Access Control, Security, and Trust : A Logical Approach by Shiu-Kai Chin

By Shiu-Kai Chin

Developed from the authors’ classes at Syracuse college and the U.S. Air strength examine Laboratory, Access regulate, safety, and belief: A Logical Approach equips readers with an entry keep watch over good judgment they could use to specify and make certain their protection designs. through the textual content, the authors use a unmarried entry keep an eye on common sense according to an easy propositional modal logic.

The first a part of the booklet provides the syntax and semantics of entry keep watch over common sense, easy entry regulate ideas, and an advent to confidentiality and integrity guidelines. the second one part covers entry keep an eye on in networks, delegation, protocols, and using cryptography. within the 3rd part, the authors concentrate on and digital machines. the ultimate half discusses confidentiality, integrity, and role-based entry control.

Taking a logical, rigorous method of entry keep an eye on, this e-book indicates how good judgment is an invaluable software for interpreting defense designs and spelling out the stipulations upon which entry regulate judgements rely. it really is designed for machine engineers and laptop scientists who're answerable for designing, enforcing, and verifying safe desktop and data systems.

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Proof: Consider arbitrary relations R, T and an arbitrary set Y . Our analysis involves two steps: 1. Consider an arbitrary element a ∈ {x | (R∪T )(x) ⊆ Y }: thus (R∪T )(a) ⊆ Y . By definition, (R ∪ T )(a) = {b | (a, b) ∈ R ∪ T } = {b | (a, b) ∈ R} ∪ {b | (a, b) ∈ T } = R(a) ∪ T (a). Therefore, R(a) ∪ T (a) ⊆ Y , and hence we also have that R(a) ⊆ Y and T (a) ⊆ Y . It follows that a ∈ {x | R(x) ⊆ Y } and a ∈ {x | T (x) ⊆ Y }, and therefore a ∈ {x | R(x) ⊆ Y } ∩ {x | T (x) ⊆ Y }. Because a was an arbitrary element of {x | (R ∪ T )(x) ⊆ Y }, we have shown that {x | (R ∪ T )(x) ⊆ Y } ⊆ {x | R(x) ⊆ Y } ∩ {x | T (x) ⊆ Y }.

We need a way to unambiguously express the policies, trust assumptions, recognized authorities, and statements made by various principals and be able to justify the resulting access-control decisions. In this chapter, we introduced a language that allows us to express our policies, trust assumptions, recognized authorities, and statements in a precise and unambiguous way. Expressions in this language are given precise, mathematical meanings through the use of Kripke structures. This Kripke semantics provides the initial basis for mathematically justifying access-control decisions: given a Kripke structure and an expression in the language, we can compute those worlds in which the expression is true.

The “forward” direction: suppose A ⊆ (A − X) ∪ Y , and consider any x ∈ X. Since X ⊆ A, x ∈ A, and thus x ∈ A − X. Therefore, x must be an element of Y . Since x was arbitrary, X ⊆ Y . 2. The “reverse” direction: suppose X ⊆ Y , and consider any a ∈ A. If a ∈ X, then by the definition of subset, a ∈ Y , and hence a ∈ (A − X) ∪Y as necessary; if, instead, a ∈ X, then a ∈ (A − X) and therefore a ∈ (A − X) ∪Y . Since a was arbitrary, A ⊆ (A − X) ∪Y . Having shown that each property implies the other, we have demonstrated that A ⊆ (A − X) ∪Y if and only if X ⊆ Y .

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