{"id":"https://openalex.org/W3110753291","doi":"https://doi.org/10.1109/tpds.2020.3030748","title":"Homomorphic Sorting With Better Scalability","display_name":"Homomorphic Sorting With Better Scalability","publication_year":2020,"publication_date":"2020-10-13","ids":{"openalex":"https://openalex.org/W3110753291","doi":"https://doi.org/10.1109/tpds.2020.3030748","mag":"3110753291"},"language":"en","primary_location":{"id":"doi:10.1109/tpds.2020.3030748","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpds.2020.3030748","pdf_url":null,"source":{"id":"https://openalex.org/S97130795","display_name":"IEEE Transactions on Parallel and Distributed Systems","issn_l":"1045-9219","issn":["1045-9219","1558-2183","2161-9883"],"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 Parallel and Distributed Systems","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/A5022944870","display_name":"Gizem S. \u00c7etin","orcid":"https://orcid.org/0000-0001-8264-2901"},"institutions":[{"id":"https://openalex.org/I107077323","display_name":"Worcester Polytechnic Institute","ror":"https://ror.org/05ejpqr48","country_code":"US","type":"education","lineage":["https://openalex.org/I107077323"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gizem S. Cetin","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, MA, USA"],"raw_orcid":"https://orcid.org/0000-0001-8264-2901","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, MA, USA","institution_ids":["https://openalex.org/I107077323"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064835031","display_name":"Erkay Sava\u015f","orcid":"https://orcid.org/0000-0002-4869-5556"},"institutions":[{"id":"https://openalex.org/I134235054","display_name":"Sabanc\u0131 \u00dcniversitesi","ror":"https://ror.org/049asqa32","country_code":"TR","type":"education","lineage":["https://openalex.org/I134235054"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Erkay Savas","raw_affiliation_strings":["Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul, Turkey"],"raw_orcid":"https://orcid.org/0000-0002-4869-5556","affiliations":[{"raw_affiliation_string":"Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul, Turkey","institution_ids":["https://openalex.org/I134235054"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066592325","display_name":"Berk Sunar","orcid":"https://orcid.org/0000-0001-5404-5368"},"institutions":[{"id":"https://openalex.org/I107077323","display_name":"Worcester Polytechnic Institute","ror":"https://ror.org/05ejpqr48","country_code":"US","type":"education","lineage":["https://openalex.org/I107077323"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Berk Sunar","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, MA, USA"],"raw_orcid":"https://orcid.org/0000-0001-5404-5368","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, MA, USA","institution_ids":["https://openalex.org/I107077323"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5416,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.74741929,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"32","issue":"4","first_page":"760","last_page":"771"},"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":0.9962000250816345,"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/T11181","display_name":"Advanced Data Storage Technologies","score":0.9778000116348267,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/computer-science","display_name":"Computer science","score":0.8152710199356079},{"id":"https://openalex.org/keywords/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.8108766078948975},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.6730517148971558},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.6700015068054199},{"id":"https://openalex.org/keywords/sorting-algorithm","display_name":"Sorting algorithm","score":0.6610342860221863},{"id":"https://openalex.org/keywords/sort","display_name":"sort","score":0.5692227482795715},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5398582220077515},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5084018111228943},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5022363662719727},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5013034343719482},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.4459640085697174},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.43596765398979187},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.30783575773239136},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.13768967986106873},{"id":"https://openalex.org/keywords/database","display_name":"Database","score":0.07879084348678589}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8152710199356079},{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.8108766078948975},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.6730517148971558},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.6700015068054199},{"id":"https://openalex.org/C108094655","wikidata":"https://www.wikidata.org/wiki/Q181593","display_name":"Sorting algorithm","level":3,"score":0.6610342860221863},{"id":"https://openalex.org/C88548561","wikidata":"https://www.wikidata.org/wiki/Q347599","display_name":"sort","level":2,"score":0.5692227482795715},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5398582220077515},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5084018111228943},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5022363662719727},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5013034343719482},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.4459640085697174},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43596765398979187},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.30783575773239136},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.13768967986106873},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.07879084348678589},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/tpds.2020.3030748","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpds.2020.3030748","pdf_url":null,"source":{"id":"https://openalex.org/S97130795","display_name":"IEEE Transactions on Parallel and Distributed Systems","issn_l":"1045-9219","issn":["1045-9219","1558-2183","2161-9883"],"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 Parallel and Distributed Systems","raw_type":"journal-article"},{"id":"pmh:oai:research.sabanciuniv.edu:43199","is_oa":false,"landing_page_url":"https://research.sabanciuniv.edu/id/eprint/43199/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402254","display_name":"Sabanci University","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I134235054","host_organization_name":"Sabanc\u0131 \u00dcniversitesi","host_organization_lineage":["https://openalex.org/I134235054"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6718884448","display_name":null,"funder_award_id":"#1561536","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W17575016","https://openalex.org/W56544557","https://openalex.org/W104209573","https://openalex.org/W236632755","https://openalex.org/W1494049356","https://openalex.org/W1755636270","https://openalex.org/W1853548709","https://openalex.org/W1966731635","https://openalex.org/W1979120705","https://openalex.org/W1992282993","https://openalex.org/W2031533839","https://openalex.org/W2048994663","https://openalex.org/W2129580084","https://openalex.org/W2146828512","https://openalex.org/W2152926062","https://openalex.org/W2156030242","https://openalex.org/W2226167778","https://openalex.org/W2290980804","https://openalex.org/W2309997581","https://openalex.org/W2398715209","https://openalex.org/W2401959250","https://openalex.org/W2519249189","https://openalex.org/W2613808774","https://openalex.org/W2752061190","https://openalex.org/W2780581388","https://openalex.org/W2794939374","https://openalex.org/W2798340061","https://openalex.org/W2921215910","https://openalex.org/W2930800432","https://openalex.org/W2949606534","https://openalex.org/W2949840108","https://openalex.org/W2953290839","https://openalex.org/W2965421783","https://openalex.org/W3028867652","https://openalex.org/W3029884494","https://openalex.org/W3030360955","https://openalex.org/W3195623142","https://openalex.org/W6602271536","https://openalex.org/W6629429546","https://openalex.org/W6637825192","https://openalex.org/W6641894941","https://openalex.org/W6688800661","https://openalex.org/W6698270547","https://openalex.org/W6712714140","https://openalex.org/W6713019613","https://openalex.org/W6747729907","https://openalex.org/W6760714629","https://openalex.org/W6778434676"],"related_works":["https://openalex.org/W2908348257","https://openalex.org/W2994182992","https://openalex.org/W2350549588","https://openalex.org/W4281648223","https://openalex.org/W2362374543","https://openalex.org/W3206496585","https://openalex.org/W2085265870","https://openalex.org/W2187267622","https://openalex.org/W2351942115","https://openalex.org/W3002909018"],"abstract_inverted_index":{"Homomorphic":[0],"sorting":[1,39,62,89,102],"is":[2,19,111,127,133,149,171,214],"an":[3,57],"operation":[4],"that":[5,66,107,144,167],"blindly":[6],"sorts":[7],"a":[8,31,52],"given":[9],"set":[10],"of":[11,40,60,81,115,131,147,157,174],"encrypted":[12],"numbers":[13],"without":[14],"decrypting":[15],"them":[16],"(thus,":[17],"there":[18],"no":[20],"need":[21],"for":[22,37,71,87,203],"the":[23,48,108,129,145,155,160,168,181,184,191,195,198,206,225],"secret":[24],"key).":[25],"In":[26],"this":[27],"article,":[28],"we":[29,55],"propose":[30],"new,":[32],"efficient,":[33],"and":[34,64,92,95],"scalable":[35],"method":[36],"homomorphic":[38,72,88],"numbers:":[41],"polynomial":[42,185],"rank":[43],"sort":[44,186],"algorithm.":[45],"To":[46],"put":[47],"new":[49,109,169],"algorithm":[50,110,170,187,193,213,226],"in":[51,77,113,159,180,194,224],"comparative":[53],"perspective,":[54],"provide":[56],"extensive":[58],"survey":[59],"classical":[61,101],"algorithms":[63,84],"networks":[65],"are":[67,209],"not":[68],"directly":[69],"suitable":[70],"computation.":[73],"We":[74,104],"also":[75],"include,":[76],"our":[78,82,200],"discussions,":[79],"two":[80],"previous":[83],"specifically":[85],"designed":[86],"operation:":[90],"direct":[91],"greedy":[93],"sort,":[94],"explain":[96],"how":[97],"they":[98],"evolve":[99],"from":[100,135],"networks.":[103],"theoretically":[105],"show":[106],"superior":[112],"terms":[114],"multiplicative":[116],"depth":[117],"when":[118],"compared":[119],"with":[120],"all":[121],"other":[122],"algorithms.":[123],"When":[124],"batched":[125],"implementation":[126,164,218],"used,":[128],"number":[130,146,156],"comparisons":[132],"reduced":[134],"O(N":[136],"<sub":[137],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[138],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[139],")":[140],"to":[141,154,197,216],"O(N)":[142],"provided":[143],"slots":[148],"larger":[150],"than":[151,177,190],"or":[152],"equal":[153],"elements":[158],"set.":[161],"Our":[162],"software":[163],"results":[165],"confirm":[166],"several":[172],"orders":[173],"magnitude":[175],"faster":[176],"many":[178],"methods":[179],"literature.":[182],"Also,":[183],"scales":[188],"better":[189],"fastest":[192],"literature":[196],"best":[199],"knowledge":[201],"although":[202],"small":[204],"sets":[205],"execution":[207],"times":[208],"comparable.":[210],"The":[211],"proposed":[212],"amenable":[215],"parallel":[217],"as":[219],"most":[220],"time":[221],"consuming":[222],"operations":[223],"can":[227],"naturally":[228],"be":[229],"performed":[230],"concurrently.":[231]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
