Quantifying Trust Metrics of Recommendation Systems in Ad-Hoc Networks

The performance of ad-hoc networks depends on trust among distributed nodes. To enhance security in ad-hoc networks, it is important to evaluate trustworthiness of other nodes without centralized authorities. This paper studies trust metrics of recommendation systems in ad-hoc networks and makes the following three contributions: 1. the notion of action is formalized by means of disjunctive normal form (DNF) over Boolean variables and then the notion of trust is formalized in terms of action via transitive disclosure graphs; 2. a new trust metrics is formalized by means of mutual information, and we show that our trust metrics enjoys the following nice features: if a subject does not trust an intermediate node in a path, then trust value of the recommendation along the path is not trusted at all; the longer of a recommendation path, the less trust value along the path; and the trust reserves the transitivity; 3. our trust metrics satisfies Yao´s Minmax principle. As a result, the expected running time of the optimal deterministic algorithm for an arbitrary chosen input distribution of auxiliary information is a lower bound on the expected running time of the optimal randomized algorithm for trust metrics. To the best of our knowledge, the ideas using mutual information to quantify trust and using maxmin to calculate trust established through multiple recommendation paths are first proposed in this paper. Since the claimed properties of our metrics cover all axioms of (Sun et al., 2006) and (Sun et al., 2006), it follows that our trust metrics can be viewed as a dynamic metrics of Sun et al´s measurement while the later should be viewed as a static trust metrics where no recommendation is allowed. Finally, the efficiency of our maxmin mechanism for computing of trust may render it to be a highly reliable tool for stimulating cooperative behavior in ad-hoc networks.