A Complete Evaluation of Arithmetic in Real Hyperelliptic Curves

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atmire.migration.oldid4893
dc.contributor.advisorScheidler, Renate
dc.contributor.advisorJacobson, Michael John Jr.
dc.contributor.authorRezai Rad, Monireh
dc.contributor.committeememberBauer, Mark
dc.contributor.committeememberDimitrov, Vassil Simeonov
dc.contributor.committeememberEberly, Wayne Michael
dc.contributor.committeememberTheriault, Nicolas
dc.date.accessioned2016-09-13T18:07:17Z
dc.date.available2016-09-13T18:07:17Z
dc.date.issued2016
dc.date.submitted2016en
dc.description.abstractReal hyperelliptic curves admit two structures: the Jacobian and the infrastructure. While both structures in real models could be employed for cryptographic purposes, it was not clear which one has better performance in practice. Mireles Morales [46] described the relationship between these two structures, and made the assertion that when implemented with balanced divisor arithmetic, the Jacobian generically yields more efficient arithmetic than the infrastructure for cryptographic applications. However, he did not support his claim via a mathematical proof or an implementation. In this thesis, we describe that exactly how the infrastructure and the Jacobian are related through an accurate and detailed mathematical and computational analysis. We suggest an alternative distance map for the infrastructure in order to improve the efficiency of this structure. Our mathematical investigation shows that the infrastructure with the new distance and the Jacobian have identical performance in practice for cryptographic sized curves. We prove this results mathematically and verify their correctness computationally.en_US
dc.identifier.citationRezai Rad, M. (2016). A Complete Evaluation of Arithmetic in Real Hyperelliptic Curves (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/24673en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/24673
dc.identifier.urihttp://hdl.handle.net/11023/3293
dc.language.isoeng
dc.publisher.facultyGraduate Studies
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subjectEducation--Mathematics
dc.subject.classificationReal Hyperelliptic Curveen_US
dc.subject.classificationJacobianen_US
dc.subject.classificationInfrastructureen_US
dc.subject.classificationScalar Multiplicationen_US
dc.subject.classificationExplicit Formulaeen_US
dc.titleA Complete Evaluation of Arithmetic in Real Hyperelliptic Curves
dc.typedoctoral thesis
thesis.degree.disciplineMathematics and Statistics
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameDoctor of Philosophy (PhD)
ucalgary.item.requestcopytrue
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