{"id":"https://openalex.org/W4285156804","doi":"https://doi.org/10.1109/tifs.2022.3188145","title":"Efficient Homomorphic Evaluation on Large Intervals","display_name":"Efficient Homomorphic Evaluation on Large Intervals","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4285156804","doi":"https://doi.org/10.1109/tifs.2022.3188145"},"language":"en","primary_location":{"id":"doi:10.1109/tifs.2022.3188145","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tifs.2022.3188145","pdf_url":null,"source":{"id":"https://openalex.org/S61310614","display_name":"IEEE Transactions on Information Forensics and Security","issn_l":"1556-6013","issn":["1556-6013","1556-6021"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Forensics and Security","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/A5044011121","display_name":"Jung Hee Cheon","orcid":"https://orcid.org/0000-0002-7085-2220"},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]},{"id":"https://openalex.org/I4210158432","display_name":"National Institute for Mathematical Sciences","ror":"https://ror.org/04n7py080","country_code":"KR","type":"education","lineage":["https://openalex.org/I4210158432"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jung Hee Cheon","raw_affiliation_strings":["Department of Mathematical Sciences, Seoul National University, Seoul, South Korea"],"raw_orcid":"https://orcid.org/0000-0002-7085-2220","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Seoul National University, Seoul, South Korea","institution_ids":["https://openalex.org/I139264467","https://openalex.org/I4210158432"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021007728","display_name":"Wootae Kim","orcid":"https://orcid.org/0000-0003-4364-3260"},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]},{"id":"https://openalex.org/I4210158432","display_name":"National Institute for Mathematical Sciences","ror":"https://ror.org/04n7py080","country_code":"KR","type":"education","lineage":["https://openalex.org/I4210158432"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Wootae Kim","raw_affiliation_strings":["Department of Mathematical Sciences, Seoul National University, Seoul, South Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Seoul National University, Seoul, South Korea","institution_ids":["https://openalex.org/I139264467","https://openalex.org/I4210158432"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031915032","display_name":"Jai Hyun Park","orcid":"https://orcid.org/0000-0002-5401-8949"},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]},{"id":"https://openalex.org/I4210158432","display_name":"National Institute for Mathematical Sciences","ror":"https://ror.org/04n7py080","country_code":"KR","type":"education","lineage":["https://openalex.org/I4210158432"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jai Hyun Park","raw_affiliation_strings":["Department of Mathematical Sciences, Seoul National University, Seoul, South Korea"],"raw_orcid":"https://orcid.org/0000-0002-5401-8949","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Seoul National University, Seoul, South Korea","institution_ids":["https://openalex.org/I139264467","https://openalex.org/I4210158432"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5801,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.71247044,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"17","issue":null,"first_page":"2553","last_page":"2568"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9998999834060669,"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":0.9998999834060669,"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9962999820709229,"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":0.9957000017166138,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.8679366111755371},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6654451489448547},{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.5455470085144043},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5424741506576538},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5324004292488098},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5034946799278259},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.4634551703929901},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.456705778837204},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4417407512664795},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.42868319153785706},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4115203022956848},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36659061908721924},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.33235612511634827},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3207641839981079},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1355518102645874}],"concepts":[{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.8679366111755371},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6654451489448547},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.5455470085144043},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5424741506576538},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5324004292488098},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5034946799278259},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.4634551703929901},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.456705778837204},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4417407512664795},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.42868319153785706},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4115203022956848},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36659061908721924},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.33235612511634827},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3207641839981079},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1355518102645874},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","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},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tifs.2022.3188145","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tifs.2022.3188145","pdf_url":null,"source":{"id":"https://openalex.org/S61310614","display_name":"IEEE Transactions on Information Forensics and Security","issn_l":"1556-6013","issn":["1556-6013","1556-6021"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Forensics and Security","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.6899999976158142,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G6880026784","display_name":null,"funder_award_id":"2020-0-00840","funder_id":"https://openalex.org/F4320335489","funder_display_name":"Institute for Information and Communications Technology Promotion"}],"funders":[{"id":"https://openalex.org/F4320335489","display_name":"Institute for Information and Communications Technology Promotion","ror":"https://ror.org/01g0hqq23"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W2017150476","https://openalex.org/W2055580199","https://openalex.org/W2056232259","https://openalex.org/W2400700555","https://openalex.org/W2435473771","https://openalex.org/W2768174108","https://openalex.org/W2792798301","https://openalex.org/W2794974431","https://openalex.org/W2801958627","https://openalex.org/W2893368739","https://openalex.org/W2895782209","https://openalex.org/W2896938420","https://openalex.org/W2903536544","https://openalex.org/W2906397833","https://openalex.org/W2942255051","https://openalex.org/W2946972653","https://openalex.org/W2966536036","https://openalex.org/W2990280959","https://openalex.org/W3079221395","https://openalex.org/W3094696138","https://openalex.org/W3117449869","https://openalex.org/W3127843656","https://openalex.org/W3169180249","https://openalex.org/W6746138031"],"related_works":["https://openalex.org/W2595172197","https://openalex.org/W2084856301","https://openalex.org/W2127970246","https://openalex.org/W4382618745","https://openalex.org/W2885125400","https://openalex.org/W1001352512","https://openalex.org/W1989889224","https://openalex.org/W1973775000","https://openalex.org/W2748922771","https://openalex.org/W1987128138"],"abstract_inverted_index":{"Homomorphic":[0],"encryption":[1],"(HE)":[2],"is":[3,18,68,144,193],"being":[4],"widely":[5],"used":[6],"for":[7,213],"privacy-preserving":[8],"computation.":[9],"Since":[10],"HE":[11,73],"schemes":[12],"only":[13],"support":[14],"polynomial":[15,22,43],"operations,":[16],"it":[17,67],"prevalent":[19],"to":[20,50,226,267],"use":[21],"approximations":[23,44],"of":[24,54,72,92,97,103,128,135,140,219,270],"non-polynomial":[25],"functions.":[26],"We":[27,263],"cannot":[28],"monitor":[29],"the":[30,34,52,55,58,89,101,104,115,126,138,141,180,197,200,214,228,247,268,271],"intermediate":[31],"values":[32],"during":[33],"homomorphic":[35],"evaluation;":[36],"as":[37],"a":[38,69,95,129,133,162,224,232,242],"consequence,":[39],"we":[40,81,120,154,221,245],"should":[41],"utilize":[42],"with":[45,118,123],"sufficiently":[46],"large":[47,59,233,252,275],"approximation":[48,60,202],"intervals":[49],"prevent":[51],"failure":[53],"evaluation.":[56,215],"However,":[57],"interval":[61,91,234],"potentially":[62],"accompanies":[63],"computational":[64],"overheads,":[65],"and":[66,171,189,203,210],"serious":[70],"bottleneck":[71],"application":[74,218],"on":[75,107,182,251,274],"real-world":[76,243],"data.":[77],"In":[78],"this":[79],"work,":[80],"introduce":[82],"domain":[83,90,110,127,149],"extension":[84],"polynomials":[85],"(DEPs)":[86],"that":[87,164],"extend":[88,122],"functions":[93],"by":[94,132,236,259],"factor":[96,134],"<i>k</i>":[98],"while":[99,137],"preserving":[100],"feature":[102,139],"original":[105,109,142,148],"function":[106,131,143,163,181,273],"its":[108,147],"interval.":[111,150],"By":[112,151],"repeatedly":[113],"iterating":[114],"domainextension":[116],"process":[117],"DEPs,":[119,153,220],"can":[121,155],"<i>O</i>(log<i>K</i>)":[124],"operations":[125,188],"given":[130],"<i>K</i>":[136],"preserved":[145],"in":[146,158,175,255],"using":[152,237,260],"efficiently":[156],"evaluate":[157],"an":[159,256],"encrypted":[160,257],"state":[161,258],"converges":[165],"at":[166],"infinities,":[167],"i.e.,":[168],"lim<sub><i>x</i>&#x2192;&#x221E;</sub>":[169],"<i>f(x)</i>":[170,173],"lim<sub><i>x</i>&#x2192;-&#x221E;</sub>":[172],"exist":[174],"R.":[176],"To":[177],"uniformly":[178],"approximate":[179],"[&#x2013;<i>R,R</i>],":[183],"our":[184,261,265],"method":[185,225,266],"exploits":[186],"<i>O</i>(log<i>R</i>)":[187,238],"<i>O</i>(1)":[190],"memory.":[191],"This":[192],"more":[194],"efficient":[195],"than":[196],"previous":[198],"approach,":[199],"minimax":[201],"Paterson-Stockmeyer":[204],"algorithm,":[205],"which":[206],"uses":[207],"&#x03A9;(&#x221A;<i>R</i>)":[208,211],"multiplications":[209],"memory":[212],"As":[216,241],"another":[217],"also":[222],"suggest":[223],"manage":[227],"risky":[229],"outliers":[230],"from":[231],"[&#x2013;<i>R,R</i>]":[235],"additional":[239],"multiplications.":[240],"application,":[244],"trained":[246],"logistic":[248,272],"regression":[249],"classifier":[250],"public":[253],"datasets":[254],"method.":[262],"exploit":[264],"evaluation":[269],"intervals,":[276],"e.g.,":[277],"[-7683,":[278],"7683].":[279]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}