Normal Forms in Artin Groups for Cryptographic Purposes

dc.contributor.authorBrien, Renaud
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.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.titleNormal Forms in Artin Groups for Cryptographic Purposes
dc.faculty.departmentMathématiques et statistique / Mathematics and Statistics
dc.contributor.supervisorNevins, Monica
dc.contributor.supervisorSalmasian, Hadi
dc.embargo.termsimmediate / Science / Science
uottawa.departmentMathématiques et statistique / Mathematics and Statistics
CollectionThèses, 2011 - // Theses, 2011 -

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