Back to results
University of Illinois at Urbana-Champaign
Function Field Arithmetic and Related Algorithms
Abstract
dc:descriptionThe second part of the thesis is focussed on developing an explicit arithmetic for the Jacobian of certain cubic superelliptic curves. We restrict our attention to curves of the form y3 = f( x). Assuming that f(x) is monic with no repeated roots and that our field does not have characteristic 3, we are able to show that the Jacobian of this curve is isomorphic to the ideal class group of K[C], the ring of regular functions on C. By exploiting the structure of ideals in K[C] as K[x] modules, we are able to produce a very efficient algorithm for performing group operations in the Jacobian which heuristically should take 46g 2 operations in the finite field K.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Bauer, Mark L.
- Contributors dc:contributor
-
- Boston, Nigel
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI3023016
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/86784