{"id":"https://openalex.org/W3034229215","doi":"https://doi.org/10.1007/s10817-020-09552-1","title":"Formalizing the LLL Basis Reduction Algorithm and the LLL Factorization Algorithm in Isabelle/HOL","display_name":"Formalizing the LLL Basis Reduction Algorithm and the LLL Factorization Algorithm in Isabelle/HOL","publication_year":2020,"publication_date":"2020-06-01","ids":{"openalex":"https://openalex.org/W3034229215","doi":"https://doi.org/10.1007/s10817-020-09552-1","mag":"3034229215","pmid":"https://pubmed.ncbi.nlm.nih.gov/32831440"},"language":"en","primary_location":{"id":"doi:10.1007/s10817-020-09552-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10817-020-09552-1","pdf_url":null,"source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Automated Reasoning","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/s10817-020-09552-1","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078037586","display_name":"Ren\u00e9 Thiemann","orcid":"https://orcid.org/0000-0002-0323-8829"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Ren\u00e9 Thiemann","raw_affiliation_strings":["University of Innsbruck, Innsbruck, Austria"],"affiliations":[{"raw_affiliation_string":"University of Innsbruck, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010343996","display_name":"Ralph Bottesch","orcid":null},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Ralph Bottesch","raw_affiliation_strings":["University of Innsbruck, Innsbruck, Austria"],"affiliations":[{"raw_affiliation_string":"University of Innsbruck, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079015937","display_name":"Jose Divas\u00f3n","orcid":"https://orcid.org/0000-0002-5173-128X"},"institutions":[{"id":"https://openalex.org/I168974976","display_name":"Universidad de La Rioja","ror":"https://ror.org/0553yr311","country_code":"ES","type":"education","lineage":["https://openalex.org/I168974976"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jose Divas\u00f3n","raw_affiliation_strings":["University of La Rioja, Logro\u00f1o, Spain"],"affiliations":[{"raw_affiliation_string":"University of La Rioja, Logro\u00f1o, Spain","institution_ids":["https://openalex.org/I168974976"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065739577","display_name":"Max W. Haslbeck","orcid":"https://orcid.org/0000-0002-9900-5746"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Max W. Haslbeck","raw_affiliation_strings":["University of Innsbruck, Innsbruck, Austria"],"affiliations":[{"raw_affiliation_string":"University of Innsbruck, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006751254","display_name":"Sebastiaan J. C. Joosten","orcid":"https://orcid.org/0000-0002-6590-6220"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Sebastiaan J. C. Joosten","raw_affiliation_strings":["University of Innsbruck, Innsbruck, Austria"],"affiliations":[{"raw_affiliation_string":"University of Innsbruck, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003947273","display_name":"Akihisa Yamada","orcid":"https://orcid.org/0000-0001-8872-2240"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Akihisa Yamada","raw_affiliation_strings":["University of Innsbruck, Innsbruck, Austria"],"affiliations":[{"raw_affiliation_string":"University of Innsbruck, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5078037586"],"corresponding_institution_ids":["https://openalex.org/I190249584"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.06160636,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"64","issue":"5","first_page":"827","last_page":"856"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9970999956130981,"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/T11130","display_name":"Coding theory and cryptography","score":0.9970999956130981,"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/T11567","display_name":"semigroups and automata theory","score":0.9955000281333923,"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":0.9954000115394592,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lattice-reduction","display_name":"Lattice reduction","score":0.7914634943008423},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.7343180775642395},{"id":"https://openalex.org/keywords/hol","display_name":"HOL","score":0.6069442629814148},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4715801775455475},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.468581885099411},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44352462887763977},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4309135675430298},{"id":"https://openalex.org/keywords/soundness","display_name":"Soundness","score":0.42067328095436096}],"concepts":[{"id":"https://openalex.org/C44274781","wikidata":"https://www.wikidata.org/wiki/Q6497132","display_name":"Lattice reduction","level":4,"score":0.7914634943008423},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7343180775642395},{"id":"https://openalex.org/C17435882","wikidata":"https://www.wikidata.org/wiki/Q17030435","display_name":"HOL","level":2,"score":0.6069442629814148},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4715801775455475},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.468581885099411},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44352462887763977},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4309135675430298},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.42067328095436096},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10817-020-09552-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10817-020-09552-1","pdf_url":null,"source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Automated Reasoning","raw_type":"journal-article"},{"id":"pmid:32831440","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/32831440","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of automated reasoning","raw_type":null},{"id":"pmh:oai:portal.dialnet.es:doc/5fa2894b2999524084dd78ae","is_oa":true,"landing_page_url":"https://investigacion.unirioja.es/documentos/5fa2894b2999524084dd78ae","pdf_url":null,"source":{"id":"https://openalex.org/S4306402551","display_name":"RIUR (Universidad de La Rioja)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I3032752892","host_organization_name":"Universidad Internacional de La Rioja","host_organization_lineage":["https://openalex.org/I3032752892"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pubmedcentral.nih.gov:7413592","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7413592","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"J Autom Reason","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s10817-020-09552-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10817-020-09552-1","pdf_url":null,"source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Automated Reasoning","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1369345469","display_name":null,"funder_award_id":"JPMJER1603","funder_id":"https://openalex.org/F4320334789","funder_display_name":"Japan Science and Technology Agency"},{"id":"https://openalex.org/G4046051807","display_name":null,"funder_award_id":"MTM2017-88804-P","funder_id":"https://openalex.org/F4320326262","funder_display_name":"Ministerio de Asuntos Econ\u00f3micos y Transformaci\u00f3n Digital, Gobierno de Espa\u00f1a"},{"id":"https://openalex.org/G6242973766","display_name":null,"funder_award_id":"Y757","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320326262","display_name":"Ministerio de Asuntos Econ\u00f3micos y Transformaci\u00f3n Digital, Gobierno de Espa\u00f1a","ror":"https://ror.org/03sv46s19"},{"id":"https://openalex.org/F4320334789","display_name":"Japan Science and Technology Agency","ror":"https://ror.org/00097mb19"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W3888705","https://openalex.org/W1479958651","https://openalex.org/W1482572800","https://openalex.org/W1523874359","https://openalex.org/W1537926751","https://openalex.org/W1562183207","https://openalex.org/W2016861963","https://openalex.org/W2061969020","https://openalex.org/W2091456056","https://openalex.org/W2106192381","https://openalex.org/W2134124371","https://openalex.org/W2141040012","https://openalex.org/W2144593761","https://openalex.org/W2167708641","https://openalex.org/W2256286306","https://openalex.org/W2295544473","https://openalex.org/W2564206325","https://openalex.org/W2615175639","https://openalex.org/W2770474258","https://openalex.org/W2776461454","https://openalex.org/W2809929373","https://openalex.org/W2811256589","https://openalex.org/W2904582217","https://openalex.org/W2907655115","https://openalex.org/W2951586102","https://openalex.org/W3130701806","https://openalex.org/W4205630623","https://openalex.org/W4205954884","https://openalex.org/W4237140674","https://openalex.org/W4250846042","https://openalex.org/W4250850800","https://openalex.org/W7057914944"],"related_works":["https://openalex.org/W2339308944","https://openalex.org/W1714698337","https://openalex.org/W2096228713","https://openalex.org/W2006789412","https://openalex.org/W2381112272","https://openalex.org/W1766548092","https://openalex.org/W2567490660","https://openalex.org/W1603921694","https://openalex.org/W2071893554","https://openalex.org/W1572157978"],"abstract_inverted_index":{"The":[0,50],"LLL":[1,70],"basis":[2,14],"reduction":[3,113],"algorithm":[4,9,51,130],"was":[5],"the":[6,26,34,40,43,47,69],"first":[7],"polynomial-time":[8],"to":[10],"compute":[11],"a":[12,16,22,94,127],"reduced":[13],"of":[15,42,68,124],"given":[17],"lattice,":[18,44],"and":[19,59,75,99,115],"hence":[20],"also":[21],"short":[23],"vector":[24],"in":[25,54,93,137],"lattice.":[27],"It":[28],"approximates":[29],"an":[30,66,91],"NP-hard":[31],"problem":[32],"where":[33],"approximation":[35],"quality":[36],"solely":[37],"depends":[38],"on":[39],"dimension":[41],"but":[45],"not":[46],"lattice":[48,112],"itself.":[49],"has":[52],"applications":[53],"number":[55],"theory,":[56],"computer":[57,96],"algebra":[58,97],"cryptography.":[60],"In":[61],"this":[62],"paper,":[63],"we":[64],"provide":[65],"implementation":[67,85,92],"algorithm.":[71],"Both":[72],"its":[73,76,100],"soundness":[74],"polynomial":[77,138],"running-time":[78],"have":[79],"been":[80],"verified":[81,128],"using":[82],"Isabelle/HOL.":[83],"Our":[84],"is":[86],"nearly":[87],"as":[88,90],"fast":[89,110],"commercial":[95],"system,":[98],"efficiency":[101],"can":[102],"be":[103],"further":[104],"increased":[105],"by":[106],"connecting":[107],"it":[108],"with":[109],"untrusted":[111],"algorithms":[114],"certifying":[116],"their":[117],"output.":[118],"We":[119],"additionally":[120],"integrate":[121],"one":[122],"application":[123],"LLL,":[125],"namely":[126],"factorization":[129],"for":[131],"univariate":[132],"integer":[133],"polynomials":[134],"which":[135],"runs":[136],"time.":[139]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}