{"id":"https://openalex.org/W2133465710","doi":"https://doi.org/10.1137/100811970","title":"A Deterministic Single Exponential Time Algorithm for Most Lattice Problems Based on Voronoi Cell Computations","display_name":"A Deterministic Single Exponential Time Algorithm for Most Lattice Problems Based on Voronoi Cell Computations","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2133465710","doi":"https://doi.org/10.1137/100811970","mag":"2133465710"},"language":"en","primary_location":{"id":"doi:10.1137/100811970","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100811970","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on 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/A5023640008","display_name":"Daniele Micciancio","orcid":"https://orcid.org/0000-0003-3323-9985"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Daniele Micciancio","raw_affiliation_strings":["University of California, San Diego"],"affiliations":[{"raw_affiliation_string":"University of California, San Diego","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032583740","display_name":"Panagiotis Voulgaris","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Panagiotis Voulgaris","raw_affiliation_strings":["University of California, San Diego"],"affiliations":[{"raw_affiliation_string":"University of California, San Diego","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023640008"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":13.8387,"has_fulltext":false,"cited_by_count":119,"citation_normalized_percentile":{"value":0.98773255,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"42","issue":"3","first_page":"1364","last_page":"1391"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data 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"}},"topics":[{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data 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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9947999715805054,"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/lattice-problem","display_name":"Lattice problem","score":0.7218247652053833},{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.6870622634887695},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6806889772415161},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6068134307861328},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5395374298095703},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5188937783241272},{"id":"https://openalex.org/keywords/deterministic-algorithm","display_name":"Deterministic algorithm","score":0.4901326596736908},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4814862012863159},{"id":"https://openalex.org/keywords/exponential-time-hypothesis","display_name":"Exponential time hypothesis","score":0.4643246531486511},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4640032649040222},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.4359019994735718},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40158283710479736},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.14333871006965637}],"concepts":[{"id":"https://openalex.org/C168482242","wikidata":"https://www.wikidata.org/wiki/Q6497128","display_name":"Lattice problem","level":3,"score":0.7218247652053833},{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.6870622634887695},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6806889772415161},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6068134307861328},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5395374298095703},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5188937783241272},{"id":"https://openalex.org/C13533509","wikidata":"https://www.wikidata.org/wiki/Q1064349","display_name":"Deterministic algorithm","level":2,"score":0.4901326596736908},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4814862012863159},{"id":"https://openalex.org/C71017364","wikidata":"https://www.wikidata.org/wiki/Q5421532","display_name":"Exponential time hypothesis","level":3,"score":0.4643246531486511},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4640032649040222},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.4359019994735718},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40158283710479736},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.14333871006965637},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/100811970","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100811970","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2305009926","display_name":"CT-ISG:    Real Time Cryptography","funder_award_id":"0831536","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6305572077","display_name":"Fourier Techniques in Cryptography and Coding","funder_award_id":"0634909","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1539643737","https://openalex.org/W1968182591","https://openalex.org/W1971400259","https://openalex.org/W1976456789","https://openalex.org/W1981326822","https://openalex.org/W1981627190","https://openalex.org/W1989510734","https://openalex.org/W1994790157","https://openalex.org/W1996271812","https://openalex.org/W2000333212","https://openalex.org/W2001093624","https://openalex.org/W2007466965","https://openalex.org/W2008930715","https://openalex.org/W2013794527","https://openalex.org/W2021907057","https://openalex.org/W2026129593","https://openalex.org/W2031600610","https://openalex.org/W2034056530","https://openalex.org/W2037426925","https://openalex.org/W2051176401","https://openalex.org/W2056492141","https://openalex.org/W2057481903","https://openalex.org/W2057728026","https://openalex.org/W2060296335","https://openalex.org/W2067935912","https://openalex.org/W2070971235","https://openalex.org/W2083175934","https://openalex.org/W2101362102","https://openalex.org/W2104242142","https://openalex.org/W2111416661","https://openalex.org/W2114616381","https://openalex.org/W2126483728","https://openalex.org/W2140940105","https://openalex.org/W2141040012","https://openalex.org/W2144593761","https://openalex.org/W2399135883","https://openalex.org/W3014312596","https://openalex.org/W3102292552","https://openalex.org/W3105421475","https://openalex.org/W3144422206"],"related_works":["https://openalex.org/W2279830512","https://openalex.org/W2007715402","https://openalex.org/W3097369619","https://openalex.org/W3046990805","https://openalex.org/W4287691960","https://openalex.org/W2963181990","https://openalex.org/W2913663107","https://openalex.org/W2187362812","https://openalex.org/W4302354049","https://openalex.org/W2133465710"],"abstract_inverted_index":{"We":[0],"give":[1],"deterministic":[2,78],"$\\tilde{O}(2^{2n})$-time":[3],"$\\tilde{O}(2^n)$-space":[4],"algorithms":[5,46,165],"to":[6,83,120],"solve":[7,121],"all":[8],"the":[9,20,37,42,64,84,99,122,131,135,143,146,159],"most":[10],"important":[11],"computational":[12],"problems":[13],"on":[14,69,104],"point":[15],"lattices":[16],"in":[17],"NP,":[18],"including":[19],"shortest":[21,30],"vector":[22,26,124],"problem":[23,27,33,125],"(SVP),":[24],"closest":[25,123],"(CVP),":[28],"and":[29,58,75,79,95,168],"independent":[31],"vectors":[32],"(SIVP).":[34],"This":[35],"improves":[36],"$n^{O(n)}$":[38],"running":[39],"time":[40,163],"of":[41,63,92,98,106,113,134,140,145,152,158],"best":[43,160],"previously":[44],"known":[45],"for":[47,90,166],"CVP":[48],"[R.":[49],"Kannan,":[50],"Math.":[51],"Oper.":[52],"Res.,":[53],"12":[54],"(1987),":[55],"pp.":[56,73,109],"415--440]":[57],"SIVP":[59],"[D.":[60],"Micciancio,":[61],"Proceedings":[62],"$19$th":[65],"Annual":[66,101],"ACM-SIAM":[67],"Symposium":[68,103],"Discrete":[70],"Algorithms,":[71],"2008,":[72],"84--93]":[74],"gives":[76],"a":[77,117,156,171],"asymptotically":[80],"faster":[81],"alternative":[82],"$2^{O(n)}$-time":[85],"(and":[86],"space)":[87],"randomized":[88],"algorithm":[89,115],"SVP":[91,167],"Ajtai,":[93],"Kumar,":[94],"Sivakumar":[96],"[Proceedings":[97],"$33$rd":[100],"ACM":[102],"Theory":[105],"Computing,":[107],"2001,":[108],"266--275].":[110],"The":[111],"core":[112],"our":[114,153],"is":[116,155],"new":[118],"method":[119],"with":[126],"preprocessing":[127,147],"(CVPP)":[128],"that":[129],"uses":[130],"Voronoi":[132],"cell":[133],"lattice":[136],"(described":[137],"as":[138,142],"intersection":[139],"half-spaces)":[141],"result":[144],"function.":[148],"A":[149],"direct":[150],"consequence":[151],"results":[154],"derandomization":[157],"current":[161],"polynomial":[162],"approximation":[164,178],"CVP,":[169],"achieving":[170],"$2^{O(n":[172],"\\log\\log":[173],"n":[174],"/":[175],"\\log":[176],"n)}$":[177],"factor.":[179]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-14T08:04:32.555800","created_date":"2025-10-10T00:00:00"}
