{"id":"https://openalex.org/W1568587963","doi":"https://doi.org/10.1007/3-540-45961-8_39","title":"Public Quadratic Polynomial-Tuples for Efficient Signature-Verification and Message-Encryption","display_name":"Public Quadratic Polynomial-Tuples for Efficient Signature-Verification and Message-Encryption","publication_year":1988,"publication_date":"1988-01-01","ids":{"openalex":"https://openalex.org/W1568587963","doi":"https://doi.org/10.1007/3-540-45961-8_39","mag":"1568587963"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-45961-8_39","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45961-8_39","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/A5057843702","display_name":"Tsutomu Matsumoto","orcid":"https://orcid.org/0000-0002-7965-4888"},"institutions":[{"id":"https://openalex.org/I180203408","display_name":"Yokohama National University","ror":"https://ror.org/03zyp6p76","country_code":"JP","type":"education","lineage":["https://openalex.org/I180203408"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tsutomu Matsumoto","raw_affiliation_strings":["Division of Electrical and Computer Engineering, Yokohama National University, Hodogaya, Yokohama, Japan","Yokohama National University,Yokohama,Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Electrical and Computer Engineering, Yokohama National University, Hodogaya, Yokohama, Japan","institution_ids":["https://openalex.org/I180203408"]},{"raw_affiliation_string":"Yokohama National University,Yokohama,Japan","institution_ids":["https://openalex.org/I180203408"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110246798","display_name":"H. Imai","orcid":null},"institutions":[{"id":"https://openalex.org/I180203408","display_name":"Yokohama National University","ror":"https://ror.org/03zyp6p76","country_code":"JP","type":"education","lineage":["https://openalex.org/I180203408"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hideki Imai","raw_affiliation_strings":["Division of Electrical and Computer Engineering, Yokohama National University, Hodogaya, Yokohama, Japan","Yokohama National University,Yokohama,Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Electrical and Computer Engineering, Yokohama National University, Hodogaya, Yokohama, Japan","institution_ids":["https://openalex.org/I180203408"]},{"raw_affiliation_string":"Yokohama National University,Yokohama,Japan","institution_ids":["https://openalex.org/I180203408"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":498,"citation_normalized_percentile":{"value":0.19808307,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"419","last_page":"453"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","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/T10237","display_name":"Cryptography and Data Security","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/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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9998000264167786,"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/computer-science","display_name":"Computer science","score":0.7045340538024902},{"id":"https://openalex.org/keywords/cryptosystem","display_name":"Cryptosystem","score":0.6830779314041138},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.6189298033714294},{"id":"https://openalex.org/keywords/tuple","display_name":"Tuple","score":0.5859230160713196},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.5504733324050903},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5135093331336975},{"id":"https://openalex.org/keywords/signature","display_name":"Signature (topology)","score":0.511382520198822},{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.5096306800842285},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.5083739161491394},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.501978874206543},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.46759316325187683},{"id":"https://openalex.org/keywords/random-oracle","display_name":"Random oracle","score":0.4642980694770813},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4632706642150879},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.45129841566085815},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.413593053817749},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37931305170059204},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3623725175857544},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.2978074848651886},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.24108195304870605},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.234361469745636},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.07713988423347473}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7045340538024902},{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.6830779314041138},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.6189298033714294},{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.5859230160713196},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.5504733324050903},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5135093331336975},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.511382520198822},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.5096306800842285},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.5083739161491394},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.501978874206543},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.46759316325187683},{"id":"https://openalex.org/C94284585","wikidata":"https://www.wikidata.org/wiki/Q228184","display_name":"Random oracle","level":4,"score":0.4642980694770813},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4632706642150879},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.45129841566085815},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.413593053817749},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37931305170059204},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3623725175857544},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.2978074848651886},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24108195304870605},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.234361469745636},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.07713988423347473},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/3-540-45961-8_39","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45961-8_39","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.14.2397","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.14.2397","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://dsns.csie.nctu.edu.tw/research/crypto/HTML/PDF/E88/419.PDF","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.6800000071525574}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1585576754","https://openalex.org/W1969333782","https://openalex.org/W1996360405","https://openalex.org/W2011039300","https://openalex.org/W2087749569","https://openalex.org/W2156186849","https://openalex.org/W2509730220","https://openalex.org/W4232836212","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2009976334","https://openalex.org/W1991617491","https://openalex.org/W2414747139","https://openalex.org/W1486255205","https://openalex.org/W3029593079","https://openalex.org/W2613410895","https://openalex.org/W2077900604","https://openalex.org/W2112914778","https://openalex.org/W2387773210","https://openalex.org/W2364255832"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":11},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":21},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":23},{"year":2020,"cited_by_count":25},{"year":2019,"cited_by_count":20},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":26},{"year":2016,"cited_by_count":22},{"year":2015,"cited_by_count":24},{"year":2014,"cited_by_count":14},{"year":2013,"cited_by_count":28},{"year":2012,"cited_by_count":24}],"updated_date":"2026-06-13T07:54:00.901334","created_date":"2025-10-10T00:00:00"}