{"id":"https://openalex.org/W2942711826","doi":"https://doi.org/10.1109/access.2019.2913850","title":"Improved Homomorphic Discrete Fourier Transforms and FHE Bootstrapping","display_name":"Improved Homomorphic Discrete Fourier Transforms and FHE Bootstrapping","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2942711826","doi":"https://doi.org/10.1109/access.2019.2913850","mag":"2942711826"},"language":"en","primary_location":{"id":"doi:10.1109/access.2019.2913850","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2913850","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08701685.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08701685.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103193729","display_name":"Kyoohyung Han","orcid":"https://orcid.org/0000-0002-8410-3386"},"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"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Kyoohyung Han","raw_affiliation_strings":["Seoul National University, Seoul, South Korea"],"raw_orcid":"https://orcid.org/0000-0002-8410-3386","affiliations":[{"raw_affiliation_string":"Seoul National University, Seoul, South Korea","institution_ids":["https://openalex.org/I139264467"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008194370","display_name":"Minki Hhan","orcid":"https://orcid.org/0000-0001-5143-4587"},"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"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Minki Hhan","raw_affiliation_strings":["Seoul National University, Seoul, South Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Seoul National University, Seoul, South Korea","institution_ids":["https://openalex.org/I139264467"]}]},{"author_position":"last","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"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jung Hee Cheon","raw_affiliation_strings":["Seoul National University, Seoul, South Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Seoul National University, Seoul, South Korea","institution_ids":["https://openalex.org/I139264467"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I139264467"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":2.965,"has_fulltext":true,"cited_by_count":64,"citation_normalized_percentile":{"value":0.92952593,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"7","issue":null,"first_page":"57361","last_page":"57370"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.991100013256073,"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":0.9907000064849854,"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":0.8745704889297485},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5756732821464539},{"id":"https://openalex.org/keywords/bootstrapping","display_name":"Bootstrapping (finance)","score":0.49372634291648865},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.4704678952693939},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.4510851800441742},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4193170368671417},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3932205140590668},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31201043725013733}],"concepts":[{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.8745704889297485},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5756732821464539},{"id":"https://openalex.org/C207609745","wikidata":"https://www.wikidata.org/wiki/Q4944086","display_name":"Bootstrapping (finance)","level":2,"score":0.49372634291648865},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.4704678952693939},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.4510851800441742},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4193170368671417},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3932205140590668},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31201043725013733},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2019.2913850","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2913850","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08701685.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:5e893040083d42579730b03861e95614","is_oa":true,"landing_page_url":"https://doaj.org/article/5e893040083d42579730b03861e95614","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 7, Pp 57361-57370 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2019.2913850","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2913850","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08701685.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5962900564","display_name":null,"funder_award_id":"2017-0-00616","funder_id":"https://openalex.org/F4320335489","funder_display_name":"Institute for Information and Communications Technology Promotion"}],"funders":[{"id":"https://openalex.org/F4320328359","display_name":"Ministry of Science and ICT, South Korea","ror":"https://ror.org/01wpjm123"},{"id":"https://openalex.org/F4320335489","display_name":"Institute for Information and Communications Technology Promotion","ror":"https://ror.org/01g0hqq23"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2942711826.pdf","grobid_xml":"https://content.openalex.org/works/W2942711826.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W774911181","https://openalex.org/W913176383","https://openalex.org/W1755636270","https://openalex.org/W2031533839","https://openalex.org/W2061171222","https://openalex.org/W2142432849","https://openalex.org/W2152407566","https://openalex.org/W2152926062","https://openalex.org/W2226167778","https://openalex.org/W2400700555","https://openalex.org/W2554750353","https://openalex.org/W2571885312","https://openalex.org/W2578913585","https://openalex.org/W2768174108","https://openalex.org/W2794634409","https://openalex.org/W2794927157","https://openalex.org/W2794974431","https://openalex.org/W3028867652","https://openalex.org/W6637825192","https://openalex.org/W6682768834","https://openalex.org/W6688800661","https://openalex.org/W6732578018","https://openalex.org/W6778434676"],"related_works":["https://openalex.org/W1534274833","https://openalex.org/W3117246195","https://openalex.org/W156620619","https://openalex.org/W2152926062","https://openalex.org/W2949607150","https://openalex.org/W2950312267","https://openalex.org/W3123945077","https://openalex.org/W2398715209","https://openalex.org/W3203896436","https://openalex.org/W913176383"],"abstract_inverted_index":{"Homomorphic":[0],"encryption":[1,186],"(HE),":[2],"which":[3,241,267],"enables":[4],"computation":[5],"on":[6,53,204],"ciphertexts":[7],"without":[8],"any":[9],"leakage,":[10],"rise":[11],"as":[12,41],"a":[13,59,85,92,125,181],"most":[14],"promising":[15],"solution":[16],"for":[17,67,107,187,257],"privacy-preserving":[18],"data":[19],"processing,":[20],"including":[21],"secure":[22,26],"machine":[23],"learning":[24],"and":[25,69,89,112,123,151,192],"out-sourcing":[27],"computation.":[28],"Despite":[29],"the":[30,35,54,62,82,104,130,168,179,197,207,220,225,247,251,276],"extensive":[31],"applicability":[32],"of":[33,65,84,91,129,206,216],"HE,":[34,68],"current":[36],"constructions":[37],"are":[38],"sometimes":[39],"considered":[40],"impractical":[42],"due":[43],"to":[44,224],"its":[45],"inefficiency.":[46],"In":[47],"this":[48],"paper,":[49],"we":[50,118,200],"propose":[51],"improvements":[52,222],"linear":[55,108,131],"transformation":[56,73,109,132],"in":[57,110,133,178],"bootstrapping,":[58],"technique":[60],"allowing":[61],"infinite":[63],"number":[64],"operation":[66],"homomorphic":[70,77,99,113,185,229],"discrete":[71],"Fourier":[72],"(DFT)":[74],"using":[75,275],"batch":[76],"encryption.":[78],"We":[79],"observe":[80],"that":[81,183],"multiplication":[83,150],"sparse":[86],"diagonal":[87],"matrix":[88,121],"ciphertext":[90],"vector":[93,149,170],"can":[94],"be":[95],"done":[96],"within":[97],"O(1)":[98],"computations.":[100],"This":[101],"observation":[102],"induces":[103],"faster":[105,245],"algorithm":[106],"bootstrapping":[111,252],"DFT.":[114],"To":[115,195],"achieve":[116],"this,":[117],"use":[119],"Cooley-Tukey":[120],"factorization":[122,128],"construct":[124],"new":[126],"recursive":[127],"bootstrapping.":[134],"Our":[135,209],"method":[136,176,203],"with":[137,212,231,264,271],"radix":[138],"r":[139],"only":[140,237],"requires":[141,190],"O(r":[142],"log":[143,153],"<sub":[144,154,162],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[145,155,163,235,260],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">r</sub>":[146,156,164],"n)":[147,157,165],"constant":[148],"O(\u221ar":[152],"rotations":[158],"by":[159],"consuming":[160],"O(log":[161],"depth":[166],"when":[167],"input":[169],"size":[171],"is":[172],"n.":[173],"The":[174],"previous":[175,226,248,277],"used":[177],"library,":[180],"library":[182],"implements":[184],"approximate":[188],"computation,":[189],"O(n)":[191],"O(\u221an),":[193],"respectively.":[194],"show":[196,219],"performance":[198],"improvement,":[199],"implement":[201],"our":[202],"top":[205],"library.":[208],"implementation,":[210],"along":[211],"further":[213],"few":[214],"techniques,":[215],"these":[217],"algorithms":[218],"significant":[221],"compared":[223],"algorithm.":[227],"New":[228],"DFT":[230],"length":[232],"2":[233,255],"<sup":[234,259],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">14</sup>":[236],"takes":[238,253,268],"about":[239,254],"8s":[240],"results":[242],"150":[243],"times":[244],"than":[246],"method.":[249,278],"Furthermore,":[250],"minutes":[256],"\u2102":[258],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">32768</sup>":[261],"plaintext":[262],"space":[263],"8-bit":[265],"precision,":[266],"26":[269],"hours":[270],"same":[272],"bit":[273],"precision":[274]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":17},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}