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Can access control matrix in addition to confidentiality provide the integrity of the objects to which access is being controlled?

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I think this question is a bit ambiguous, since you're not being very specific about your terminology. Some of these terms are overloaded, and mean different things in different contexts. Can you elaborate a bit? – AviD♦ Oct 27 '12 at 20:27

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Of course! Yes, absolutely. To explain I need to give a refresher on these terms.

What's an access control matrix? It's a matrix A, where Ai,j indicates the permissions that subject i has to access resource j. The permissions might be something like "read" or "read,write" or "read,execute". The access control matrix is an abstraction that captures the policy that is enforced by an access control mechanism.

So, can you use access control to protect the integrity of a resource? Sure. Just limit who receives write permission to that resource to only entities who are trusted not to screw up its integrity. This is indeed one of the primary motivations for access control.

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In theory, yes. The Biba integrity matrix is the traditional theoretical description of such an ACL. Unfortunately it turns out to be rather difficult to describe "integrity" in a way that facilitate development of a Biba based system. I'm not aware of any real world implementations of Biba, although if I remember correctly, the concept was applied to parts of the Trusted Computing Station.

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Biba (integrity) and Bell-La Padula (confidentiality) are 'duals' of one another, so whatever you can do with one you can do with the other. – Marcin Oct 26 '12 at 13:26
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ACL belongs to the DACL model... Also Biba and Bell-LaPadula are MAC implementations, whereas matrix-based systems are (usually) something else altogether. – AviD♦ Oct 26 '12 at 13:50
You could do with a Biba model what you could do with a LaPadula model IF you could define integrity the way we currently define confidentiality. Confidentiality is defined by fiat, but no such fiat has occurred for integrity – Mark C. Wallace Oct 26 '12 at 13:57
@AviD - Both Biba and LaPadula are abstractions which describe an Access Control Policy; Access Control Lists can be implemented to support either Mandatory or Discretionary Access Control Policies. The distinction is what privilege is required to edit the ACL. However, I've a niggling suspicion that you're still on to something. I need to think about it further. I suspect however that the distinction is more subtle than the OP's question. – Mark C. Wallace Oct 26 '12 at 14:02
This answer doesn't make sense to me. The answer is not just "in theory, yes", but a plain unadorned "yes". You don't need to invoke the Biba model or any fancy MAC stuff. Ordinary everyday access control can be used to protect the integrity of a resource -- indeed, that's probably the number-one most common use of access control. If Alice doesn't have write access to resource R, she cannot mess up its integrity. – D.W. Oct 28 '12 at 2:05

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