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University of Illinois at Urbana-Champaign
Applications of Algebraic Curves to Cryptography
Abstract
dc:descriptionSecondly, we use algebraic functions with two poles to obtain efficient secret sharing schemes. We present a method to find the lower bounds for the minimum distance of geometric codes. We apply this to the two-point codes on a Hermitian function field. The lower bounds turn out to be sharp and they meet the formulas by Homma and Kim for the actual minimum distance of the Hermitian two-point codes with a shorter proof and fewer cases for the formulas. Moreover, our approach gives an efficient error correcting algorithm to decode up to half the actual minimum distance.
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
-
- Park, Seung Kook
- Contributors dc:contributor
-
- Duursma, Iwan M.
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI3290346
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/86890