{"id":"https://openalex.org/W4312275876","doi":"https://doi.org/10.1109/tdsc.2022.3218793","title":"Hercules: Boosting the Performance of Privacy-Preserving Federated Learning","display_name":"Hercules: Boosting the Performance of Privacy-Preserving Federated Learning","publication_year":2022,"publication_date":"2022-11-04","ids":{"openalex":"https://openalex.org/W4312275876","doi":"https://doi.org/10.1109/tdsc.2022.3218793"},"language":"en","primary_location":{"id":"doi:10.1109/tdsc.2022.3218793","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tdsc.2022.3218793","pdf_url":null,"source":{"id":"https://openalex.org/S133795288","display_name":"IEEE Transactions on Dependable and Secure Computing","issn_l":"1545-5971","issn":["1545-5971","1941-0018","2160-9209"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Dependable and Secure Computing","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/A5046950426","display_name":"Guowen Xu","orcid":"https://orcid.org/0000-0002-9764-9345"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Guowen Xu","raw_affiliation_strings":["School of Computer Science and Engineering, Nanyang Technological University, Singapore"],"raw_orcid":"https://orcid.org/0000-0002-9764-9345","affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011727294","display_name":"Xingshuo Han","orcid":"https://orcid.org/0000-0001-9431-5342"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Xingshuo Han","raw_affiliation_strings":["School of Computer Science and Engineering, Nanyang Technological University, Singapore"],"raw_orcid":"https://orcid.org/0000-0001-9431-5342","affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061574999","display_name":"Shengmin Xu","orcid":"https://orcid.org/0000-0002-9121-0171"},"institutions":[{"id":"https://openalex.org/I111753288","display_name":"Fujian Normal University","ror":"https://ror.org/020azk594","country_code":"CN","type":"education","lineage":["https://openalex.org/I111753288"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shengmin Xu","raw_affiliation_strings":["College of Computer and Cyber Security, Fujian Normal University, Fuzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-9121-0171","affiliations":[{"raw_affiliation_string":"College of Computer and Cyber Security, Fujian Normal University, Fuzhou, China","institution_ids":["https://openalex.org/I111753288"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101591101","display_name":"Tianwei Zhang","orcid":"https://orcid.org/0000-0001-6595-6650"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Tianwei Zhang","raw_affiliation_strings":["School of Computer Science and Engineering, Nanyang Technological University, Singapore"],"raw_orcid":"https://orcid.org/0000-0001-6595-6650","affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100325334","display_name":"Hongwei Li","orcid":"https://orcid.org/0000-0002-1961-7946"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongwei Li","raw_affiliation_strings":["School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0002-1961-7946","affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031931063","display_name":"Xinyi Huang","orcid":"https://orcid.org/0000-0003-0070-1707"},"institutions":[{"id":"https://openalex.org/I111753288","display_name":"Fujian Normal University","ror":"https://ror.org/020azk594","country_code":"CN","type":"education","lineage":["https://openalex.org/I111753288"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinyi Huang","raw_affiliation_strings":["College of Computer and Cyber Security, Fujian Normal University, Fuzhou, China"],"raw_orcid":"https://orcid.org/0000-0003-0070-1707","affiliations":[{"raw_affiliation_string":"College of Computer and Cyber Security, Fujian Normal University, Fuzhou, China","institution_ids":["https://openalex.org/I111753288"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001712801","display_name":"Robert H. Deng","orcid":"https://orcid.org/0000-0003-3491-8146"},"institutions":[{"id":"https://openalex.org/I79891267","display_name":"Singapore Management University","ror":"https://ror.org/050qmg959","country_code":"SG","type":"education","lineage":["https://openalex.org/I79891267"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Robert H. Deng","raw_affiliation_strings":["School of Information Systems, Singapore Management University, Singapore"],"raw_orcid":"https://orcid.org/0000-0003-3491-8146","affiliations":[{"raw_affiliation_string":"School of Information Systems, Singapore Management University, Singapore","institution_ids":["https://openalex.org/I79891267"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3618,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.90280909,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"20","issue":"5","first_page":"4418","last_page":"4433"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10764","display_name":"Privacy-Preserving Technologies in Data","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/T10764","display_name":"Privacy-Preserving Technologies in Data","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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9990000128746033,"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/T10237","display_name":"Cryptography and Data Security","score":0.995199978351593,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5655115246772766},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5118030905723572},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.4728056788444519},{"id":"https://openalex.org/keywords/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.46727192401885986},{"id":"https://openalex.org/keywords/mnist-database","display_name":"MNIST database","score":0.42118000984191895},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4121144413948059},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3925405740737915},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31469517946243286},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.27157002687454224},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.26628702878952026},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.2150254249572754},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17856314778327942}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5655115246772766},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5118030905723572},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.4728056788444519},{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.46727192401885986},{"id":"https://openalex.org/C190502265","wikidata":"https://www.wikidata.org/wiki/Q17069496","display_name":"MNIST database","level":3,"score":0.42118000984191895},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4121144413948059},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3925405740737915},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31469517946243286},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.27157002687454224},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26628702878952026},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.2150254249572754},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17856314778327942},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tdsc.2022.3218793","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tdsc.2022.3218793","pdf_url":null,"source":{"id":"https://openalex.org/S133795288","display_name":"IEEE Transactions on Dependable and Secure Computing","issn_l":"1545-5971","issn":["1545-5971","1941-0018","2160-9209"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Dependable and Secure Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3247241453","display_name":null,"funder_award_id":"2MOE-T2EP20121-0006","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"},{"id":"https://openalex.org/G5669255772","display_name":null,"funder_award_id":"62032005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7528015336","display_name":null,"funder_award_id":"62102090","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W236632755","https://openalex.org/W774911181","https://openalex.org/W913176383","https://openalex.org/W1499407211","https://openalex.org/W1500237345","https://openalex.org/W2007339694","https://openalex.org/W2055580199","https://openalex.org/W2136530453","https://openalex.org/W2137591724","https://openalex.org/W2435473771","https://openalex.org/W2473418344","https://openalex.org/W2535690855","https://openalex.org/W2591882872","https://openalex.org/W2701059868","https://openalex.org/W2742491462","https://openalex.org/W2765200655","https://openalex.org/W2768174108","https://openalex.org/W2776696187","https://openalex.org/W2795036470","https://openalex.org/W2889746123","https://openalex.org/W2927692314","https://openalex.org/W2964261135","https://openalex.org/W2964347220","https://openalex.org/W2969695741","https://openalex.org/W2970408908","https://openalex.org/W2983140679","https://openalex.org/W2984644945","https://openalex.org/W2985527074","https://openalex.org/W2989605743","https://openalex.org/W2990280959","https://openalex.org/W2994111940","https://openalex.org/W3008381581","https://openalex.org/W3008493372","https://openalex.org/W3015535799","https://openalex.org/W3016063723","https://openalex.org/W3016632787","https://openalex.org/W3035616549","https://openalex.org/W3071470454","https://openalex.org/W3093021001","https://openalex.org/W3102360395","https://openalex.org/W3104454153","https://openalex.org/W3106873467","https://openalex.org/W3107031453","https://openalex.org/W3108672920","https://openalex.org/W3117449869","https://openalex.org/W3138090943","https://openalex.org/W3138596485","https://openalex.org/W3149291386","https://openalex.org/W3157813311","https://openalex.org/W3184856066","https://openalex.org/W4287822453","https://openalex.org/W6746635490","https://openalex.org/W6760122430","https://openalex.org/W6763192249","https://openalex.org/W6763393679","https://openalex.org/W6763736615","https://openalex.org/W6775563089","https://openalex.org/W6778252690","https://openalex.org/W6780438843","https://openalex.org/W6785814594","https://openalex.org/W6798046383"],"related_works":["https://openalex.org/W4386603768","https://openalex.org/W2950475743","https://openalex.org/W2886711096","https://openalex.org/W2750384547","https://openalex.org/W4380078352","https://openalex.org/W3046591097","https://openalex.org/W4389249638","https://openalex.org/W2733410219","https://openalex.org/W2734358244","https://openalex.org/W4388700941"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,60,127],"address":[4],"the":[5,39,56,84,96,109,113,117,123,133,138,155,194],"problem":[6],"of":[7,31,86,112],"privacy-preserving":[8],"federated":[9],"neural":[10,114],"network":[11,115],"training":[12,25,110],"with":[13,55,154,176],"<inline-formula><tex-math":[14,34,88,100,103,190],"notation=\"LaTeX\">$N$</tex-math></inline-formula>":[15],"users.":[16,36],"We":[17],"present":[18,128],"<b>Hercules</b>":[19,37,178],",":[20],"an":[21,129],"efficient":[22,130],"and":[23,76,151,171,187,196],"high-precision":[24],"framework":[26,41],"that":[27,174],"can":[28],"tolerate":[29],"collusion":[30],"up":[32,180,188],"to":[33,102,145,181,189],"notation=\"LaTeX\">$N-1$</tex-math></inline-formula>":[35],"follows":[38],"POSEIDON":[40],"proposed":[42],"by":[43,122],"Sav":[44],"et":[45],"al.":[46],"(NDSS\u201921),":[47],"but":[48],"makes":[49],"a":[50,62],"qualitative":[51],"leap":[52],"in":[53,184,193],"performance":[54],"following":[57],"contributions:":[58],"(i)":[59],"design":[61],"novel":[63],"parallel":[64],"homomorphic":[65],"computation":[66,97,119,195],"method":[67,94],"for":[68],"matrix":[69],"operations,":[70],"which":[71],"enables":[72],"fast":[73],"Single":[74],"Instruction":[75],"Multiple":[77],"Data":[78],"(SIMD)":[79],"operations":[80],"over":[81],"ciphertexts.":[82],"For":[83],"multiplication":[85],"two":[87],"notation=\"LaTeX\">$h\\times":[89],"h$</tex-math></inline-formula>":[90],"dimensional":[91],"matrices,":[92],"our":[93],"reduces":[95],"complexity":[98],"from":[99],"notation=\"LaTeX\">$O(h^{3})$</tex-math></inline-formula>":[101],"notation=\"LaTeX\">$O(h)$</tex-math></inline-formula>":[104],".":[105],"This":[106],"greatly":[107],"improves":[108],"efficiency":[111],"since":[116],"ciphertext":[118],"is":[120,143],"dominated":[121],"convolution":[124],"operations;":[125],"(ii)":[126],"approximation":[131],"on":[132,137,161],"sign":[134],"function":[135],"based":[136],"composite":[139],"polynomial":[140],"approximation.":[141],"It":[142],"used":[144],"approximate":[146],"non-polynomial":[147],"functions":[148],"(i.e.,":[149],"<monospace>ReLU</monospace>":[150],"<monospace>max</monospace>":[152],"),":[153],"optimal":[156],"asymptotic":[157],"complexity.":[158],"Extensive":[159],"experiments":[160],"various":[162],"benchmark":[163],"datasets":[164],"(BCW,":[165],"ESR,":[166],"CREDIT,":[167],"MNIST,":[168],"SVHN,":[169],"CIFAR-10":[170],"CIFAR-100)":[172],"show":[173],"compared":[175],"POSEIDON,":[177],"obtains":[179],"4%":[182],"increase":[183],"model":[185],"accuracy,":[186],"notation=\"LaTeX\">$60\\times$</tex-math></inline-formula>":[191],"reduction":[192],"communication":[197],"cost.":[198]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
