{"id":"https://openalex.org/W1606363966","doi":"https://doi.org/10.1007/978-3-540-79456-1_6","title":"On Prime-Order Elliptic Curves with Embedding Degrees k\u2009=\u20093, 4, and 6","display_name":"On Prime-Order Elliptic Curves with Embedding Degrees k\u2009=\u20093, 4, and 6","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1606363966","doi":"https://doi.org/10.1007/978-3-540-79456-1_6","mag":"1606363966"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-79456-1_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-79456-1_6","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/A5087800081","display_name":"Koray Karabina","orcid":"https://orcid.org/0000-0001-9538-8877"},"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":true,"raw_author_name":"Koray Karabina","raw_affiliation_strings":["Dept. of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, 0N2L 3G1","DEPARTMENT OF COMBINATORICS AND OPTIMIZATION; UNIVERSITY OF WATERLOO; WATERLOO ONTARIO CANADA"],"affiliations":[{"raw_affiliation_string":"Dept. of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, 0N2L 3G1","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"DEPARTMENT OF COMBINATORICS AND OPTIMIZATION; UNIVERSITY OF WATERLOO; WATERLOO ONTARIO CANADA","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003024529","display_name":"Edlyn Teske","orcid":null},"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":"Edlyn Teske","raw_affiliation_strings":["Dept. of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, 0N2L 3G1","DEPARTMENT OF COMBINATORICS AND OPTIMIZATION; UNIVERSITY OF WATERLOO; WATERLOO ONTARIO CANADA"],"affiliations":[{"raw_affiliation_string":"Dept. of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, 0N2L 3G1","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"DEPARTMENT OF COMBINATORICS AND OPTIMIZATION; UNIVERSITY OF WATERLOO; WATERLOO ONTARIO CANADA","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087800081"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.9108,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.87715134,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"102","last_page":"117"},"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":0.9781000018119812,"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":0.95660001039505,"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/elliptic-curve","display_name":"Elliptic curve","score":0.7236151099205017},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.6861704587936401},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6833133697509766},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.608393669128418},{"id":"https://openalex.org/keywords/diophantine-equation","display_name":"Diophantine equation","score":0.5274834036827087},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48704198002815247},{"id":"https://openalex.org/keywords/discriminant","display_name":"Discriminant","score":0.48031964898109436},{"id":"https://openalex.org/keywords/schoofs-algorithm","display_name":"Schoof's algorithm","score":0.43315353989601135},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.42316097021102905},{"id":"https://openalex.org/keywords/edwards-curve","display_name":"Edwards curve","score":0.4207385778427124},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3544212877750397},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34527191519737244},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33150047063827515},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2747318148612976},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.08301511406898499},{"id":"https://openalex.org/keywords/quarter-period","display_name":"Quarter period","score":0.07819080352783203},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0739583671092987}],"concepts":[{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.7236151099205017},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6861704587936401},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6833133697509766},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.608393669128418},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.5274834036827087},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48704198002815247},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.48031964898109436},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.43315353989601135},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.42316097021102905},{"id":"https://openalex.org/C92727272","wikidata":"https://www.wikidata.org/wiki/Q3001190","display_name":"Edwards curve","level":5,"score":0.4207385778427124},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3544212877750397},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34527191519737244},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33150047063827515},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2747318148612976},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.08301511406898499},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"score":0.07819080352783203},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0739583671092987},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-79456-1_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-79456-1_6","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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.7699999809265137}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W50404213","https://openalex.org/W1486898453","https://openalex.org/W1508193711","https://openalex.org/W1532836984","https://openalex.org/W1534733761","https://openalex.org/W1544736259","https://openalex.org/W1553083934","https://openalex.org/W1569612250","https://openalex.org/W1572007451","https://openalex.org/W1610688607","https://openalex.org/W1921672120","https://openalex.org/W1970580817","https://openalex.org/W1990160499","https://openalex.org/W1998368731","https://openalex.org/W2001395864","https://openalex.org/W2021553056","https://openalex.org/W2055083041","https://openalex.org/W2060770809","https://openalex.org/W2070030672","https://openalex.org/W2071011219","https://openalex.org/W2073749641","https://openalex.org/W2086042811","https://openalex.org/W2094556471","https://openalex.org/W2097493047","https://openalex.org/W2111310412","https://openalex.org/W2112842125","https://openalex.org/W2159366854","https://openalex.org/W2477011922","https://openalex.org/W2521692633","https://openalex.org/W2602645338","https://openalex.org/W2894888219","https://openalex.org/W3028978996","https://openalex.org/W3028988668","https://openalex.org/W3175367423","https://openalex.org/W4243587538","https://openalex.org/W4248480617","https://openalex.org/W4298159580"],"related_works":["https://openalex.org/W2548082687","https://openalex.org/W3211097549","https://openalex.org/W2336533864","https://openalex.org/W3172172454","https://openalex.org/W4237299327","https://openalex.org/W2090515343","https://openalex.org/W74147110","https://openalex.org/W2121110380","https://openalex.org/W4248011490","https://openalex.org/W2997813048"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
