{"id":"https://openalex.org/W7140143706","doi":"https://doi.org/10.3390/e28030358","title":"Secure Multiplicative Aggregation and Key-Reuse Optimization: Achieving Dropout Resilience with Amortized Efficiency","display_name":"Secure Multiplicative Aggregation and Key-Reuse Optimization: Achieving Dropout Resilience with Amortized Efficiency","publication_year":2026,"publication_date":"2026-03-22","ids":{"openalex":"https://openalex.org/W7140143706","doi":"https://doi.org/10.3390/e28030358","pmid":"https://pubmed.ncbi.nlm.nih.gov/41900010"},"language":"en","primary_location":{"id":"doi:10.3390/e28030358","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030358","pdf_url":null,"source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/e28030358","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070427118","display_name":"Hongyuan Cai","orcid":"https://orcid.org/0009-0008-1226-8545"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongyuan Cai","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China"],"raw_orcid":"https://orcid.org/0009-0008-1226-8545","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054747769","display_name":"Bei Liang","orcid":"https://orcid.org/0000-0002-8622-8596"},"institutions":[{"id":"https://openalex.org/I4403928416","display_name":"Beijing Institute of Mathematical Sciences and Applications","ror":"https://ror.org/05t6hvr95","country_code":null,"type":"education","lineage":["https://openalex.org/I4403928416","https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bei Liang","raw_affiliation_strings":["Beijing Institute of Mathematical Sciences and Applications, Beijing 101408, China"],"raw_orcid":"https://orcid.org/0000-0002-8622-8596","affiliations":[{"raw_affiliation_string":"Beijing Institute of Mathematical Sciences and Applications, Beijing 101408, China","institution_ids":["https://openalex.org/I4403928416"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130353572","display_name":"Yue Qin","orcid":null},"institutions":[{"id":"https://openalex.org/I4403928416","display_name":"Beijing Institute of Mathematical Sciences and Applications","ror":"https://ror.org/05t6hvr95","country_code":null,"type":"education","lineage":["https://openalex.org/I4403928416","https://openalex.org/I99065089"]},{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yue Qin","raw_affiliation_strings":["Beijing Institute of Mathematical Sciences and Applications, Beijing 101408, China","School of Cyber Science and Technology, Beihang University, Beijing 100191, China"],"raw_orcid":"https://orcid.org/0000-0002-3593-9902","affiliations":[{"raw_affiliation_string":"Beijing Institute of Mathematical Sciences and Applications, Beijing 101408, China","institution_ids":["https://openalex.org/I4403928416"]},{"raw_affiliation_string":"School of Cyber Science and Technology, Beihang University, Beijing 100191, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055357255","display_name":"J\u00edntai Ding","orcid":"https://orcid.org/0000-0003-1257-7598"},"institutions":[{"id":"https://openalex.org/I69356397","display_name":"Xi\u2019an Jiaotong-Liverpool University","ror":"https://ror.org/03zmrmn05","country_code":"CN","type":"education","lineage":["https://openalex.org/I69356397"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jintai Ding","raw_affiliation_strings":["School of Mathematics and Physics, Xi\u2019an Jiaotong-Liverpool University, Suzhou 215123, China"],"raw_orcid":"https://orcid.org/0000-0003-1257-7598","affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Xi\u2019an Jiaotong-Liverpool University, Suzhou 215123, China","institution_ids":["https://openalex.org/I69356397"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5054747769"],"corresponding_institution_ids":["https://openalex.org/I4403928416"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.31463907,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"3","first_page":"358","last_page":"358"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11498","display_name":"Security in Wireless Sensor Networks","score":0.5073999762535095,"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"}},"topics":[{"id":"https://openalex.org/T11498","display_name":"Security in Wireless Sensor Networks","score":0.5073999762535095,"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"}},{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.21799999475479126,"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/T10927","display_name":"Access Control and Trust","score":0.06080000102519989,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.7106999754905701},{"id":"https://openalex.org/keywords/overhead","display_name":"Overhead (engineering)","score":0.6658999919891357},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5044999718666077},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.4952999949455261},{"id":"https://openalex.org/keywords/universal-composability","display_name":"Universal composability","score":0.4844000041484833},{"id":"https://openalex.org/keywords/resilience","display_name":"Resilience (materials science)","score":0.4706000089645386},{"id":"https://openalex.org/keywords/protocol","display_name":"Protocol (science)","score":0.45980000495910645},{"id":"https://openalex.org/keywords/flexibility","display_name":"Flexibility (engineering)","score":0.3840000033378601}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7767000198364258},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.7106999754905701},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.6658999919891357},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5044999718666077},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.4952999949455261},{"id":"https://openalex.org/C165751822","wikidata":"https://www.wikidata.org/wiki/Q7894118","display_name":"Universal composability","level":4,"score":0.4844000041484833},{"id":"https://openalex.org/C2779585090","wikidata":"https://www.wikidata.org/wiki/Q3457762","display_name":"Resilience (materials science)","level":2,"score":0.4706000089645386},{"id":"https://openalex.org/C2780385302","wikidata":"https://www.wikidata.org/wiki/Q367158","display_name":"Protocol (science)","level":3,"score":0.45980000495910645},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.44449999928474426},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.41290000081062317},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.3840000033378601},{"id":"https://openalex.org/C18396474","wikidata":"https://www.wikidata.org/wiki/Q2465888","display_name":"Secure multi-party computation","level":3,"score":0.3675999939441681},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3671000003814697},{"id":"https://openalex.org/C206588197","wikidata":"https://www.wikidata.org/wiki/Q846574","display_name":"Reuse","level":2,"score":0.3472000062465668},{"id":"https://openalex.org/C93996380","wikidata":"https://www.wikidata.org/wiki/Q44127","display_name":"Server","level":2,"score":0.3248000144958496},{"id":"https://openalex.org/C510870077","wikidata":"https://www.wikidata.org/wiki/Q7444868","display_name":"Secure communication","level":3,"score":0.2888999879360199},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.2816999852657318},{"id":"https://openalex.org/C12269588","wikidata":"https://www.wikidata.org/wiki/Q132364","display_name":"Communications protocol","level":2,"score":0.2639999985694885},{"id":"https://openalex.org/C94284585","wikidata":"https://www.wikidata.org/wiki/Q228184","display_name":"Random oracle","level":4,"score":0.26019999384880066},{"id":"https://openalex.org/C82578977","wikidata":"https://www.wikidata.org/wiki/Q16773055","display_name":"Data aggregator","level":3,"score":0.2563999891281128},{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.25609999895095825}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e28030358","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030358","pdf_url":null,"source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:41900010","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41900010","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:0ab3923ea2fa4b1cbfa5535902196a12","is_oa":true,"landing_page_url":"https://doaj.org/article/0ab3923ea2fa4b1cbfa5535902196a12","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":"Entropy, Vol 28, Iss 3, p 358 (2026)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:13025810","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13025810/","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e28030358","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030358","pdf_url":null,"source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1946934755","display_name":null,"funder_award_id":"2023YFC3305501","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,61,103,194],"present":[1],"the":[2,21,25,32,47,68,99,118,167,188,217,228,241,250,257],"first":[3],"secure":[4,12,48,57,64,89,199],"multiplicative":[5,113],"aggregation":[6,49,65,81,90,114,200],"protocol":[7,38,50,201],"as":[8],"a":[9,17,105,157,173],"variant":[10],"of":[11,24,28,35,101,108,120],"aggregation.":[13],"In":[14,148],"this":[15],"case,":[16],"server":[18,150,179,185,230,242],"can":[19,74],"compute":[20],"component-wise":[22],"product":[23],"input":[26,129,168],"vectors":[27],"users":[29,36,73,121],"while":[30,184,239],"handling":[31],"possible":[33],"dropout":[34,146],"during":[37],"execution.":[39],"Using":[40],"pairwise":[41],"masks,":[42],"threshold":[43],"secret":[44],"sharing":[45],"and":[46,56,84,141,155,178,197,209,226],"itself,":[51],"our":[52,109],"construction":[53],"is":[54,142,152,254],"correct":[55],"against":[58],"semi-honest":[59],"adversaries.":[60],"also":[62],"consider":[63],"protocols":[66,93],"for":[67],"case":[69],"in":[70,98],"which":[71,247],"fixed":[72,128,174],"reuse":[75],"their":[76],"private":[77],"keys":[78],"to":[79,125,145,163],"do":[80],"many":[82],"times,":[83],"we":[85],"propose":[86],"key":[87],"reusable":[88,196],"protocols.":[91,111],"Our":[92],"have":[94],"an":[95],"overhead":[96,232,244,253],"polynomial":[97],"number":[100,119],"users.":[102],"conduct":[104],"comprehensive":[106],"evaluation":[107],"proposed":[110],"For":[112],"protocol,":[115],"experiments":[116],"varying":[117,166],"(K)":[122],"from":[123],"50":[124],"300":[126],"(with":[127],"size":[130,169],"Xu=100":[131,207],"KB)":[132,171],"demonstrate":[133],"that":[134,212,249],"user":[135,177,219],"computation":[136,151,186,220,231],"scales":[137],"monotonically":[138],"with":[139,161,172],"K":[140],"largely":[143],"insensitive":[144],"rates.":[147],"contrast,":[149],"highly":[153],"dropout-sensitive":[154],"exhibits":[156],"steeper":[158],"growth":[159],"rate":[160],"respect":[162],"K.":[164],"When":[165],"(10\u2013250":[170],"K,":[175],"both":[176],"communication":[180,243,252],"overheads":[181],"increase":[182],"linearly,":[183],"remains":[187],"primary":[189],"bottleneck":[190],"affected":[191],"by":[192,222,233,256],"dropouts.":[193],"compare":[195],"non-reusable":[198],"over":[202],"repeated":[203],"interactions":[204],"q\u2208{1,\u2026,10}":[205],"at":[206,237],"KB":[208],"K=100,":[210],"showing":[211],"reusing":[213],"Round":[214],"1":[215],"reduces":[216,227],"cumulative":[218,229],"time":[221],"about":[223,234],"2.5":[224],"times":[225,236],"1.2":[235],"q=10":[238],"leaving":[240],"nearly":[245],"unchanged,":[246],"indicates":[248],"overall":[251],"dominated":[255],"non-reused":[258],"rounds.":[259]},"counts_by_year":[],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2026-03-24T00:00:00"}