{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86890"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86890","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Applications of Algebraic Curves to Cryptography","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Park, Seung Kook"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Duursma, Iwan M."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:20:02Z","date_published":"2015-09-28T15:20:02Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3290346"],"render_values":[{"text":"(MiAaPQ)AAI3290346","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86890","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Duursma, Iwan M."]},{"key":"dc:creator","label":"Author","values":["Park, Seung Kook"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:20:02Z","10000-01-01","2007"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86890","(MiAaPQ)AAI3290346"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Made available in DSpace on 2015-09-28T15:20:02Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3290346.pdf: 2389171 bytes, checksum: 4223a4f8e73bfea7d929ffe7add860d2 (MD5) Previous issue date: 2007","Embargo set by: Seth Robbins for item 88171 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","107 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007."]},{"key":"dc:title","label":"Title","values":["Applications of Algebraic Curves to Cryptography"]}]}],"canonical_facts":{"dc:contributor":["Duursma, Iwan M."],"dc:creator":["Park, Seung Kook"],"dc:date":["2015-09-28T15:20:02Z","10000-01-01","2007"],"dc:description":["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.","Made available in DSpace on 2015-09-28T15:20:02Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3290346.pdf: 2389171 bytes, checksum: 4223a4f8e73bfea7d929ffe7add860d2 (MD5) Previous issue date: 2007","Embargo set by: Seth Robbins for item 88171 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","107 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007."],"dc:identifier":["http://hdl.handle.net/2142/86890","(MiAaPQ)AAI3290346"],"dc:language":["eng"],"dc:subject":["Mathematics"],"dc:title":["Applications of Algebraic Curves to Cryptography"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:28Z"}