{"id":"https://openalex.org/W42212624","doi":"https://doi.org/10.1007/978-3-319-11659-4_3","title":"A Polynomial-Time Algorithm for Solving a Class of Underdetermined Multivariate Quadratic Equations over Fields of Odd Characteristics","display_name":"A Polynomial-Time Algorithm for Solving a Class of Underdetermined Multivariate Quadratic Equations over Fields of Odd Characteristics","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W42212624","doi":"https://doi.org/10.1007/978-3-319-11659-4_3","mag":"42212624"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-319-11659-4_3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-11659-4_3","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/A5100509533","display_name":"Chen-Mou Cheng","orcid":null},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Chen-Mou Cheng","raw_affiliation_strings":["Kyushu University, Fukuoka-shi, 819-0395, Japan"],"affiliations":[{"raw_affiliation_string":"Kyushu University, Fukuoka-shi, 819-0395, Japan","institution_ids":["https://openalex.org/I135598925"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040861342","display_name":"Yasufumi Hashimoto","orcid":"https://orcid.org/0000-0001-6011-1683"},"institutions":[{"id":"https://openalex.org/I32915989","display_name":"University of the Ryukyus","ror":"https://ror.org/02z1n9q24","country_code":"JP","type":"education","lineage":["https://openalex.org/I32915989"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yasufumi Hashimoto","raw_affiliation_strings":["University of the Ryukyus, Okinawa-ken, 903-0213, Japan"],"affiliations":[{"raw_affiliation_string":"University of the Ryukyus, Okinawa-ken, 903-0213, Japan","institution_ids":["https://openalex.org/I32915989"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067616418","display_name":"Hiroyuki Miura","orcid":"https://orcid.org/0000-0002-0789-564X"},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroyuki Miura","raw_affiliation_strings":["Kyushu University, Fukuoka-shi, 819-0395, Japan"],"affiliations":[{"raw_affiliation_string":"Kyushu University, Fukuoka-shi, 819-0395, Japan","institution_ids":["https://openalex.org/I135598925"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000004915","display_name":"Tsuyoshi Takagi","orcid":null},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tsuyoshi Takagi","raw_affiliation_strings":["Kyushu University, Fukuoka-shi, 819-0395, Japan"],"affiliations":[{"raw_affiliation_string":"Kyushu University, Fukuoka-shi, 819-0395, Japan","institution_ids":["https://openalex.org/I135598925"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100509533"],"corresponding_institution_ids":["https://openalex.org/I135598925"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":2.0021,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.85143545,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"40","last_page":"58"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.998199999332428,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.984000027179718,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/underdetermined-system","display_name":"Underdetermined system","score":0.9765349626541138},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6762946844100952},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5732377171516418},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5273460149765015},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5119910836219788},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5051911473274231},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46802836656570435},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.46762996912002563},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4532313644886017},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4433855414390564},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4217604398727417},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4140357971191406},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12828966975212097},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09029838442802429},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0855647623538971}],"concepts":[{"id":"https://openalex.org/C179690561","wikidata":"https://www.wikidata.org/wiki/Q4316110","display_name":"Underdetermined system","level":2,"score":0.9765349626541138},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6762946844100952},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5732377171516418},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5273460149765015},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5119910836219788},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5051911473274231},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46802836656570435},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.46762996912002563},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4532313644886017},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4433855414390564},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4217604398727417},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4140357971191406},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12828966975212097},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09029838442802429},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0855647623538971},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-319-11659-4_3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-11659-4_3","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","score":0.41999998688697815,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W46786753","https://openalex.org/W68643468","https://openalex.org/W70370491","https://openalex.org/W122159218","https://openalex.org/W206356891","https://openalex.org/W1513904472","https://openalex.org/W1527450129","https://openalex.org/W1536729852","https://openalex.org/W1568587963","https://openalex.org/W1583871653","https://openalex.org/W1618496890","https://openalex.org/W1628272610","https://openalex.org/W1717763854","https://openalex.org/W1821087317","https://openalex.org/W1976677460","https://openalex.org/W2011039300","https://openalex.org/W2038345254","https://openalex.org/W2099172492","https://openalex.org/W2100408583","https://openalex.org/W2123147311","https://openalex.org/W2127064687","https://openalex.org/W2128687423","https://openalex.org/W2128968394","https://openalex.org/W2150548144","https://openalex.org/W2477827689","https://openalex.org/W2480001466","https://openalex.org/W2483988241","https://openalex.org/W2484860292","https://openalex.org/W2485210947","https://openalex.org/W2494421621","https://openalex.org/W2495595500","https://openalex.org/W2495889793","https://openalex.org/W2499339068","https://openalex.org/W2503514047","https://openalex.org/W2770583616","https://openalex.org/W2982614133","https://openalex.org/W3035112273"],"related_works":["https://openalex.org/W133751542","https://openalex.org/W2066796569","https://openalex.org/W2997320962","https://openalex.org/W4287906532","https://openalex.org/W3011121006","https://openalex.org/W176802781","https://openalex.org/W2084978503","https://openalex.org/W3213509687","https://openalex.org/W2914855010","https://openalex.org/W1774334694"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-28T23:10:37.245301","created_date":"2025-10-10T00:00:00"}
