Degree Type

Dissertation

Date of Award

2006

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Clifford Bergman

Abstract

A quasigroup is a set of elements with one binary operation whose multiplication table forms a Latin square. Because quasigroups are not required to be associative, multiplying a string of elements together in different orders can produce different results. A message authentication code, or a MAC, is a cryptographical tool used to verify the authenticity of a message. In this dissertation, we create a new message authentication code called QMAC whose security is based on this non-associativity. In order to obtain security against forgeries, a highly non-associative quasigroup of large order must be used. Methods for efficiently creating and representing such quasigroups are also discussed.

DOI

https://doi.org/10.31274/rtd-180813-58

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu

Copyright Owner

Kristen Ann Meyer

Language

en

Proquest ID

AAI3218982

File Format

application/pdf

File Size

91 pages

Included in

Mathematics Commons

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