Normal Forms in Artin Groups for Cryptographic Purposes

FieldValue
dc.contributor.authorBrien, Renaud
dc.date.accessioned2012-08-10T10:15:51Z
dc.date.available2012-08-10T10:15:51Z
dc.date.created2012
dc.date.issued2012
dc.identifier.urihttp://hdl.handle.net/10393/23145
dc.identifier.urihttp://dx.doi.org/10.20381/ruor-5909
dc.description.abstractWith the advent of quantum computers, the security of number-theoretic cryptography has been compromised. Consequently, new cryptosystems have been suggested in the field of non-commutative group theory. In this thesis, we provide all the necessary background to understand and work with the Artin groups. We then show that Artin groups of finite type and Artin groups of large type possess an easily-computable normal form by explicitly writing the algorithms. This solution to the word problem makes these groups candidates to be cryptographic platforms. Finally, we present some combinatorial problems that can be used in group-based cryptography and we conjecture, through empirical evidence, that the conjugacy problem in Artin groups of large type is not a hard problem.
dc.language.isoen
dc.publisherUniversité d'Ottawa / University of Ottawa
dc.subjectGroup Based Cryptography
dc.subjectArtin groups
dc.subjectBraid group
dc.subjectArtin groups of Finite Type
dc.subjectArtin Groups of Large Type
dc.subjectCoxeter systems
dc.subjectNormal Forms
dc.subjectWord Problem
dc.subjectAlgorithms
dc.subjectCryptography
dc.titleNormal Forms in Artin Groups for Cryptographic Purposes
dc.typeThesis
dc.faculty.departmentMathématiques et statistique / Mathematics and Statistics
dc.contributor.supervisorNevins, Monica
dc.contributor.supervisorSalmasian, Hadi
dc.embargo.termsimmediate
dc.degree.nameMSc
dc.degree.levelmasters
dc.degree.disciplineSciences / Science
thesis.degree.nameMSc
thesis.degree.levelMasters
thesis.degree.disciplineSciences / Science
uottawa.departmentMathématiques et statistique / Mathematics and Statistics
CollectionThèses, 2011 - // Theses, 2011 -

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