{"id":"https://openalex.org/W2059382275","doi":"https://doi.org/10.1515/jmc-2013-0017","title":"A new method of choosing primitive elements for Brezing\u2013Weng families of pairing-friendly elliptic curves","display_name":"A new method of choosing primitive elements for Brezing\u2013Weng families of pairing-friendly elliptic curves","publication_year":2014,"publication_date":"2014-10-01","ids":{"openalex":"https://openalex.org/W2059382275","doi":"https://doi.org/10.1515/jmc-2013-0017","mag":"2059382275"},"language":"en","primary_location":{"id":"doi:10.1515/jmc-2013-0017","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2013-0017","pdf_url":null,"source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1515/jmc-2013-0017","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009550950","display_name":"Kisoon Yoon","orcid":"https://orcid.org/0000-0001-8090-6096"},"institutions":[{"id":"https://openalex.org/I110630785","display_name":"NSK (United States)","ror":"https://ror.org/027qba521","country_code":"US","type":"company","lineage":["https://openalex.org/I110630785","https://openalex.org/I4210157453"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Kisoon Yoon","raw_affiliation_strings":["NSHC Inc. 55, Gwangjinmal-gil, Uiwang-si, Gyeonggi-do, 437-060, Republic of Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NSHC Inc. 55, Gwangjinmal-gil, Uiwang-si, Gyeonggi-do, 437-060, Republic of Korea","institution_ids":["https://openalex.org/I110630785"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009550950"],"corresponding_institution_ids":["https://openalex.org/I110630785"],"apc_list":{"value":1000,"currency":"EUR","value_usd":1078},"apc_paid":{"value":1000,"currency":"EUR","value_usd":1078},"fwci":1.1022,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.86414149,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"9","issue":"1","first_page":"1","last_page":"9"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9697999954223633,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pairing","display_name":"Pairing","score":0.6698745489120483},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5250434875488281},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4924674928188324},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.467947393655777},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.45848366618156433},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.44702720642089844},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3816869258880615},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32075566053390503},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17935332655906677},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17883417010307312},{"id":"https://openalex.org/keywords/superconductivity","display_name":"Superconductivity","score":0.15138545632362366},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.13093134760856628},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11172428727149963},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.058870136737823486}],"concepts":[{"id":"https://openalex.org/C14103023","wikidata":"https://www.wikidata.org/wiki/Q11681459","display_name":"Pairing","level":3,"score":0.6698745489120483},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5250434875488281},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4924674928188324},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.467947393655777},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.45848366618156433},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.44702720642089844},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3816869258880615},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32075566053390503},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17935332655906677},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17883417010307312},{"id":"https://openalex.org/C54101563","wikidata":"https://www.wikidata.org/wiki/Q124131","display_name":"Superconductivity","level":2,"score":0.15138545632362366},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13093134760856628},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11172428727149963},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.058870136737823486},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/jmc-2013-0017","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2013-0017","pdf_url":null,"source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:f7c994e3de024f2bac208851e1a0eca4","is_oa":true,"landing_page_url":"https://doaj.org/article/f7c994e3de024f2bac208851e1a0eca4","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Mathematical Cryptology, Vol 9, Iss 1, Pp 1-9 (2015)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/jmc-2013-0017","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2013-0017","pdf_url":null,"source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3015473028","https://openalex.org/W3201176751","https://openalex.org/W2057898405","https://openalex.org/W2029180842","https://openalex.org/W2051379014","https://openalex.org/W2953807518","https://openalex.org/W1993094293","https://openalex.org/W4319323581","https://openalex.org/W2949714594","https://openalex.org/W1904757850"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper":[3],"we":[4,24],"present":[5],"a":[6,68,81,85,97],"new":[7],"method":[8],"of":[9,16,31,64,102,112],"choosing":[10],"primitive":[11,98],"elements":[12,63],"for":[13,47,78,109,119],"Brezing\u2013Weng":[14],"families":[15,32],"pairing-friendly":[17],"elliptic":[18],"curves":[19],"with":[20],"small":[21],"rho-values,":[22],"and":[23,59,84],"improve":[25],"on":[26],"previously":[27],"known":[28],"best":[29],"rho-values":[30],"[J.":[33],"Cryptology":[34],"23":[35],"(2010),":[36],"224\u2013280],":[37],"[Lecture":[38],"Notes":[39],"in":[40],"Comput.":[41],"Sci.":[42],"5209,":[43],"Springer":[44],"(2008),":[45],"126\u2013135]":[46],"the":[48,65,107,113],"embedding":[49],"degrees":[50],"k":[51,75,93,99],"=":[52],"16":[53],"$k=16$":[54],",":[55,82,90],"22,":[56],"28,":[57],"40":[58],"46.":[60],"We":[61,104],"consider":[62],"form":[66,115],"(":[67],"+":[69],"b":[70,83],"-":[71],"D":[72,89],")":[73],"\u03b6":[74,92],"$(a+b\\sqrt{-D})\\zeta":[76],"_k$":[77,95],"rational":[79],"numbers":[80],"square-free":[86],"positive":[87],"integer":[88],"where":[91],"$\\zeta":[94],"is":[96],"-th":[100],"root":[101],"unity.":[103],"also":[105],"investigate":[106],"conditions":[108],"an":[110],"element":[111],"proposed":[114],"to":[116],"be":[117],"suitable":[118],"our":[120],"construction.":[121],"Our":[122],"construction":[123],"uses":[124],"fixed":[125],"discriminants.":[126]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-08-19T15:00:24.278416","created_date":"2025-10-10T00:00:00"}
