{"id":"https://openalex.org/W1520994478","doi":"https://doi.org/10.1007/3-540-46416-6_28","title":"Building Cyclic Elliptic Curves Modulo Large Primes","display_name":"Building Cyclic Elliptic Curves Modulo Large Primes","publication_year":2007,"publication_date":"2007-08-06","ids":{"openalex":"https://openalex.org/W1520994478","doi":"https://doi.org/10.1007/3-540-46416-6_28","mag":"1520994478"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-46416-6_28","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-46416-6_28","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-46416-6_28.pdf","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":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-46416-6_28.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050945933","display_name":"Fran\u00e7ois Morain","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Fran\u00e7ois Morain","raw_affiliation_strings":["INRIA, B. P. 105, 78153, Le Chesnay Cedex, France"],"affiliations":[{"raw_affiliation_string":"INRIA, B. P. 105, 78153, Le Chesnay Cedex, France","institution_ids":["https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050945933"],"corresponding_institution_ids":["https://openalex.org/I1326498283"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":6.6884,"has_fulltext":true,"cited_by_count":63,"citation_normalized_percentile":{"value":0.97333589,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"328","last_page":"336"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9969000220298767,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/primality-test","display_name":"Primality test","score":0.9076862335205078},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7267050743103027},{"id":"https://openalex.org/keywords/schoofs-algorithm","display_name":"Schoof's algorithm","score":0.6633940935134888},{"id":"https://openalex.org/keywords/counting-points-on-elliptic-curves","display_name":"Counting points on elliptic curves","score":0.6628881096839905},{"id":"https://openalex.org/keywords/discrete-logarithm","display_name":"Discrete logarithm","score":0.6491730213165283},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.6398597955703735},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.6164166331291199},{"id":"https://openalex.org/keywords/edwards-curve","display_name":"Edwards curve","score":0.5298454761505127},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.4969682991504669},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4959205090999603},{"id":"https://openalex.org/keywords/supersingular-elliptic-curve","display_name":"Supersingular elliptic curve","score":0.4592023491859436},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.44177696108818054},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4229177236557007},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34650588035583496},{"id":"https://openalex.org/keywords/prime-number","display_name":"Prime number","score":0.33571571111679077},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20378908514976501},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15148016810417175},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.08816248178482056}],"concepts":[{"id":"https://openalex.org/C191421660","wikidata":"https://www.wikidata.org/wiki/Q829546","display_name":"Primality test","level":3,"score":0.9076862335205078},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7267050743103027},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.6633940935134888},{"id":"https://openalex.org/C68782407","wikidata":"https://www.wikidata.org/wiki/Q5177153","display_name":"Counting points on elliptic curves","level":5,"score":0.6628881096839905},{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.6491730213165283},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6398597955703735},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.6164166331291199},{"id":"https://openalex.org/C92727272","wikidata":"https://www.wikidata.org/wiki/Q3001190","display_name":"Edwards curve","level":5,"score":0.5298454761505127},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.4969682991504669},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4959205090999603},{"id":"https://openalex.org/C157567686","wikidata":"https://www.wikidata.org/wiki/Q7644139","display_name":"Supersingular elliptic curve","level":3,"score":0.4592023491859436},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.44177696108818054},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4229177236557007},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34650588035583496},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.33571571111679077},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20378908514976501},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15148016810417175},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.08816248178482056},{"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/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/3-540-46416-6_28","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-46416-6_28","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-46416-6_28.pdf","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:CiteSeerX.psu:10.1.1.25.9036","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.9036","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://khan.postech.ac.kr/crypto/ecc/eurocrypt91.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/3-540-46416-6_28","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-46416-6_28","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-46416-6_28.pdf","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1520994478.pdf","grobid_xml":"https://content.openalex.org/works/W1520994478.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W134647183","https://openalex.org/W1486898453","https://openalex.org/W1529949246","https://openalex.org/W1835682632","https://openalex.org/W1970580817","https://openalex.org/W1983287134","https://openalex.org/W1984377013","https://openalex.org/W1996360405","https://openalex.org/W2003736153","https://openalex.org/W2005317356","https://openalex.org/W2009129512","https://openalex.org/W2012276725","https://openalex.org/W2027028382","https://openalex.org/W2028358228","https://openalex.org/W2036378739","https://openalex.org/W2072307680","https://openalex.org/W2075252632","https://openalex.org/W2081882878","https://openalex.org/W2156186849","https://openalex.org/W2203317094","https://openalex.org/W2322172566","https://openalex.org/W4232836212","https://openalex.org/W4242424230","https://openalex.org/W4245047333"],"related_works":["https://openalex.org/W2548082687","https://openalex.org/W3138493780","https://openalex.org/W2374597101","https://openalex.org/W3172172454","https://openalex.org/W2559355736","https://openalex.org/W74147110","https://openalex.org/W1520994478","https://openalex.org/W2334728557","https://openalex.org/W4388284288","https://openalex.org/W2348491713"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
