{"id":"https://openalex.org/W2177209050","doi":"https://doi.org/10.1145/2633600","title":"(Leveled) Fully Homomorphic Encryption without Bootstrapping","display_name":"(Leveled) Fully Homomorphic Encryption without Bootstrapping","publication_year":2014,"publication_date":"2014-07-01","ids":{"openalex":"https://openalex.org/W2177209050","doi":"https://doi.org/10.1145/2633600","mag":"2177209050"},"language":"en","primary_location":{"id":"doi:10.1145/2633600","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2633600","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computation Theory","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/A5023852532","display_name":"Zvika Brakerski","orcid":"https://orcid.org/0000-0002-4867-7999"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Zvika Brakerski","raw_affiliation_strings":["Weizmann Institute of Science"],"affiliations":[{"raw_affiliation_string":"Weizmann Institute of Science","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044697595","display_name":"Craig Gentry","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Craig Gentry","raw_affiliation_strings":["IBM Research"],"affiliations":[{"raw_affiliation_string":"IBM Research","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000240220","display_name":"Vinod Vaikuntanathan","orcid":"https://orcid.org/0000-0002-2666-0045"},"institutions":[{"id":"https://openalex.org/I4210109586","display_name":"Moscow Institute of Thermal Technology","ror":"https://ror.org/021es5e59","country_code":"RU","type":"facility","lineage":["https://openalex.org/I4210109586"]},{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA","RU"],"is_corresponding":false,"raw_author_name":"Vinod Vaikuntanathan","raw_affiliation_strings":["MIT and University of Toronto"],"affiliations":[{"raw_affiliation_string":"MIT and University of Toronto","institution_ids":["https://openalex.org/I4210109586","https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5023852532"],"corresponding_institution_ids":["https://openalex.org/I53964585"],"apc_list":null,"apc_paid":null,"fwci":30.0229,"has_fulltext":false,"cited_by_count":1332,"citation_normalized_percentile":{"value":0.99697288,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"6","issue":"3","first_page":"1","last_page":"36"},"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":0.998199999332428,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9911999702453613,"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/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.9074550271034241},{"id":"https://openalex.org/keywords/bootstrapping","display_name":"Bootstrapping (finance)","score":0.816889762878418},{"id":"https://openalex.org/keywords/learning-with-errors","display_name":"Learning with errors","score":0.7730509042739868},{"id":"https://openalex.org/keywords/security-parameter","display_name":"Security parameter","score":0.6353616714477539},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5496208071708679},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5278494358062744},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.449154794216156},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.4476366639137268},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4418216347694397},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4253196716308594},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3526233732700348},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.33185774087905884},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3001721203327179}],"concepts":[{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.9074550271034241},{"id":"https://openalex.org/C207609745","wikidata":"https://www.wikidata.org/wiki/Q4944086","display_name":"Bootstrapping (finance)","level":2,"score":0.816889762878418},{"id":"https://openalex.org/C2779014939","wikidata":"https://www.wikidata.org/wiki/Q6510239","display_name":"Learning with errors","level":3,"score":0.7730509042739868},{"id":"https://openalex.org/C2776711565","wikidata":"https://www.wikidata.org/wiki/Q7445058","display_name":"Security parameter","level":3,"score":0.6353616714477539},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5496208071708679},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5278494358062744},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.449154794216156},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.4476366639137268},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4418216347694397},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4253196716308594},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3526233732700348},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.33185774087905884},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3001721203327179},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2633600","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2633600","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computation Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.41999998688697815,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G2647081911","display_name":null,"funder_award_id":"FA8750-11-2-0225","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G3000816038","display_name":null,"funder_award_id":"FA8750-11-C-0096","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"}],"funders":[{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W17575016","https://openalex.org/W104209573","https://openalex.org/W150223756","https://openalex.org/W1494049356","https://openalex.org/W1497981337","https://openalex.org/W1518622464","https://openalex.org/W1575598731","https://openalex.org/W1623766202","https://openalex.org/W1755636270","https://openalex.org/W1798609567","https://openalex.org/W1825240531","https://openalex.org/W1850468005","https://openalex.org/W1853548709","https://openalex.org/W1966731635","https://openalex.org/W1989510734","https://openalex.org/W1992282993","https://openalex.org/W2000956176","https://openalex.org/W2031533839","https://openalex.org/W2050689197","https://openalex.org/W2058785578","https://openalex.org/W2061949491","https://openalex.org/W2098290658","https://openalex.org/W2111809688","https://openalex.org/W2113333997","https://openalex.org/W2122086332","https://openalex.org/W2129580084","https://openalex.org/W2156030242","https://openalex.org/W2164327070","https://openalex.org/W2226167778","https://openalex.org/W2401959250","https://openalex.org/W2561675875","https://openalex.org/W4210300416"],"related_works":["https://openalex.org/W3029045823","https://openalex.org/W2400565204","https://openalex.org/W2885113919","https://openalex.org/W2398715209","https://openalex.org/W2949607150","https://openalex.org/W2248085730","https://openalex.org/W2951031027","https://openalex.org/W2952267894","https://openalex.org/W2232688100","https://openalex.org/W3021037411"],"abstract_inverted_index":{"We":[0,80,181,214],"present":[1],"a":[2,28,55,197,216,240,282],"novel":[3],"approach":[4,284],"to":[5,221,261],"fully":[6,34],"homomorphic":[7,35],"encryption":[8,36],"(FHE)":[9],"that":[10,72,89,141],"dramatically":[11],"improves":[12],"performance":[13],"and":[14,205,298],"bases":[15],"security":[16,76,113],"on":[17,61,118,169,210,225],"weaker":[18],"assumptions.":[19,213],"A":[20,85,137],"central":[21],"conceptual":[22],"contribution":[23],"in":[24,111,125,289],"our":[25,222,279],"work":[26],"is":[27,116,161,167,281],"new":[29,283],"way":[30],"of":[31,39,44,57,97,149,163,200,207,218,235,243,257,267,278,296],"constructing":[32],"leveled,":[33],"schemes":[37,59,195],"(capable":[38],"evaluating":[40],"arbitrary":[41],"polynomial-size":[42],"circuits":[43,95,147,234],"a-priori":[45],"bounded":[46],"depth),":[47],"without":[48],"Gentry\u2019s":[49],"bootstrapping":[50,134,177,273],"procedure.":[51,135],"Specifically,":[52],"we":[53,251],"offer":[54],"choice":[56],"FHE":[58,87,139,194],"based":[60,117,168,224],"the":[62,82,112,133,226,254,258,272,276,287,294],"learning":[63],"with":[64,188],"error":[65],"(LWE)":[66],"or":[67],"Ring":[68,227],"LWE":[69,228],"(RLWE)":[70],"problems":[71],"have":[73,245],"2":[74,99,151],"\u03bb":[75,104,156,203,249,264],"against":[77],"known":[78],"attacks.":[79],"construct":[81],"following.":[83],"(1)":[84],"leveled":[86,138],"scheme":[88,140,223],"can":[90,142,252],"evaluate":[91,143],"depth-":[92,144],"L":[93,106,126,145,164,268],"arithmetic":[94,146],"(composed":[96,148],"fan-in":[98,150],"gates)":[100,152],"using":[101,153],"O":[102,154,262],"(":[103,155,202,248,263],".":[105,127,165],"3)":[107],"per-gate":[108,158,198,255],"computation,":[109,159],"quasilinear":[110],"parameter.":[114],"Security":[115,166],"RLWE":[119,170],"for":[120,171,185,233,285],"an":[121,179,231],"approximation":[122],"factor":[123],"exponential":[124],"This":[128,174],"construction":[129,175,280],"does":[130],"not":[131],"use":[132],"(2)":[136],"2)":[157],"which":[160],"independent":[162,266],"quasipolynomial":[172],"factors.":[173],"uses":[176],"as":[178],"optimization.":[180],"obtain":[182],"similar":[183],"results":[184],"LWE,":[186],"but":[187],"worse":[189],"performance.":[190],"All":[191],"previous":[192],"(leveled)":[193],"required":[196],"computation":[199,256],"\u03a9":[201,247],"3.5),":[204],"all":[206],"them":[208],"relied":[209],"subexponential":[211],"hardness":[212],"introduce":[215],"number":[217],"further":[219],"optimizations":[220],"assumption.":[229],"As":[230],"example,":[232],"large":[236],"width":[237,246],"(e.g.,":[238],"where":[239],"constant":[241],"fraction":[242],"levels":[244],")),":[250],"reduce":[253],"bootstrapped":[259],"version":[260],"),":[265],",":[269],"by":[270],"batching":[271],"operation.":[274],"At":[275],"core":[277],"managing":[286],"noise":[288],"lattice-based":[290],"ciphertexts,":[291],"significantly":[292],"extending":[293],"techniques":[295],"Brakerski":[297],"Vaikuntanathan":[299],"[2011b].":[300]},"counts_by_year":[{"year":2026,"cited_by_count":43},{"year":2025,"cited_by_count":241},{"year":2024,"cited_by_count":236},{"year":2023,"cited_by_count":196},{"year":2022,"cited_by_count":144},{"year":2021,"cited_by_count":146},{"year":2020,"cited_by_count":106},{"year":2019,"cited_by_count":100},{"year":2018,"cited_by_count":49},{"year":2017,"cited_by_count":33},{"year":2016,"cited_by_count":18},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":5}],"updated_date":"2026-04-14T08:04:32.555800","created_date":"2025-10-10T00:00:00"}
