{"id":"https://openalex.org/W148359017","doi":"https://doi.org/10.1007/978-3-642-34931-7_22","title":"Efficient Arithmetic on Elliptic Curves in Characteristic 2","display_name":"Efficient Arithmetic on Elliptic Curves in Characteristic 2","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W148359017","doi":"https://doi.org/10.1007/978-3-642-34931-7_22","mag":"148359017"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-34931-7_22","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-34931-7_22","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1601.03669","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067104694","display_name":"David Kohel","orcid":null},"institutions":[{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]},{"id":"https://openalex.org/I4210138206","display_name":"Institut de Math\u00e9matiques de Marseille","ror":"https://ror.org/042h2y225","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210138206","https://openalex.org/I4210141950","https://openalex.org/I4210142724"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"David Kohel","raw_affiliation_strings":["Institut de Math\u00e9matiques de Luminy, Universit\u00e9 d\u2019Aix-Marseille, 163, avenue de Luminy, Case 907, 13288, Marseille Cedex 9, France","Universit\u00e9  d'Aix-Marseille"],"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Luminy, Universit\u00e9 d\u2019Aix-Marseille, 163, avenue de Luminy, Case 907, 13288, Marseille Cedex 9, France","institution_ids":["https://openalex.org/I4210138206","https://openalex.org/I21491767"]},{"raw_affiliation_string":"Universit\u00e9  d'Aix-Marseille","institution_ids":["https://openalex.org/I21491767"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067104694"],"corresponding_institution_ids":["https://openalex.org/I21491767","https://openalex.org/I4210138206"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11259957,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"378","last_page":"398"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998000264167786,"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":0.9998000264167786,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9750000238418579,"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/scalar-multiplication","display_name":"Scalar multiplication","score":0.9229744672775269},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7788941264152527},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.7157254219055176},{"id":"https://openalex.org/keywords/edwards-curve","display_name":"Edwards curve","score":0.663284182548523},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6283113956451416},{"id":"https://openalex.org/keywords/elliptic-curve-point-multiplication","display_name":"Elliptic curve point multiplication","score":0.5883439183235168},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5434972643852234},{"id":"https://openalex.org/keywords/multiplication-algorithm","display_name":"Multiplication algorithm","score":0.5431948304176331},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5355230569839478},{"id":"https://openalex.org/keywords/complex-multiplication","display_name":"Complex multiplication","score":0.5186018943786621},{"id":"https://openalex.org/keywords/hessian-form-of-an-elliptic-curve","display_name":"Hessian form of an elliptic curve","score":0.48488649725914},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.4706760346889496},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.4204787611961365},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36964988708496094},{"id":"https://openalex.org/keywords/schoofs-algorithm","display_name":"Schoof's algorithm","score":0.3529208302497864},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3239237070083618},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3223724365234375},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11699441075325012},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10660526156425476},{"id":"https://openalex.org/keywords/quarter-period","display_name":"Quarter period","score":0.08733421564102173},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.06697893142700195}],"concepts":[{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.9229744672775269},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7788941264152527},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.7157254219055176},{"id":"https://openalex.org/C92727272","wikidata":"https://www.wikidata.org/wiki/Q3001190","display_name":"Edwards curve","level":5,"score":0.663284182548523},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6283113956451416},{"id":"https://openalex.org/C117121985","wikidata":"https://www.wikidata.org/wiki/Q78380999","display_name":"Elliptic curve point multiplication","level":3,"score":0.5883439183235168},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5434972643852234},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.5431948304176331},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5355230569839478},{"id":"https://openalex.org/C80146680","wikidata":"https://www.wikidata.org/wiki/Q2654923","display_name":"Complex multiplication","level":3,"score":0.5186018943786621},{"id":"https://openalex.org/C104993295","wikidata":"https://www.wikidata.org/wiki/Q17023345","display_name":"Hessian form of an elliptic curve","level":5,"score":0.48488649725914},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4706760346889496},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.4204787611961365},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36964988708496094},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.3529208302497864},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3239237070083618},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3223724365234375},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11699441075325012},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10660526156425476},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"score":0.08733421564102173},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.06697893142700195},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/978-3-642-34931-7_22","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-34931-7_22","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"},{"id":"pmh:oai:arXiv.org:1601.03669","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.03669","pdf_url":"https://arxiv.org/pdf/1601.03669","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:148359017","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1601.03669.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-01257333v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01257333","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Progress in Cryptology - INDOCRYPT 2012, Dec 2012, Kolkata, India. pp.378-398, ⟨10.1007/978-3-642-34931-7_22⟩","raw_type":"Conference papers"},{"id":"doi:10.48550/arxiv.1601.03669","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1601.03669","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1601.03669","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.03669","pdf_url":"https://arxiv.org/pdf/1601.03669","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7400000095367432,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1514429798","https://openalex.org/W1539740938","https://openalex.org/W1565369953","https://openalex.org/W1595728311","https://openalex.org/W1971605365","https://openalex.org/W1972442530","https://openalex.org/W2009129512","https://openalex.org/W2021358506","https://openalex.org/W2055403242","https://openalex.org/W2085997550","https://openalex.org/W2095423754","https://openalex.org/W2096133993","https://openalex.org/W2134258244","https://openalex.org/W2154290215","https://openalex.org/W2154777362","https://openalex.org/W2167712295","https://openalex.org/W2951379724"],"related_works":["https://openalex.org/W2963884061","https://openalex.org/W2072580767","https://openalex.org/W1939936032","https://openalex.org/W2765821314","https://openalex.org/W3115797793","https://openalex.org/W1514429798","https://openalex.org/W3051211446","https://openalex.org/W3211891709","https://openalex.org/W2920091699","https://openalex.org/W3146834286","https://openalex.org/W3012212132","https://openalex.org/W2112883752","https://openalex.org/W2053294172","https://openalex.org/W2491141181","https://openalex.org/W2075252632","https://openalex.org/W2806604060","https://openalex.org/W2950815192","https://openalex.org/W1511292221","https://openalex.org/W196348009"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}