{"id":"https://openalex.org/W3207129726","doi":"https://doi.org/10.1007/s10623-022-01119-y","title":"The irreducible vectors of a lattice: Some theory and applications.","display_name":"The irreducible vectors of a lattice: Some theory and applications.","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3207129726","doi":"https://doi.org/10.1007/s10623-022-01119-y","mag":"3207129726"},"language":"en","primary_location":{"id":"pmh:oai:pure.tue.nl:openaire/0fa0b3a5-2424-4dbe-8102-4d3d18bb3663","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/0fa0b3a5-2424-4dbe-8102-4d3d18bb3663","pdf_url":"https://pure.tue.nl/ws/files/281851749/s10623_022_01119_y.pdf","source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Doulgerakis, E, Laarhoven, T M M & de Weger, B M M 2023, 'The irreducible vectors of a lattice : Some theory and applications', Designs, Codes and Cryptography, vol. 91, no. 2, pp. 609-643. https://doi.org/10.1007/s10623-022-01119-y","raw_type":"info:eu-repo/semantics/article"},"type":"article","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://pure.tue.nl/ws/files/281851749/s10623_022_01119_y.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004281203","display_name":"Emmanouil Doulgerakis","orcid":"https://orcid.org/0000-0002-0437-1525"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Emmanouil Doulgerakis","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-0437-1525","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023482258","display_name":"Thijs Laarhoven","orcid":"https://orcid.org/0000-0002-2369-9067"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thijs Laarhoven","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-2369-9067","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109904175","display_name":"Benne de Weger","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Benne de Weger","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18806991,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2021","issue":null,"first_page":"1203","last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991000294685364,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991000294685364,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.998199999332428,"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/T12288","display_name":"Optimization and Search Problems","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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","display_name":"Lattice (music)","score":0.5811004042625427},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5323330163955688},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3279034495353699},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32034873962402344},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.29707688093185425},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28428542613983154},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.178641676902771}],"concepts":[{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5811004042625427},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5323330163955688},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3279034495353699},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32034873962402344},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29707688093185425},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28428542613983154},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.178641676902771},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"pmh:oai:pure.tue.nl:openaire/0fa0b3a5-2424-4dbe-8102-4d3d18bb3663","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/0fa0b3a5-2424-4dbe-8102-4d3d18bb3663","pdf_url":"https://pure.tue.nl/ws/files/281851749/s10623_022_01119_y.pdf","source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Doulgerakis, E, Laarhoven, T M M & de Weger, B M M 2023, 'The irreducible vectors of a lattice : Some theory and applications', Designs, Codes and Cryptography, vol. 91, no. 2, pp. 609-643. https://doi.org/10.1007/s10623-022-01119-y","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/4cc52d22-129f-48fc-80d5-99fb0077f5e6","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/4cc52d22-129f-48fc-80d5-99fb0077f5e6","pdf_url":"https://pure.tue.nl/ws/files/363969986/2021-1203.pdf","source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Doulgerakis, E, Laarhoven, T & de Weger, B 2021 'The irreducible vectors of a lattice : Some theory and applications' International Association for Cryptologic Research. < https://eprint.iacr.org/2021/1203 >","raw_type":"info:eu-repo/semantics/preprint"},{"id":"mag:3207129726","is_oa":false,"landing_page_url":"https://eprint.iacr.org/2021/1203.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2764847869","display_name":"IACR Cryptology ePrint Archive","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4322614454"],"host_organization_lineage_names":["Cryptology ePrint Archive"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IACR Cryptology ePrint Archive","raw_type":null},{"id":"pmh:oai:oai-pmh.tno.nl:55092","is_oa":false,"landing_page_url":"https://resolver.tno.nl/uuid:038d1d8a-8cdd-4f43-b498-bf628e619fa1","pdf_url":null,"source":{"id":"https://openalex.org/S7407055233","display_name":"TNO Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Designs, Codes, and Cryptography","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.tue.nl:openaire/4cc52d22-129f-48fc-80d5-99fb0077f5e6","is_oa":true,"landing_page_url":"https://eprint.iacr.org/2021/1203","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Doulgerakis, E, Laarhoven, T & de Weger, B 2021 'The irreducible vectors of a lattice : Some theory and applications' International Association for Cryptologic Research. < https://eprint.iacr.org/2021/1203 >","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:tue:oai:pure.tue.nl:publications/0fa0b3a5-2424-4dbe-8102-4d3d18bb3663","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/0fa0b3a5-2424-4dbe-8102-4d3d18bb3663","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"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":"Designs, Codes and Cryptography, 91(2), 609 - 643. Springer","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:pure.tue.nl:openaire/0fa0b3a5-2424-4dbe-8102-4d3d18bb3663","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/0fa0b3a5-2424-4dbe-8102-4d3d18bb3663","pdf_url":"https://pure.tue.nl/ws/files/281851749/s10623_022_01119_y.pdf","source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Doulgerakis, E, Laarhoven, T M M & de Weger, B M M 2023, 'The irreducible vectors of a lattice : Some theory and applications', Designs, Codes and Cryptography, vol. 91, no. 2, pp. 609-643. https://doi.org/10.1007/s10623-022-01119-y","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7010378412","display_name":null,"funder_award_id":"016.Veni","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G7226962176","display_name":"Faster and Stronger Onion Routing (FASOR)","funder_award_id":"628.001.028","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G8335564440","display_name":"Lattices and nearest neighbor searching","funder_award_id":"016.Veni.192.005","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3207129726.pdf"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1520127302","https://openalex.org/W1845765495","https://openalex.org/W1980073965","https://openalex.org/W1994069625","https://openalex.org/W1996271812","https://openalex.org/W2013568176","https://openalex.org/W2021907057","https://openalex.org/W2042556188","https://openalex.org/W2065550084","https://openalex.org/W2092901733","https://openalex.org/W2100061495","https://openalex.org/W2140940105","https://openalex.org/W2516575385","https://openalex.org/W2901659531","https://openalex.org/W2920734175","https://openalex.org/W2986394561"],"related_works":["https://openalex.org/W1529152196","https://openalex.org/W1975653971","https://openalex.org/W3135068738","https://openalex.org/W1978579918","https://openalex.org/W69870232","https://openalex.org/W2065037624","https://openalex.org/W2478201035","https://openalex.org/W3028452882","https://openalex.org/W1482523625","https://openalex.org/W1559342928","https://openalex.org/W3170523711","https://openalex.org/W373031252","https://openalex.org/W2908311851","https://openalex.org/W2325810907","https://openalex.org/W938386347","https://openalex.org/W2797863226","https://openalex.org/W2064946749","https://openalex.org/W1991039671","https://openalex.org/W1496020233","https://openalex.org/W1966015386"],"abstract_inverted_index":{"The":[0,161],"main":[1],"idea":[2],"behind":[3],"lattice":[4,15,153,178],"sieving":[5,138],"algorithms":[6,179,187],"is":[7,28,37,78],"to":[8,40,105,136],"reduce":[9],"a":[10,22,31,52,79,110,133],"sufficiently":[11],"large":[12],"number":[13],"of":[14,24,33,55,63,66,75,81,84,109,113,128,146,152],"vectors":[16,27,42,77,86],"with":[17],"each":[18],"other":[19],"so":[20],"that":[21,72],"set":[23,65,74,83,95,130,148],"short":[25],"enough":[26],"obtained,":[29],"including":[30],"basis":[32],"the":[34,61,64,73,82,107,122,144,150,171],"lattice.":[35],"It":[36],"therefore":[38],"natural":[39],"study":[41,60,88,126,151],"which":[43,102],"cannot":[44],"be":[45,119],"reduced.":[46],"In":[47],"this":[48,94,129,147],"work":[49],"we":[50,141],"give":[51],"concrete":[53],"definition":[54],"an":[56],"irreducible":[57,76,114],"vector":[58],"and":[59,87,131,159,180],"properties":[62,127],"all":[67],"such":[68,155],"vectors.":[69],"We":[70,125],"show":[71],"subset":[80],"relevant":[85],"its":[89],"properties.":[90],"For":[91],"extremal":[92],"lattices":[93],"may":[96,173],"contain":[97],"as":[98,100,156,164,166],"many":[99],"vectors,":[101,115],"leads":[103],"us":[104],"define":[106],"notion":[108],"complete":[111],"system":[112],"whose":[116],"size":[117],"can":[118],"upper-bounded":[120],"by":[121],"kissing":[123],"number.":[124],"observe":[132],"close":[134],"relation":[135],"heuristic":[137],"algorithms.":[139],"Finally":[140],"briefly":[142],"examine":[143],"use":[145],"in":[149],"problems":[154],"SVP,":[157],"SIVP":[158],"CVPP.":[160],"introduced":[162],"notions,":[163],"well":[165],"various":[167],"results":[168],"derived":[169],"along":[170],"way,":[172],"provide":[174],"further":[175],"insights":[176],"into":[177,184],"motivate":[181],"new":[182],"research":[183],"understanding":[185],"these":[186],"better.":[188]},"counts_by_year":[],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}