Files in this item
Files | Description | Format |
---|---|---|
application/pdf ![]() ![]() | (no description provided) |
Description
Title: | Applications of Algebraic Curves to Cryptography |
Author(s): | Park, Seung Kook |
Doctoral Committee Chair(s): | Duursma, Iwan M. |
Department / Program: | Mathematics |
Discipline: | Mathematics |
Degree Granting Institution: | University of Illinois at Urbana-Champaign |
Degree: | Ph.D. |
Genre: | Dissertation |
Subject(s): | Mathematics |
Abstract: | Secondly, 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. |
Issue Date: | 2007 |
Type: | Text |
Language: | English |
Description: | 107 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007. |
URI: | http://hdl.handle.net/2142/86890 |
Other Identifier(s): | (MiAaPQ)AAI3290346 |
Date Available in IDEALS: | 2015-09-28 |
Date Deposited: | 2007 |
This item appears in the following Collection(s)
-
Dissertations and Theses - Mathematics
-
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois