UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.

More information is available at Theses and Dissertations at University of Maryland Libraries.

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Author: search.filters.author.Draper, Thomas GordonSubject: search.filters.subject.Nonlinear

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    Nonlinear Complexity of Boolean Permutations
    (2009) Draper, Thomas Gordon; Washington, Lawrence C; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    We introduce the concept of nonlinear complexity, where the complexity of a function is determined by the number of nonlinear building blocks required for construction. We group functions by linear equivalence, and induce a complexity hierarchy for the affine equivalent double cosets. We prove multiple invariants of double cosets over the affine general linear group, and develop a specialized double coset equivalence test. This is used to classify the 16! permutations over 4 bits into 302 equivalence classes, which have a maximal nonlinear depth of 6. In addition, we present a new complexity class defined in terms of nonlinearity.