{"id":"https://openalex.org/W2103861171","doi":"https://doi.org/10.1109/isit.2009.5206002","title":"Elliptic curves with a pre-determined embedding degree","display_name":"Elliptic curves with a pre-determined embedding degree","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2103861171","doi":"https://doi.org/10.1109/isit.2009.5206002","mag":"2103861171"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2009.5206002","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2009.5206002","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://dspace.jaist.ac.jp/dspace/bitstream/10119/9095/1/13747-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076971671","display_name":"Shoujirou Hirasawa","orcid":null},"institutions":[{"id":"https://openalex.org/I177738480","display_name":"Japan Advanced Institute of Science and Technology","ror":"https://ror.org/03frj4r98","country_code":"JP","type":"education","lineage":["https://openalex.org/I177738480"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Shoujirou Hirasawa","raw_affiliation_strings":["Science and Technology, Japan Advanced Institute of Science and Technology, Ishikawa, Japan","Japan Advanced Institute of Science and Technology, 1-1, Asahidai, Nomi, Ishikawa, 923-1292 Japan"],"affiliations":[{"raw_affiliation_string":"Science and Technology, Japan Advanced Institute of Science and Technology, Ishikawa, Japan","institution_ids":["https://openalex.org/I177738480"]},{"raw_affiliation_string":"Japan Advanced Institute of Science and Technology, 1-1, Asahidai, Nomi, Ishikawa, 923-1292 Japan","institution_ids":["https://openalex.org/I177738480"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010929606","display_name":"Atsuko Miyaji","orcid":"https://orcid.org/0000-0001-8822-5287"},"institutions":[{"id":"https://openalex.org/I177738480","display_name":"Japan Advanced Institute of Science and Technology","ror":"https://ror.org/03frj4r98","country_code":"JP","type":"education","lineage":["https://openalex.org/I177738480"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Atsuko Miyaji","raw_affiliation_strings":["Science and Technology, Japan Advanced Institute of Science and Technology, Ishikawa, Japan","Japan Advanced Institute of Science and Technology, 1-1, Asahidai, Nomi, Ishikawa, 923-1292 Japan"],"affiliations":[{"raw_affiliation_string":"Science and Technology, Japan Advanced Institute of Science and Technology, Ishikawa, Japan","institution_ids":["https://openalex.org/I177738480"]},{"raw_affiliation_string":"Japan Advanced Institute of Science and Technology, 1-1, Asahidai, Nomi, Ishikawa, 923-1292 Japan","institution_ids":["https://openalex.org/I177738480"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5076971671"],"corresponding_institution_ids":["https://openalex.org/I177738480"],"apc_list":null,"apc_paid":null,"fwci":0.7747,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.83615674,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"3897","issue":"284","first_page":"2391","last_page":"2395"},"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/T10237","display_name":"Cryptography and Data Security","score":0.9986000061035156,"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":0.9901999831199646,"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/discrete-logarithm","display_name":"Discrete logarithm","score":0.7024583220481873},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6169414520263672},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5693563222885132},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.5660122036933899},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4714841842651367},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4021313786506653},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3516486883163452},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32523858547210693},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28730344772338867},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.22778069972991943},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16439548134803772},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16402891278266907},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.15679675340652466}],"concepts":[{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.7024583220481873},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6169414520263672},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5693563222885132},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.5660122036933899},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4714841842651367},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4021313786506653},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3516486883163452},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32523858547210693},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28730344772338867},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.22778069972991943},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16439548134803772},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16402891278266907},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.15679675340652466},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/isit.2009.5206002","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2009.5206002","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"},{"id":"pmh:oai:irdb.nii.ac.jp:01333:0002022634","is_oa":true,"landing_page_url":"http://hdl.handle.net/10119/9095","pdf_url":"https://dspace.jaist.ac.jp/dspace/bitstream/10119/9095/1/13747-1.pdf","source":{"id":"https://openalex.org/S7407056385","display_name":"Institutional Repositories DataBase (IRDB)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184597095","host_organization_name":"National Institute of Informatics","host_organization_lineage":["https://openalex.org/I184597095"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE International Symposium on Information Theory, 2009. ISIT 2009.","raw_type":"conference paper"},{"id":"mag:2592076015","is_oa":false,"landing_page_url":"https://www.ieice.org/ken/paper/20090310ga9j/eng/","pdf_url":null,"source":{"id":"https://openalex.org/S4306512848","display_name":"IEICE Technical Report; IEICE Tech. Rep.","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"IEICE Technical Report; IEICE Tech. Rep.","raw_type":null}],"best_oa_location":{"id":"pmh:oai:irdb.nii.ac.jp:01333:0002022634","is_oa":true,"landing_page_url":"http://hdl.handle.net/10119/9095","pdf_url":"https://dspace.jaist.ac.jp/dspace/bitstream/10119/9095/1/13747-1.pdf","source":{"id":"https://openalex.org/S7407056385","display_name":"Institutional Repositories DataBase (IRDB)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184597095","host_organization_name":"National Institute of Informatics","host_organization_lineage":["https://openalex.org/I184597095"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE International Symposium on Information Theory, 2009. ISIT 2009.","raw_type":"conference paper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2103861171.pdf","grobid_xml":"https://content.openalex.org/works/W2103861171.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1483451858","https://openalex.org/W1545876477","https://openalex.org/W1553083934","https://openalex.org/W1904757850","https://openalex.org/W1921672120","https://openalex.org/W2028358228","https://openalex.org/W2034710402","https://openalex.org/W2071680489","https://openalex.org/W2086042811","https://openalex.org/W2111310412","https://openalex.org/W6633001808","https://openalex.org/W6639979892"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W27999159","https://openalex.org/W1577834786","https://openalex.org/W2219990189","https://openalex.org/W2794946234","https://openalex.org/W1904757850","https://openalex.org/W2915223967","https://openalex.org/W2149528579","https://openalex.org/W4253628591","https://openalex.org/W1499161345"],"abstract_inverted_index":{"A":[0],"pairing":[1,38],"over":[2,71,81,140],"an":[3,12,50,104],"elliptic":[4,57,88,126,138],"curve":[5,58,89],"E(F":[6,72],"<sub":[7,17,73,83,146],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[8,18,74,84,147],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">pm</sub>":[9,75,148],")":[10,76],"to":[11,22,79],"extension":[13],"field":[14],"of":[15,52,122,125,136],"F":[16,82,145],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">pmk</sub>":[19,85],"has":[20,107],"begun":[21],"be":[23],"attractive":[24],"in":[25,111],"cryptosystems,":[26],"where":[27,69],"k":[28,47],"is":[29,48,77,90],"called":[30,40],"the":[31,41,53,56,64,97,123,137],"embedding":[32,45,105,130],"degree.":[33],"The":[34,44],"cryptosystems":[35],"using":[36],"a":[37,119],"are":[39],"pairing-based":[42],"cryptosystems.":[43],"degree":[46,106],"also":[49],"indicator":[51],"relationship":[54],"between":[55,100],"discrete":[59,65],"logarithm":[60,66],"problem":[61,67],"(ECDLP)":[62],"and":[63,103,132,143],"(DLP),":[68],"ECDLP":[70],"reduced":[78],"DLP":[80],".":[86,149],"An":[87],"determined":[91],"by":[92],"j-invarient":[93],"or":[94],"order,":[95],"however":[96],"explicit":[98],"condition":[99,121],"these":[101],"parameters":[102],"been":[108],"described":[109],"only":[110],"some":[112,134],"degrees.":[113],"In":[114],"this":[115],"paper,":[116],"we":[117],"investigate":[118],"new":[120],"existence":[124],"curves":[127,139],"with":[128],"pre-determined":[129],"degrees,":[131],"present":[133],"examples":[135],"160-bit,":[141],"192-bit":[142],"224-bit":[144]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}