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Full-Text Articles in Mathematics
An Analysis Of A Linear Algebra Based Group Key Exchange Protocol, Annie Zhang
An Analysis Of A Linear Algebra Based Group Key Exchange Protocol, Annie Zhang
Graduate College Dissertations and Theses
Group key exchange protocols are used to establish session keys, which can then be used as encryption keys to set up secure channels of communication, between more than two parties simultaneously. Many different group key exchange protocols exist and require security proofs in order to determine the strength of the protocol and answer the following questions: does the protocol provide authentication, and if so, to what degree? Does the protocol provide key secrecy? In this thesis we examine a particular group key exchange protocol that we call the \textit{vector space projection protocol} as first described in “A Group Key Establishment …
Applications Of Centrality Measures And Extremal Combinatorics, Hunter Dane Rehm
Applications Of Centrality Measures And Extremal Combinatorics, Hunter Dane Rehm
Graduate College Dissertations and Theses
Centrality measures assign numbers or rankings to network nodes that reflect their importance. There are many types of centrality measures, each suitable for different types of networks and applications. In Chapter 2, we consider a model of astronaut health during a space mission. Katz centrality is commonly used to measure the influence of nodes in social and biological networks. We motivate its use in this application to estimate the expected quality time lost due to the progression of medical conditions. In Chapter 3, we find dominating sets in satellite networks. To do this, we use the Shapley value, a centrality …
Data-Driven Reachability Of Non-Linear Systems Via Optimization Of Chen-Fliess Series, Ivan Perez Avellaneda
Data-Driven Reachability Of Non-Linear Systems Via Optimization Of Chen-Fliess Series, Ivan Perez Avellaneda
Graduate College Dissertations and Theses
A reachable set is the set of all possible states produced by applying a set of inputs, initial states, and parameters. The fundamental problem of reachability is checking if a set of states is reached provided a set of inputs, initial states, and parameters, typically, in a finite time. In the engineering field, reachability analysis is used to test the guarantees of the operation’s safety of a system. In the present work, the reachability analysis of nonlinear control affine systems is studied by means of the Chen-Fliess series. Different perspectives for addressing the reachability problem, such as interval arithmetic, mixed-monotonicity, …