{"id":"https://openalex.org/W2918629785","doi":"https://doi.org/10.1109/tnse.2019.2901887","title":"Securely Solving Linear Algebraic Equations in a Distributed Framework Enhanced With Communication-Efficient Algorithms","display_name":"Securely Solving Linear Algebraic Equations in a Distributed Framework Enhanced With Communication-Efficient Algorithms","publication_year":2019,"publication_date":"2019-02-27","ids":{"openalex":"https://openalex.org/W2918629785","doi":"https://doi.org/10.1109/tnse.2019.2901887","mag":"2918629785"},"language":"en","primary_location":{"id":"doi:10.1109/tnse.2019.2901887","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2019.2901887","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"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 Network Science and Engineering","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/A5004923751","display_name":"Bo Yin","orcid":"https://orcid.org/0000-0001-9574-7032"},"institutions":[{"id":"https://openalex.org/I180949307","display_name":"Illinois Institute of Technology","ror":"https://ror.org/037t3ry66","country_code":"US","type":"education","lineage":["https://openalex.org/I180949307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bo Yin","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Illinois Institute of Technology, Chicago, USA"],"raw_orcid":"https://orcid.org/0000-0001-9574-7032","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Illinois Institute of Technology, Chicago, USA","institution_ids":["https://openalex.org/I180949307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020087391","display_name":"Wenlong Shen","orcid":"https://orcid.org/0000-0002-5021-0183"},"institutions":[{"id":"https://openalex.org/I180949307","display_name":"Illinois Institute of Technology","ror":"https://ror.org/037t3ry66","country_code":"US","type":"education","lineage":["https://openalex.org/I180949307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wenlong Shen","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Illinois Institute of Technology, Chicago, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Illinois Institute of Technology, Chicago, USA","institution_ids":["https://openalex.org/I180949307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085757528","display_name":"Xianghui Cao","orcid":"https://orcid.org/0000-0002-6771-0571"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xianghui Cao","raw_affiliation_strings":["School of Automation, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-6771-0571","affiliations":[{"raw_affiliation_string":"School of Automation, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084146010","display_name":"Yu Cheng","orcid":"https://orcid.org/0000-0002-4837-3370"},"institutions":[{"id":"https://openalex.org/I180949307","display_name":"Illinois Institute of Technology","ror":"https://ror.org/037t3ry66","country_code":"US","type":"education","lineage":["https://openalex.org/I180949307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yu Cheng","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Illinois Institute of Technology, Chicago, USA"],"raw_orcid":"https://orcid.org/0000-0002-4837-3370","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Illinois Institute of Technology, Chicago, USA","institution_ids":["https://openalex.org/I180949307"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100404176","display_name":"Qing Li","orcid":"https://orcid.org/0000-0003-3370-471X"},"institutions":[{"id":"https://openalex.org/I1308906816","display_name":"NortonLifeLock (United States)","ror":"https://ror.org/0449t3a80","country_code":"US","type":"company","lineage":["https://openalex.org/I1308906816"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qing Li","raw_affiliation_strings":["Symantec Corporation, Mountain View, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Symantec Corporation, Mountain View, USA","institution_ids":["https://openalex.org/I1308906816"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7438,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.73388106,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"7","issue":"3","first_page":"1027","last_page":"1042"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9994000196456909,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9994000196456909,"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/T11498","display_name":"Security in Wireless Sensor Networks","score":0.9984999895095825,"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/T10080","display_name":"Energy Efficient Wireless Sensor Networks","score":0.989799976348877,"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":0.6873345375061035},{"id":"https://openalex.org/keywords/overhead","display_name":"Overhead (engineering)","score":0.6380110383033752},{"id":"https://openalex.org/keywords/distributed-algorithm","display_name":"Distributed algorithm","score":0.6006873846054077},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.5151063799858093},{"id":"https://openalex.org/keywords/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.477420449256897},{"id":"https://openalex.org/keywords/consensus","display_name":"Consensus","score":0.46491795778274536},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46236374974250793},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.4465397298336029},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4448174834251404},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4129228889942169},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34242379665374756},{"id":"https://openalex.org/keywords/distributed-computing","display_name":"Distributed computing","score":0.31478118896484375},{"id":"https://openalex.org/keywords/multi-agent-system","display_name":"Multi-agent system","score":0.24280637502670288},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20890772342681885},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.13305681943893433},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.11234647035598755},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09599795937538147}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6873345375061035},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.6380110383033752},{"id":"https://openalex.org/C130120984","wikidata":"https://www.wikidata.org/wiki/Q2835898","display_name":"Distributed algorithm","level":2,"score":0.6006873846054077},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5151063799858093},{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.477420449256897},{"id":"https://openalex.org/C107107730","wikidata":"https://www.wikidata.org/wiki/Q2994424","display_name":"Consensus","level":3,"score":0.46491795778274536},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46236374974250793},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.4465397298336029},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4448174834251404},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4129228889942169},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34242379665374756},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.31478118896484375},{"id":"https://openalex.org/C41550386","wikidata":"https://www.wikidata.org/wiki/Q529909","display_name":"Multi-agent system","level":2,"score":0.24280637502670288},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20890772342681885},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.13305681943893433},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.11234647035598755},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09599795937538147},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tnse.2019.2901887","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2019.2901887","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"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 Network Science and Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4360356194","display_name":null,"funder_award_id":"ECCS-1610874","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4837342209","display_name":null,"funder_award_id":"61573103","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"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":51,"referenced_works":["https://openalex.org/W379260703","https://openalex.org/W1506342804","https://openalex.org/W1517358265","https://openalex.org/W1571821840","https://openalex.org/W1582713334","https://openalex.org/W1601098769","https://openalex.org/W1635348707","https://openalex.org/W1683514625","https://openalex.org/W1743877615","https://openalex.org/W1760770890","https://openalex.org/W1971565861","https://openalex.org/W1973124816","https://openalex.org/W1973184571","https://openalex.org/W1984398840","https://openalex.org/W2001772313","https://openalex.org/W2009062222","https://openalex.org/W2038651258","https://openalex.org/W2044212084","https://openalex.org/W2067561390","https://openalex.org/W2077412176","https://openalex.org/W2084279514","https://openalex.org/W2093909024","https://openalex.org/W2114791779","https://openalex.org/W2121039643","https://openalex.org/W2130093830","https://openalex.org/W2131877481","https://openalex.org/W2134616143","https://openalex.org/W2140372921","https://openalex.org/W2146039063","https://openalex.org/W2153486647","https://openalex.org/W2153775930","https://openalex.org/W2154625773","https://openalex.org/W2187366271","https://openalex.org/W2294760900","https://openalex.org/W2460519802","https://openalex.org/W2538426395","https://openalex.org/W2555951933","https://openalex.org/W2560424697","https://openalex.org/W2567931453","https://openalex.org/W2569977969","https://openalex.org/W2626045462","https://openalex.org/W2962775700","https://openalex.org/W2963125098","https://openalex.org/W2963583670","https://openalex.org/W3137092842","https://openalex.org/W4242086383","https://openalex.org/W4250776762","https://openalex.org/W4302460564","https://openalex.org/W6643269824","https://openalex.org/W6680082670","https://openalex.org/W6720464435"],"related_works":["https://openalex.org/W2539930818","https://openalex.org/W4406779505","https://openalex.org/W4403623784","https://openalex.org/W4393118461","https://openalex.org/W4390664647","https://openalex.org/W3012147850","https://openalex.org/W4313300189","https://openalex.org/W2537685543","https://openalex.org/W4308216136","https://openalex.org/W1561685359"],"abstract_inverted_index":{"Solving":[0],"linear":[1],"algebraic":[2],"equations":[3],"(a.k.a.,":[4],"an":[5,101,148,184],"LAE":[6,69],"problem)":[7],"distributedly":[8],"in":[9,18,32,100,114,180,219,253],"a":[10,40,46,56,92,109,135,214],"network":[11],"with":[12],"multiple":[13],"agents":[14,54,164],"has":[15,76],"wide":[16],"applications":[17],"distributed":[19,27,93],"control,":[20],"estimation,":[21],"and":[22,51,117,201],"signal":[23],"processing.":[24],"A":[25],"consensus-based":[26,57],"computing":[28,121],"framework":[29],"is":[30,95,183],"studied":[31],"this":[33,105,115,181],"paper.":[34],"Specifically,":[35],"each":[36],"agent":[37],"knows":[38],"only":[39],"subproblem":[41],"of":[42,48,63,67,111,172,217,242,255],"the":[43,64,68,81,85,142,155,166,191,195,207,240,248,256],"LAE,":[44],"i.e.,":[45],"subset":[47],"all":[49,53,80],"equations,":[50],"then":[52],"apply":[55],"algorithm":[58],"to":[59,84,97,129,140,246],"update":[60],"their":[61],"estimates":[62,82],"correct":[65],"solution":[66,87],"problem":[70],"iteratively.":[71],"Under":[72],"certain":[73],"conditions,":[74],"it":[75],"been":[77],"shown":[78],"that":[79],"converge":[83],"exact":[86],"exponentially":[88],"fast.":[89],"However,":[90],"such":[91],"paradigm":[94],"vulnerable":[96],"malicious":[98],"behaviors":[99],"adversarial":[102],"environment.":[103],"In":[104,225],"paper,":[106],"we":[107,133,146,204],"indicate":[108],"number":[110],"security":[112],"threats":[113],"process,":[116],"thus":[118],"develop":[119,134],"robust":[120],"solutions":[122],"against":[123],"those":[124],"attacks.":[125],"With":[126],"particular":[127],"attention":[128],"low":[130],"storage":[131],"overhead,":[132],"new":[136],"alternating":[137],"projection":[138],"method":[139,160],"enhance":[141],"consensus":[143,196,208],"algorithm.":[144],"Furthermore,":[145],"design":[147],"innovative":[149],"misbehavior":[150],"detection":[151],"mechanism":[152],"by":[153],"exploiting":[154],"homomorphic":[156],"signature":[157],"technique.":[158],"Our":[159],"can":[161,209,234],"detect":[162],"misbehaving":[163],"without":[165],"common,":[167],"yet":[168],"sometimes":[169],"infeasible,":[170],"assumption":[171],"local":[173],"good":[174],"majority.":[175],"Another":[176],"significant":[177],"contribution":[178],"presented":[179],"paper":[182],"original":[185],"component":[186],"dropping":[187],"approach":[188],"for":[189],"mitigating":[190],"communication":[192,257],"overhead":[193],"during":[194],"process.":[197],"From":[198],"both":[199],"theoretical":[200],"engineering":[202],"perspectives,":[203],"study":[205],"how":[206],"still":[210],"be":[211,235],"reached":[212],"when":[213],"big":[215],"portion":[216],"elements":[218],"exchanged":[220],"message":[221],"vectors":[222],"are":[223],"dropped.":[224],"our":[226],"preliminary":[227],"numerical":[228],"results,":[229],"roughly":[230],"80%":[231],"data":[232],"transmission":[233],"reduced":[236],"per":[237],"epoch":[238],"at":[239],"expense":[241],"35%":[243],"extra":[244],"epochs":[245],"reach":[247],"consensus,":[249],"implying":[250],"73%":[251],"reduction":[252],"terms":[254],"overhead.":[258]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}