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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


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