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https://hdl.handle.net/2142/86890
Description
Title
Applications of Algebraic Curves to Cryptography
Author(s)
Park, Seung Kook
Issue Date
2007
Doctoral Committee Chair(s)
Duursma, Iwan M.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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.
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