{"id":"https://openalex.org/W2117506096","doi":"https://doi.org/10.1137/0221071","title":"Optimal Algorithms for Multiplication in Certain Finite Fields Using Elliptic Curves","display_name":"Optimal Algorithms for Multiplication in Certain Finite Fields Using Elliptic Curves","publication_year":1992,"publication_date":"1992-12-01","ids":{"openalex":"https://openalex.org/W2117506096","doi":"https://doi.org/10.1137/0221071","mag":"2117506096"},"language":"en","primary_location":{"id":"doi:10.1137/0221071","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0221071","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/99696","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017248993","display_name":"Mohammad Amin Shokrollahi","orcid":"https://orcid.org/0000-0002-7177-1000"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mohammad Amin Shokrollahi","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5017248993"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.555,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.75691674,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"21","issue":"6","first_page":"1193","last_page":"1198"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9997000098228455,"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/T10849","display_name":"Finite Group Theory Research","score":0.9904000163078308,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/finite-field","display_name":"Finite field","score":0.7103312611579895},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.671582043170929},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6622093915939331},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.5224782228469849},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.47699645161628723},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4667062759399414},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.43008914589881897},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42670369148254395},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09698930382728577},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07825347781181335}],"concepts":[{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.7103312611579895},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.671582043170929},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6622093915939331},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5224782228469849},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.47699645161628723},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4667062759399414},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.43008914589881897},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42670369148254395},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09698930382728577},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07825347781181335},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/0221071","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0221071","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:99696","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/99696","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:99696","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/99696","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1486898453","https://openalex.org/W1545876477","https://openalex.org/W1966394702","https://openalex.org/W2023832849","https://openalex.org/W2035284794","https://openalex.org/W2038162974","https://openalex.org/W2108375536","https://openalex.org/W2152069626","https://openalex.org/W4231186598"],"related_works":["https://openalex.org/W3102623159","https://openalex.org/W2893614166","https://openalex.org/W2366911843","https://openalex.org/W2052299349","https://openalex.org/W2003769335","https://openalex.org/W2350577681","https://openalex.org/W2322239237","https://openalex.org/W1955455432","https://openalex.org/W4299961354","https://openalex.org/W4287980070"],"abstract_inverted_index":{"Using":[0],"the":[1,38,46,71],"results":[2],"given":[3],"in":[4],"[D,.":[5],"V.":[6],"Chudnovsky":[7],"and":[8,21,91],"G.":[9],"V":[10],"Chudnovsky,":[11],"Proc.":[12],"Nat.":[13],"Acad.":[14],"Sci.":[15,26],"USA,":[16],"84":[17],"(1987),":[18],"pp.":[19,32],"1739-1743]":[20],"[W.":[22],"C.":[23],"Waterhouse,":[24],"Ann.":[25],"\u00c9cole":[27],"Norm.":[28],"Sup.,":[29],"4":[30],"(1969),":[31],"521\u2013560],":[33],"it":[34],"is":[35,57,70,80,86,100],"proven":[36],"that":[37],"rank":[39],"(=":[40],"bilinear":[41],"complexity":[42],"of":[43,45],"multiplication)":[44],"finite":[47],"field":[48],"$\\mathbb{F}_{q^n":[49],"}":[50],"$":[51,74,78,97],"viewed":[52],"as":[53],"an":[54],"$\\mathbb{F}_q":[55],"$-algebra":[56],"$2n$":[58],"if":[59,84,98],"n":[60,63],"satisfies":[61],"$\\frac{1}{2}q+1<":[62],"<\\frac{1}{2}(q+1+":[64],"\\epsilon":[65],"(q))$.":[66],"Here":[67],"$\\epsilon":[68,92],"(q)$":[69],"greatest":[72],"integer":[73],"\\leq":[75],"2\\sqrt":[76,95],"q":[77,83,85,96,99],"which":[79],"prime":[81],"to":[82],"not":[87],"a":[88,101],"perfect":[89,102],"square":[90],"(q)":[93],"=":[94],"square.":[103]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-21T08:13:44.787528","created_date":"2025-10-10T00:00:00"}