{"id":"https://openalex.org/W1584385726","doi":"https://doi.org/10.1007/978-3-642-20465-4_5","title":"Faster Explicit Formulas for Computing Pairings over Ordinary Curves","display_name":"Faster Explicit Formulas for Computing Pairings over Ordinary Curves","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1584385726","doi":"https://doi.org/10.1007/978-3-642-20465-4_5","mag":"1584385726"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-20465-4_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-20465-4_5","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020557476","display_name":"Diego F. Aranha","orcid":"https://orcid.org/0000-0002-2457-0783"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Diego F. Aranha","raw_affiliation_strings":["University of Campinas, Brazil","University of Campinas;"],"affiliations":[{"raw_affiliation_string":"University of Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]},{"raw_affiliation_string":"University of Campinas;","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087800081","display_name":"Koray Karabina","orcid":"https://orcid.org/0000-0001-9538-8877"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Koray Karabina","raw_affiliation_strings":["Certicom Research, Canada","Certicom Research#TAB#"],"affiliations":[{"raw_affiliation_string":"Certicom Research, Canada","institution_ids":[]},{"raw_affiliation_string":"Certicom Research#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053260383","display_name":"Patrick Longa","orcid":"https://orcid.org/0000-0001-5791-6341"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Patrick Longa","raw_affiliation_strings":["University of Waterloo, Canada","(University of Waterloo)"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"(University of Waterloo)","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035154433","display_name":"Catherine H. Gebotys","orcid":"https://orcid.org/0000-0002-7835-3741"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Catherine H. Gebotys","raw_affiliation_strings":["University of Waterloo, Canada","(University of Waterloo)"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"(University of Waterloo)","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040849996","display_name":"Julio L\u00f3pez","orcid":"https://orcid.org/0000-0001-5139-0158"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Julio L\u00f3pez","raw_affiliation_strings":["University of Campinas, Brazil","University of Campinas;"],"affiliations":[{"raw_affiliation_string":"University of Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]},{"raw_affiliation_string":"University of Campinas;","institution_ids":["https://openalex.org/I181391015"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5020557476"],"corresponding_institution_ids":["https://openalex.org/I181391015"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":63.2417,"has_fulltext":false,"cited_by_count":193,"citation_normalized_percentile":{"value":0.99951937,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"48","last_page":"68"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998999834060669,"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":0.9998999834060669,"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/T10237","display_name":"Cryptography and Data Security","score":0.9850999712944031,"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/T11130","display_name":"Coding theory and cryptography","score":0.982200026512146,"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/exponentiation","display_name":"Exponentiation","score":0.8342645168304443},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.684495747089386},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.626537561416626},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6258906126022339},{"id":"https://openalex.org/keywords/pairing","display_name":"Pairing","score":0.616316556930542},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5165292620658875},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5064271688461304},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4878706932067871},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.44606438279151917},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4379718601703644},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.41940736770629883},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3695948123931885},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34316760301589966},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3426159918308258},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3116663992404938},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.19756615161895752},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.15268313884735107},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1264142394065857}],"concepts":[{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.8342645168304443},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.684495747089386},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.626537561416626},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6258906126022339},{"id":"https://openalex.org/C14103023","wikidata":"https://www.wikidata.org/wiki/Q11681459","display_name":"Pairing","level":3,"score":0.616316556930542},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5165292620658875},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5064271688461304},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4878706932067871},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.44606438279151917},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4379718601703644},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.41940736770629883},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3695948123931885},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34316760301589966},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3426159918308258},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3116663992404938},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.19756615161895752},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.15268313884735107},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1264142394065857},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C54101563","wikidata":"https://www.wikidata.org/wiki/Q124131","display_name":"Superconductivity","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-20465-4_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-20465-4_5","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.8100000023841858}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W104728622","https://openalex.org/W150295176","https://openalex.org/W1501115028","https://openalex.org/W1508193711","https://openalex.org/W1553083934","https://openalex.org/W1553314411","https://openalex.org/W1553871775","https://openalex.org/W1556920856","https://openalex.org/W1584385726","https://openalex.org/W1594784822","https://openalex.org/W1637905077","https://openalex.org/W1846967348","https://openalex.org/W1971605365","https://openalex.org/W1990220158","https://openalex.org/W1998368731","https://openalex.org/W2003736153","https://openalex.org/W2004814164","https://openalex.org/W2021553056","https://openalex.org/W2069900560","https://openalex.org/W2086042811","https://openalex.org/W2097493047","https://openalex.org/W2101181582","https://openalex.org/W2110698954","https://openalex.org/W2114609370","https://openalex.org/W2128593792","https://openalex.org/W2141395382","https://openalex.org/W2152924492","https://openalex.org/W2153726795","https://openalex.org/W2159868780","https://openalex.org/W2162548688","https://openalex.org/W2164960664","https://openalex.org/W2218949749","https://openalex.org/W2296489817","https://openalex.org/W2613018503","https://openalex.org/W3028759481","https://openalex.org/W3031052868","https://openalex.org/W4213382482","https://openalex.org/W4236402571"],"related_works":["https://openalex.org/W192788341","https://openalex.org/W2400487092","https://openalex.org/W2952575986","https://openalex.org/W4319323581","https://openalex.org/W2950832472","https://openalex.org/W1553871775","https://openalex.org/W2401618370","https://openalex.org/W2031177322","https://openalex.org/W4226476440","https://openalex.org/W1577956677"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":14},{"year":2015,"cited_by_count":19},{"year":2014,"cited_by_count":30},{"year":2013,"cited_by_count":26},{"year":2012,"cited_by_count":16}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
