{"id":"https://openalex.org/W2917997992","doi":"https://doi.org/10.3934/amc.2019023","title":"Efficient public-key operation in multivariate schemes","display_name":"Efficient public-key operation in multivariate schemes","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2917997992","doi":"https://doi.org/10.3934/amc.2019023","mag":"2917997992"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2019023","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2019023","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=1a5dc2e2-d954-4609-852b-ada7863e3d56","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/article/exportPdf?id=1a5dc2e2-d954-4609-852b-ada7863e3d56","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026623616","display_name":"Felipe Cabarcas","orcid":"https://orcid.org/0000-0002-8966-0405"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Felipe Cabarcas","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006503080","display_name":"Daniel Cabarcas","orcid":null},"institutions":[{"id":"https://openalex.org/I36243813","display_name":"Universidad Nacional de Colombia","ror":"https://ror.org/059yx9a68","country_code":"CO","type":"education","lineage":["https://openalex.org/I36243813"]},{"id":"https://openalex.org/I4210133585","display_name":"Universidad de Medell\u00edn","ror":"https://ror.org/030kw0b65","country_code":"CO","type":"education","lineage":["https://openalex.org/I4210133585"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"Daniel Cabarcas","raw_affiliation_strings":["Universidad Nacional de Colombia Sede Medell\u00edn, Calle 59 A N 63-20, Medell\u00edn, Colombia"],"affiliations":[{"raw_affiliation_string":"Universidad Nacional de Colombia Sede Medell\u00edn, Calle 59 A N 63-20, Medell\u00edn, Colombia","institution_ids":["https://openalex.org/I36243813","https://openalex.org/I4210133585"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064594134","display_name":"John Baena","orcid":"https://orcid.org/0000-0003-4185-1613"},"institutions":[{"id":"https://openalex.org/I36243813","display_name":"Universidad Nacional de Colombia","ror":"https://ror.org/059yx9a68","country_code":"CO","type":"education","lineage":["https://openalex.org/I36243813"]},{"id":"https://openalex.org/I4210133585","display_name":"Universidad de Medell\u00edn","ror":"https://ror.org/030kw0b65","country_code":"CO","type":"education","lineage":["https://openalex.org/I4210133585"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"John Baena","raw_affiliation_strings":["Universidad Nacional de Colombia Sede Medell\u00edn, Calle 59 A N 63-20, Medell\u00edn, Colombia"],"affiliations":[{"raw_affiliation_string":"Universidad Nacional de Colombia Sede Medell\u00edn, Calle 59 A N 63-20, Medell\u00edn, Colombia","institution_ids":["https://openalex.org/I36243813","https://openalex.org/I4210133585"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5026623616"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1206,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.43635235,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"13","issue":"2","first_page":"343","last_page":"371"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.8452000021934509,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.8452000021934509,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8736926317214966},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.7233715057373047},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.71060711145401},{"id":"https://openalex.org/keywords/multivariate-analysis","display_name":"Multivariate analysis","score":0.44531869888305664},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.30435478687286377},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0640648901462555},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.05655893683433533}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8736926317214966},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.7233715057373047},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.71060711145401},{"id":"https://openalex.org/C38180746","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate analysis","level":2,"score":0.44531869888305664},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.30435478687286377},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0640648901462555},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.05655893683433533}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2019023","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2019023","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=1a5dc2e2-d954-4609-852b-ada7863e3d56","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2019023","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2019023","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=1a5dc2e2-d954-4609-852b-ada7863e3d56","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.5400000214576721,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2917997992.pdf","grobid_xml":"https://content.openalex.org/works/W2917997992.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W29048791","https://openalex.org/W150779690","https://openalex.org/W206356891","https://openalex.org/W1495277689","https://openalex.org/W1525538022","https://openalex.org/W1531850752","https://openalex.org/W1532849667","https://openalex.org/W1536729852","https://openalex.org/W1543112302","https://openalex.org/W1568587963","https://openalex.org/W1569499052","https://openalex.org/W1576359684","https://openalex.org/W1607525463","https://openalex.org/W1618439507","https://openalex.org/W1628272610","https://openalex.org/W1717763854","https://openalex.org/W1821087317","https://openalex.org/W1974527567","https://openalex.org/W1976677460","https://openalex.org/W2006504364","https://openalex.org/W2093643075","https://openalex.org/W2099172492","https://openalex.org/W2218982563","https://openalex.org/W4230183876","https://openalex.org/W4297991408"],"related_works":["https://openalex.org/W2406638334","https://openalex.org/W40745829","https://openalex.org/W1978357124","https://openalex.org/W1578824628","https://openalex.org/W2032728545","https://openalex.org/W1570805059","https://openalex.org/W4250754046","https://openalex.org/W4318262572","https://openalex.org/W2036849593","https://openalex.org/W1978174651"],"abstract_inverted_index":{"The":[0],"public-key":[1],"operation":[2,29,127],"in":[3,15,114],"multivariate":[4],"encryption":[5],"and":[6,47,102],"signature":[7],"schemes":[8],"evaluates":[9],"$":[10,12,16,18],"m":[11],"quadratic":[13],"polynomials":[14],"n":[17],"variables.":[19],"In":[20,65],"this":[21,27],"paper":[22],"we":[23,76],"analyze":[24,78],"how":[25],"fast":[26],"simple":[28],"can":[30],"be":[31],"made.":[32],"We":[33,43,93,105,117],"optimize":[34],"it":[35],"for":[36,72,98],"different":[37,73,99],"finite":[38,100],"fields":[39,101],"on":[40,83],"modern":[41],"architectures.":[42],"provide":[44,68,119],"an":[45],"objective":[46],"inherent":[48],"efficiency":[49,97,124],"measure":[50],"of":[51,62,123,125],"our":[52],"implementations,":[53],"by":[54],"comparing":[55],"their":[56],"performance":[57,61],"with":[58],"the":[59,63,79,84,90,95,107,110,115],"peak":[60],"CPU.":[64],"order":[66],"to":[67],"a":[69,120],"fair":[70],"comparison":[71],"parameter":[74],"sets,":[75],"also":[77],"expected":[80],"security":[81],"based":[82],"algebraic":[85],"attack":[86],"taking":[87],"into":[88],"consideration":[89],"hybrid":[91],"approach.":[92],"compare":[94],"attack's":[96],"establish":[103],"trends.":[104],"detail":[106],"role":[108],"that":[109],"field":[111],"equations":[112],"play":[113],"attack.":[116],"then":[118],"broad":[121],"picture":[122],"MQ-public-key":[126],"against":[128],"security.":[129]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}