{"id":"https://openalex.org/W3193495651","doi":"https://doi.org/10.1109/tifs.2021.3106167","title":"Efficient Sorting of Homomorphic Encrypted Data With <i>k</i>-Way Sorting Network","display_name":"Efficient Sorting of Homomorphic Encrypted Data With <i>k</i>-Way Sorting Network","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3193495651","doi":"https://doi.org/10.1109/tifs.2021.3106167","mag":"3193495651"},"language":"en","primary_location":{"id":"doi:10.1109/tifs.2021.3106167","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tifs.2021.3106167","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/A5081078847","display_name":"Seungwan Hong","orcid":"https://orcid.org/0000-0001-8560-7925"},"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":"Seungwan Hong","raw_affiliation_strings":["Department of Mathematical Sciences, Seoul National University, Seoul, South Korea"],"raw_orcid":"https://orcid.org/0000-0001-8560-7925","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/A5041693939","display_name":"Seunghong Kim","orcid":null},"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":"Seunghong 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":"middle","author":{"id":"https://openalex.org/A5023981513","display_name":"Jiheon Choi","orcid":null},"institutions":[{"id":"https://openalex.org/I148751991","display_name":"Sogang University","ror":"https://ror.org/056tn4839","country_code":"KR","type":"education","lineage":["https://openalex.org/I148751991"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jiheon Choi","raw_affiliation_strings":["Department of Mathematics, Sogang University, Seoul, South Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sogang University, Seoul, South Korea","institution_ids":["https://openalex.org/I148751991"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007851185","display_name":"Younho Lee","orcid":"https://orcid.org/0000-0003-1767-6165"},"institutions":[{"id":"https://openalex.org/I118373667","display_name":"Seoul National University of Science and Technology","ror":"https://ror.org/00chfja07","country_code":"KR","type":"education","lineage":["https://openalex.org/I118373667"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Younho Lee","raw_affiliation_strings":["Department of Industrial Engineering, ITM Division, SeoulTech, Seoul, South Korea"],"raw_orcid":"https://orcid.org/0000-0003-1767-6165","affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, ITM Division, SeoulTech, Seoul, South Korea","institution_ids":["https://openalex.org/I118373667"]}]},{"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":["CryptoLab, Seoul National University, Seoul, South Korea"],"raw_orcid":"https://orcid.org/0000-0002-7085-2220","affiliations":[{"raw_affiliation_string":"CryptoLab, Seoul National University, Seoul, South Korea","institution_ids":["https://openalex.org/I139264467"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8674,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.92119415,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":100},"biblio":{"volume":"16","issue":null,"first_page":"4389","last_page":"4404"},"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9937999844551086,"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":0.9919999837875366,"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":0.8247083425521851},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.7654596567153931},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.650398313999176},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.5755717158317566},{"id":"https://openalex.org/keywords/sort","display_name":"sort","score":0.5042966604232788},{"id":"https://openalex.org/keywords/sorting-algorithm","display_name":"Sorting algorithm","score":0.48121407628059387},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4556998014450073},{"id":"https://openalex.org/keywords/sorting-network","display_name":"Sorting network","score":0.43493399024009705},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.41537004709243774},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39479711651802063},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3787754774093628},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3696538805961609},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34304314851760864},{"id":"https://openalex.org/keywords/information-retrieval","display_name":"Information retrieval","score":0.2725899815559387},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23499521613121033},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.12732258439064026}],"concepts":[{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.8247083425521851},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.7654596567153931},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.650398313999176},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.5755717158317566},{"id":"https://openalex.org/C88548561","wikidata":"https://www.wikidata.org/wiki/Q347599","display_name":"sort","level":2,"score":0.5042966604232788},{"id":"https://openalex.org/C108094655","wikidata":"https://www.wikidata.org/wiki/Q181593","display_name":"Sorting algorithm","level":3,"score":0.48121407628059387},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4556998014450073},{"id":"https://openalex.org/C64540648","wikidata":"https://www.wikidata.org/wiki/Q646477","display_name":"Sorting network","level":4,"score":0.43493399024009705},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41537004709243774},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39479711651802063},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3787754774093628},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3696538805961609},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34304314851760864},{"id":"https://openalex.org/C23123220","wikidata":"https://www.wikidata.org/wiki/Q816826","display_name":"Information retrieval","level":1,"score":0.2725899815559387},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23499521613121033},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.12732258439064026}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tifs.2021.3106167","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tifs.2021.3106167","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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W56544557","https://openalex.org/W104209573","https://openalex.org/W148003122","https://openalex.org/W913176383","https://openalex.org/W1575598731","https://openalex.org/W1621599745","https://openalex.org/W1895952394","https://openalex.org/W2029176461","https://openalex.org/W2059451742","https://openalex.org/W2156030242","https://openalex.org/W2177209050","https://openalex.org/W2226167778","https://openalex.org/W2233194383","https://openalex.org/W2290980804","https://openalex.org/W2342763106","https://openalex.org/W2397066487","https://openalex.org/W2401959250","https://openalex.org/W2435473771","https://openalex.org/W2554750353","https://openalex.org/W2620783544","https://openalex.org/W2768174108","https://openalex.org/W2792798301","https://openalex.org/W2794974431","https://openalex.org/W2801958627","https://openalex.org/W2893368739","https://openalex.org/W2894537844","https://openalex.org/W2896938420","https://openalex.org/W2903536544","https://openalex.org/W2939905551","https://openalex.org/W2950819909","https://openalex.org/W2952761761","https://openalex.org/W2989605743","https://openalex.org/W2990280959","https://openalex.org/W3006531732","https://openalex.org/W3028867652","https://openalex.org/W3116399859","https://openalex.org/W3117449869","https://openalex.org/W3127074922","https://openalex.org/W3176470128","https://openalex.org/W3197799064","https://openalex.org/W6755106959","https://openalex.org/W6764236736","https://openalex.org/W6770640134","https://openalex.org/W6778434676","https://openalex.org/W6787227821","https://openalex.org/W6787658090","https://openalex.org/W6787835554","https://openalex.org/W6790066906"],"related_works":["https://openalex.org/W2085265870","https://openalex.org/W2396743875","https://openalex.org/W2362374543","https://openalex.org/W2094179388","https://openalex.org/W2126436988","https://openalex.org/W2325315917","https://openalex.org/W2372558933","https://openalex.org/W2348196682","https://openalex.org/W2385397541","https://openalex.org/W4391130025"],"abstract_inverted_index":{"In":[0,80],"this":[1,63,150],"study,":[2],"we":[3,152,166,187],"propose":[4,153,167,188],"an":[5,154,168,189],"efficient":[6,155,169],"sorting":[7,24,30,87,174,240,246,254],"method":[8,19,25,64,184],"for":[9,32,52,123],"encrypted":[10],"data":[11,243,257],"using":[12,176,244,258],"fully":[13],"homomorphic":[14,77,107,163],"encryption":[15],"(FHE).":[16],"The":[17,105],"proposed":[18,183,234],"extends":[20],"the":[21,28,38,85,89,111,124,127,133,136,142,159,182,194,202,207,210,214,217,221,229,233],"existing":[22],"2-way":[23],"by":[26,220],"applying":[27],"k-way":[29,86,173],"network":[31,175,247],"any":[33],"prime":[34],"k":[35,53,196],"to":[36,47,65,73,82,200],"reduce":[37,201],"depth":[39],"in":[40,144],"terms":[41],"of":[42,76,114,126,135,161,171,209,216,232],"comparison":[43,97,115,137,143],"operation":[44],"from":[45],"O(log22n)":[46],"O(klogk2n),":[48],"thereby":[49],"improving":[50],"performance":[51,215],"slightly":[54],"larger":[55],"than":[56,253],"2,":[57],"such":[58],"as":[59,101,129],"k=5.":[60],"We":[61,226],"apply":[62],"approximate":[66,106,118,162,222],"FHE":[67,223],"which":[68,91,109],"is":[69,99,110,131,138,198],"widely":[70],"used":[71,100,122],"due":[72],"its":[74],"efficiency":[75],"arithmetic":[78],"operations.":[79,179],"order":[81],"build":[83],"up":[84],"network,":[88],"k-sorter,":[90],"sorts":[92],"k-numbers":[93],"with":[94],"a":[95,102,172],"minimal":[96],"depth,":[98],"building":[103],"block.":[104],"comparison,":[108],"only":[112],"type":[113],"working":[116],"on":[117],"FHE,":[119],"cannot":[120],"be":[121,249],"construction":[125,157,170],"k-sorter":[128,156],"it":[130,237],"because":[132],"result":[134],"not":[139],"binary,":[140],"unlike":[141],"conventional":[145],"bit-wise":[146],"FHEs.":[147],"To":[148,180],"overcome":[149],"problem,":[151],"utilizing":[158],"features":[160],"comparison.":[164],"Also,":[165],"cryptographic":[177],"SIMD":[178],"use":[181],"most":[185],"efficiently,":[186],"estimation":[190],"formula":[191],"that":[192,197,239],"finds":[193],"appropriate":[195],"expected":[199],"total":[203],"time":[204],"cost":[205],"when":[206],"parameters":[208],"approximating":[211],"comparisons":[212],"and":[213,236],"operations":[218],"provided":[219],"are":[224],"given.":[225],"also":[227],"show":[228],"implementation":[230],"results":[231],"method,":[235],"shows":[238],"56=":[241],"15625":[242],"5-way":[245],"can":[248],"about":[250],"23.3%":[251],"faster":[252],"214=":[255],"16384":[256],"2-way.":[259]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":17},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}