Because it does not define the granularity of protection mechanisms, the Access Control Matrix can be used as a model of the static access permissions in any type of <a href="Access_control" title="Access control">access control</a> system. It does not model the rules by which permissions can change in any particular system, and therefore only gives an incomplete description of the system's access control <a href="Security_policy" title="Security policy">security policy</a>.
</p><p>An Access Control Matrix should be thought of only as an abstract model of permissions at a given point in time; a literal implementation of it as a two-dimensional array would have excessive memory requirements. <a href="Capability-based_security" title="Capability-based security">Capability-based security</a> and <a href="Access_control_list" class="mw-redirect" title="Access control list">access control lists</a> are categories of concrete access control mechanisms whose static permissions can be modeled using Access Control Matrices. Although these two mechanisms have sometimes been presented (for example in Butler Lampson's <a rel="nofollow" class="external text" href="http://portal.acm.org/citation.cfm?id=775268"><i>Protection</i></a> paper) as simply row-based and column-based <i>implementations</i> of the Access Control Matrix, this view has been criticized as drawing a misleading equivalence between systems that does not take into account dynamic behaviour.
<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="Access_control_list" class="mw-redirect" title="Access control list">Access control list</a> (ACL)</li>
<li><a href="Capability-based_security" title="Capability-based security">Capability-based security</a></li>
<li><a href="Computer_security_model" title="Computer security model">Computer security model</a></li>
<li><a href="Computer_security_policy" title="Computer security policy">Computer security policy</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
<div class="mw-references-wrap"><ol class="references">
<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">
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</style><cite id="CITEREFLampson1971" class="citation conference cs1">Lampson, Butler W. (1971). "Protection". <i>Proceedings of the 5th Princeton Conference on Information Sciences and Systems</i>. p. 437.</cite></span>
</li>
<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">RFC 4949</span>
</li>
<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite id="CITEREFMark_S._MillerKa-Ping_YeeJonathan_Shapiro.2003" class="citation journal cs1">Mark S. Miller; Ka-Ping Yee; Jonathan Shapiro. (March 2003). <a rel="nofollow" class="external text" href="http://srl.cs.jhu.edu/pubs/SRL2003-02.pdf">"Capability Myths Demolished"</a> <span class="cs1-format">(PDF)</span>. Technical Report SRL2003-02. Systems Research Laboratory, Department of Computer Science, Johns Hopkins University.</cite> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{cite journal}}</code>: </span><span class="cs1-visible-error citation-comment">Cite journal requires <code class="cs1-code">|journal=</code> (help)</span></span>
</li>
</ol></div>
<ul><li><cite id="CITEREFBishop2004" class="citation book cs1">Bishop, Matt (2004). <i>Computer security: art and science</i>. Addison-Wesley. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-201-44099-7</bdi>.</cite></li></ul></div><!--htdig_noindex--><div><div class="zim-footer">
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