Lecture Notes in Computer Science 5185

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30 I. Agudo, C. Fernandez-Gago, and J. Lopez Those implicit trust relations depend on the kind of trust dependability that we allow in our system. The dependability rules have to be taken into account when reducing the trust graph for a given task. The dependency among tasks that we use in this paper is inspired in the definitions of the syntax of the RT framework, a family of Role-based Trust management languages for representing policies and credentials in distributed authorization [14]. In this work the authors define four different types of relationships among roles. If the relationships in the model are simple, these relationships can be modelled by using a partial order. This is the case for our purpose in this paper, a model of tasks, which are quite an objective concept. Next we will give some definitions. Definition 1 (Trust Domain). A trust domain is a partially ordered set (TD,
A Model for Trust Metrics Analysis 31 3.1 Trust Functions Definition 3 (Trust Evaluation). A trust evaluation for a trust graph G is a function FG : E × E × T −→ TD, where E, T and T D are the sets mentioned in Definition 2. We say that a trust evaluation is local if for any tuple (s,t,x) ∈ E × E × T, FG(s,t,x)= F s,t G (s,t,x), i.e., only those trust statements in Gs,t x are relevant for the evaluation. x In this work we focus on local trust evaluations, in particular on those trust evaluations that can be decomposed in two elemental functions: the Sequential Trust Function and the Parallel Trust Function. By decomposed functions we mean that the trust evaluation is computed by applying the Parallel Trust function to the results of applying the Sequential Trust Function over all the paths connecting two given entities. Definition 4 (Sequential Trust Function). A sequential trust function is a function, f : � n � �� ∞ n=2 TD×···×TD −→ T D, that calculates the trust level associated to a path or chain of trust statements, such that f (v1,...,vn) =0 if, and only if, vi = 0 for any i ∈ {1,...,n},wherevi∈TDand TD is a trust domain. Each path of trust statements in G is represented as the chain, t1 −→ t2 −→ ··· vn−1 −→ tn vn −→ xn+1, wheretiare entities in E and vi are respectively the trust values associated to each statement. The sequential trust function, f , may verify some of the following properties: – Monotony (Parallel Monotony): f (v1,...,vn) ≤ f (v ′ 1 ,...,v′ n ) if vi ≤ v ′ i for all i ∈ {1,...,n}. – Minimality: f (v1,...,vn) ≤ min(v1,...,vn) – Sequential monotony: f (v1,...,vn−1,vn) ≤ f (v1,...,vn−1) – Preference Preserving: f (v1,...,vi,...,v j,...,vn) < f (v1,...,v j,...,vi,...,vn) if vi < v j. – Recursion: f (v1,...,vn)= f ( f (v1,...,vn−1),vn) When defining a recursive sequential function we have to take into account that it is enough to define it over pairs of elements in TD, since by applying the recursion property we could obtain the value of the function for any tuple. We call generator sequential function or sequential operator to the function f restricted over the domain TD× TD. We represent it by ⊙. Thus, Definition 5 (Sequential Operator). A Sequential Operator or Generator Sequential Function is defined as a function ⊙ : TD× TD−→ TD such that a ⊙ b = 0 if and only if a = 0 or b = 0. ⊙(a,b) or a ⊙ b are used indistinctively for representing the same, whatever is more convenient. Given a recursive sequential function, f , the associated sequential operator ⊙ f , can be defined as a⊙b = f (a,b). Viceversa, given a sequential operator, the recursive inference sequential function can be defined as f⊙(z1,...,zn−1,zn)= f⊙(z1,...,zn−1) ⊙ zn. Note that a recursive sequential function verifies the reference preserving property only if the associated sequential operator, ⊙ f , is not commutative. Moreover, if a ⊙ b ≤ min(a,b),foranya and b, we could conclude that f verifies the minimality property. v1 v2
Page 1 and 2: Lecture Notes in Computer Science 5
Page 3 and 4: Volume Editors Steven Furnell Unive
Page 5 and 6: Program Committee General Chairpers
Page 7 and 8: Invited Lecture Table of Contents B
Page 9 and 10: Biometrics - How to Put to Use and
Page 11 and 12: Biometrics-HowtoPuttoUseandHowNotat
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Page 15 and 16: 7 Outlook Biometrics-HowtoPuttoUsea
Page 17 and 18: A Map of Trust between Trading Part
Page 27 and 28: Implementation of a TCG-Based Trust
Page 37: A Model for Trust Metrics Analysis
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Page 47 and 48: Patterns and Pattern Diagrams for A
Page 51 and 52: Policy Model AC model Patterns and
Page 53 and 54: Broker Investor Doctor Patient 1
Page 57 and 58: A Spatio-temporal Access Control Mo
Page 67 and 68: A Mechanism for Ensuring the Validi
Page 77 and 78: Multilateral Secure Cross-Community
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Fairness Emergence through Simple R
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Combining Trust and Reputation Mana
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Controlling Usage in Business Proce
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A Semantics Rules for POLPA-Control
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BusiROLE: A Model for Integrating B
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A Generic Intrusion Detection Game
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On the Design Dilemma in Dining Cry
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Agudo, Isaac 28 Aich, Subhendu 118
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Lecture Notes in Computer Science 5185

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