{"id":"https://openalex.org/W2327995849","doi":"https://doi.org/10.1007/s00200-016-0291-x","title":"Computational hardness of IFP and ECDLP","display_name":"Computational hardness of IFP and ECDLP","publication_year":2016,"publication_date":"2016-04-09","ids":{"openalex":"https://openalex.org/W2327995849","doi":"https://doi.org/10.1007/s00200-016-0291-x","mag":"2327995849"},"language":"en","primary_location":{"id":"doi:10.1007/s00200-016-0291-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00200-016-0291-x","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"},"type":"article","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/A5086472078","display_name":"Masaya Yasuda","orcid":"https://orcid.org/0000-0002-1534-5648"},"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":"Masaya Yasuda","raw_affiliation_strings":["Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan","institution_ids":["https://openalex.org/I135598925"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075302675","display_name":"Takeshi Shimoyama","orcid":null},"institutions":[{"id":"https://openalex.org/I2252096349","display_name":"Fujitsu (Japan)","ror":"https://ror.org/038e2g226","country_code":"JP","type":"company","lineage":["https://openalex.org/I2252096349"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takeshi Shimoyama","raw_affiliation_strings":["Fujitsu Laboratories LTD, 4-1-1, Kamikodanaka, Nakahara-ku, Kawasaki, 211-8588, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fujitsu Laboratories LTD, 4-1-1, Kamikodanaka, Nakahara-ku, Kawasaki, 211-8588, Japan","institution_ids":["https://openalex.org/I2252096349"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037862602","display_name":"Jun Kogure","orcid":null},"institutions":[{"id":"https://openalex.org/I2252096349","display_name":"Fujitsu (Japan)","ror":"https://ror.org/038e2g226","country_code":"JP","type":"company","lineage":["https://openalex.org/I2252096349"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Jun Kogure","raw_affiliation_strings":["Fujitsu Laboratories LTD, 4-1-1, Kamikodanaka, Nakahara-ku, Kawasaki, 211-8588, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fujitsu Laboratories LTD, 4-1-1, Kamikodanaka, Nakahara-ku, Kawasaki, 211-8588, Japan","institution_ids":["https://openalex.org/I2252096349"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005516737","display_name":"Tetsuya Izu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210153853","display_name":"Fujitsu (United Kingdom)","ror":"https://ror.org/053ny5136","country_code":"GB","type":"company","lineage":["https://openalex.org/I2252096349","https://openalex.org/I4210153853"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Tetsuya Izu","raw_affiliation_strings":["Data Analytics Research Division, FUJITSU Laboratories of Europe Ltd., Hayes Park Central, Hayes End Road, Middlesex, UB4 8FE, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Data Analytics Research Division, FUJITSU Laboratories of Europe Ltd., Hayes Park Central, Hayes End Road, Middlesex, UB4 8FE, United Kingdom","institution_ids":["https://openalex.org/I4210153853"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5086472078"],"corresponding_institution_ids":["https://openalex.org/I135598925"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":4.511,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.9503855,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"27","issue":"6","first_page":"493","last_page":"521"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9944000244140625,"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":0.9933000206947327,"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":0.6500157117843628},{"id":"https://openalex.org/keywords/integer-factorization","display_name":"Integer factorization","score":0.6484237313270569},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.6229654550552368},{"id":"https://openalex.org/keywords/post-quantum-cryptography","display_name":"Post-quantum cryptography","score":0.5769439935684204},{"id":"https://openalex.org/keywords/cryptosystem","display_name":"Cryptosystem","score":0.5251690745353699},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.5122405886650085},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.5062922239303589},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5054588317871094},{"id":"https://openalex.org/keywords/hyperelliptic-curve-cryptography","display_name":"Hyperelliptic curve cryptography","score":0.46247684955596924},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45972368121147156},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4050784409046173},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.370303213596344},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34575068950653076},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27731871604919434},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.19513848423957825},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14407366514205933},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.13402748107910156}],"concepts":[{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.6500157117843628},{"id":"https://openalex.org/C119677069","wikidata":"https://www.wikidata.org/wiki/Q4846249","display_name":"Integer factorization","level":4,"score":0.6484237313270569},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.6229654550552368},{"id":"https://openalex.org/C108277079","wikidata":"https://www.wikidata.org/wiki/Q7233576","display_name":"Post-quantum cryptography","level":4,"score":0.5769439935684204},{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.5251690745353699},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.5122405886650085},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.5062922239303589},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5054588317871094},{"id":"https://openalex.org/C166780011","wikidata":"https://www.wikidata.org/wiki/Q3005926","display_name":"Hyperelliptic curve cryptography","level":5,"score":0.46247684955596924},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45972368121147156},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4050784409046173},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.370303213596344},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34575068950653076},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27731871604919434},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.19513848423957825},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14407366514205933},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.13402748107910156}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00200-016-0291-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00200-016-0291-x","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320335839","display_name":"National Institute of Information and Communications Technology","ror":"https://ror.org/016bgq349"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W172077068","https://openalex.org/W258537497","https://openalex.org/W287913276","https://openalex.org/W975156810","https://openalex.org/W1480802403","https://openalex.org/W1480958376","https://openalex.org/W1508193711","https://openalex.org/W1538333734","https://openalex.org/W1581948531","https://openalex.org/W1596482432","https://openalex.org/W1602086557","https://openalex.org/W1603217046","https://openalex.org/W1751074114","https://openalex.org/W1785867541","https://openalex.org/W1880212920","https://openalex.org/W1979485530","https://openalex.org/W1985265065","https://openalex.org/W1996360405","https://openalex.org/W2003736153","https://openalex.org/W2008272678","https://openalex.org/W2019816098","https://openalex.org/W2036378739","https://openalex.org/W2042173287","https://openalex.org/W2046569422","https://openalex.org/W2078234463","https://openalex.org/W2095980625","https://openalex.org/W2111310412","https://openalex.org/W2123355614","https://openalex.org/W2132967177","https://openalex.org/W2142778315","https://openalex.org/W2144007792","https://openalex.org/W2159214235","https://openalex.org/W2166957790","https://openalex.org/W2168139972","https://openalex.org/W2168986093","https://openalex.org/W2189087655","https://openalex.org/W2286477783","https://openalex.org/W4232836212"],"related_works":["https://openalex.org/W4251990811","https://openalex.org/W1494454048","https://openalex.org/W2387862062","https://openalex.org/W2540612917","https://openalex.org/W3123167884","https://openalex.org/W2353428286","https://openalex.org/W4382407602","https://openalex.org/W2281332536","https://openalex.org/W2198520256","https://openalex.org/W149665908"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
