{"id":"https://openalex.org/W2108826934","doi":"https://doi.org/10.1007/3-540-45961-8_26","title":"How to Break Okamoto\u2019s Cryptosystem by Reducing Lattice Bases","display_name":"How to Break Okamoto\u2019s Cryptosystem by Reducing Lattice Bases","publication_year":1988,"publication_date":"1988-01-01","ids":{"openalex":"https://openalex.org/W2108826934","doi":"https://doi.org/10.1007/3-540-45961-8_26","mag":"2108826934"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-45961-8_26","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-45961-8_26","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-45961-8_26.pdf","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":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-45961-8_26.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111497028","display_name":"Brigitte Vall\u00e9e","orcid":null},"institutions":[{"id":"https://openalex.org/I3019441195","display_name":"Laboratoire de Math\u00e9matiques d'Orsay","ror":"https://ror.org/03ab0zs98","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I3019441195"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Brigitte Vall\u00e9e","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matiques, Universit\u00e9, 14032, Caen Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques, Universit\u00e9, 14032, Caen Cedex, France","institution_ids":["https://openalex.org/I3019441195"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080688983","display_name":"Marc Girault","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marc Girault","raw_affiliation_strings":["Service d\u2019Etudes communes des Postes et T\u00e9l\u00e9communications, BP 6243, 14066, Caen Cedex, France","Service d'Etudes communes des Postes et T\u00e9l\u00e9communications, BP 6243, 14066, Caen Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Service d\u2019Etudes communes des Postes et T\u00e9l\u00e9communications, BP 6243, 14066, Caen Cedex, France","institution_ids":[]},{"raw_affiliation_string":"Service d'Etudes communes des Postes et T\u00e9l\u00e9communications, BP 6243, 14066, Caen Cedex, France","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013767099","display_name":"Philippe Toffin","orcid":null},"institutions":[{"id":"https://openalex.org/I3019441195","display_name":"Laboratoire de Math\u00e9matiques d'Orsay","ror":"https://ror.org/03ab0zs98","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I3019441195"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Philippe Toffin","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matiques, Universit\u00e9, 14032, Caen Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques, Universit\u00e9, 14032, Caen Cedex, France","institution_ids":["https://openalex.org/I3019441195"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.9069,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.79917846,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"281","last_page":"291"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":1.0,"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":1.0,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9968000054359436,"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/T11130","display_name":"Coding theory and cryptography","score":0.996399998664856,"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/cryptosystem","display_name":"Cryptosystem","score":0.7682546973228455},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.6622053384780884},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6095813512802124},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.45916682481765747},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4550131857395172},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.44708871841430664},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.43829113245010376},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4372374713420868},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.42772865295410156},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42492926120758057},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3801010251045227},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3383742570877075},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.3302091956138611},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2591921091079712},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23596680164337158},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07389557361602783}],"concepts":[{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.7682546973228455},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.6622053384780884},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6095813512802124},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.45916682481765747},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4550131857395172},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.44708871841430664},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.43829113245010376},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4372374713420868},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.42772865295410156},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42492926120758057},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3801010251045227},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3383742570877075},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.3302091956138611},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2591921091079712},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23596680164337158},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07389557361602783},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-45961-8_26","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-45961-8_26","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-45961-8_26.pdf","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":{"id":"doi:10.1007/3-540-45961-8_26","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-45961-8_26","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-45961-8_26.pdf","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"},"sustainable_development_goals":[{"score":0.41999998688697815,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2108826934.pdf","grobid_xml":"https://content.openalex.org/works/W2108826934.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1577571951","https://openalex.org/W1804795452","https://openalex.org/W2024142753","https://openalex.org/W2056579313","https://openalex.org/W2080017147","https://openalex.org/W2098318916","https://openalex.org/W2111416661","https://openalex.org/W2141040012","https://openalex.org/W2464048625"],"related_works":["https://openalex.org/W2117548279","https://openalex.org/W2807449856","https://openalex.org/W238211858","https://openalex.org/W2070252991","https://openalex.org/W2025727968","https://openalex.org/W2941201715","https://openalex.org/W2803761277","https://openalex.org/W2965484163","https://openalex.org/W4232705780","https://openalex.org/W2096221836"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
