{"id":"https://openalex.org/W2900975904","doi":"https://doi.org/10.1109/tcc.2018.2880181","title":"Efficient and Secure Outsourcing of Large-Scale Linear System of Equations","display_name":"Efficient and Secure Outsourcing of Large-Scale Linear System of Equations","publication_year":2018,"publication_date":"2018-11-12","ids":{"openalex":"https://openalex.org/W2900975904","doi":"https://doi.org/10.1109/tcc.2018.2880181","mag":"2900975904"},"language":"en","primary_location":{"id":"doi:10.1109/tcc.2018.2880181","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcc.2018.2880181","pdf_url":null,"source":{"id":"https://openalex.org/S2492498579","display_name":"IEEE Transactions on Cloud Computing","issn_l":"2168-7161","issn":["2168-7161","2372-0018"],"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 Cloud 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/A5100732281","display_name":"Qi Ding","orcid":"https://orcid.org/0000-0002-7605-3649"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qi Ding","raw_affiliation_strings":["School of Mathematical Sciences, Dalian University of Technology, Dalian, P.R.China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Dalian University of Technology, Dalian, P.R.China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032238171","display_name":"Guobiao Weng","orcid":null},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guobiao Weng","raw_affiliation_strings":["School of Mathematical Sciences, Dalian University of Technology, Dalian, P.R.China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Dalian University of Technology, Dalian, P.R.China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101178549","display_name":"Guohui Zhao","orcid":"https://orcid.org/0009-0007-5378-0820"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guohui Zhao","raw_affiliation_strings":["School of Mathematical Sciences, Dalian University of Technology, Dalian, P.R.China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Dalian University of Technology, Dalian, P.R.China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101995782","display_name":"Changhui Hu","orcid":"https://orcid.org/0000-0002-6177-6019"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Changhui Hu","raw_affiliation_strings":["School of Mathematical Sciences, Dalian University of Technology, Dalian, P.R.China"],"raw_orcid":"https://orcid.org/0000-0002-6177-6019","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Dalian University of Technology, Dalian, P.R.China","institution_ids":["https://openalex.org/I27357992"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I27357992"],"apc_list":null,"apc_paid":null,"fwci":1.3104,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.85698938,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"9","issue":"2","first_page":"587","last_page":"597"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9993000030517578,"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":0.9993000030517578,"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":0.996399998664856,"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/T11614","display_name":"Cloud Data Security Solutions","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/cloud-computing","display_name":"Cloud computing","score":0.7831042408943176},{"id":"https://openalex.org/keywords/outsourcing","display_name":"Outsourcing","score":0.781140923500061},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7775624990463257},{"id":"https://openalex.org/keywords/server","display_name":"Server","score":0.49262315034866333},{"id":"https://openalex.org/keywords/linear-equation","display_name":"Linear equation","score":0.48125478625297546},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.48002997040748596},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.4630935490131378},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.4573878347873688},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.42829856276512146},{"id":"https://openalex.org/keywords/information-privacy","display_name":"Information privacy","score":0.4199480712413788},{"id":"https://openalex.org/keywords/distributed-computing","display_name":"Distributed computing","score":0.3451283574104309},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.23100700974464417},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.14882192015647888},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.09740042686462402},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.0755322277545929}],"concepts":[{"id":"https://openalex.org/C79974875","wikidata":"https://www.wikidata.org/wiki/Q483639","display_name":"Cloud computing","level":2,"score":0.7831042408943176},{"id":"https://openalex.org/C46934059","wikidata":"https://www.wikidata.org/wiki/Q61515","display_name":"Outsourcing","level":2,"score":0.781140923500061},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7775624990463257},{"id":"https://openalex.org/C93996380","wikidata":"https://www.wikidata.org/wiki/Q44127","display_name":"Server","level":2,"score":0.49262315034866333},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.48125478625297546},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.48002997040748596},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.4630935490131378},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.4573878347873688},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.42829856276512146},{"id":"https://openalex.org/C123201435","wikidata":"https://www.wikidata.org/wiki/Q456632","display_name":"Information privacy","level":2,"score":0.4199480712413788},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.3451283574104309},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.23100700974464417},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.14882192015647888},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.09740042686462402},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0755322277545929},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcc.2018.2880181","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcc.2018.2880181","pdf_url":null,"source":{"id":"https://openalex.org/S2492498579","display_name":"IEEE Transactions on Cloud Computing","issn_l":"2168-7161","issn":["2168-7161","2372-0018"],"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 Cloud Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1557386445","https://openalex.org/W1601098769","https://openalex.org/W1892798954","https://openalex.org/W1981220107","https://openalex.org/W1981577150","https://openalex.org/W1988007981","https://openalex.org/W2072335624","https://openalex.org/W2093909024","https://openalex.org/W2114296561","https://openalex.org/W2132172731","https://openalex.org/W2136624667","https://openalex.org/W2294277361","https://openalex.org/W2798909945","https://openalex.org/W4300349690","https://openalex.org/W4312258136","https://openalex.org/W6645816922"],"related_works":["https://openalex.org/W4226548185","https://openalex.org/W2506892714","https://openalex.org/W2037819582","https://openalex.org/W2365527693","https://openalex.org/W2046729504","https://openalex.org/W2162572068","https://openalex.org/W4382519919","https://openalex.org/W2550490477","https://openalex.org/W288746350","https://openalex.org/W2905003348"],"abstract_inverted_index":{"Solving":[0],"the":[1,10,34,45,49,64,70,76,131,136,141,147,153,167,173,177,196,203,210],"large-scale":[2,119],"linear":[3,78,99,122,142],"system":[4,79,143],"of":[5,9,37,59,80,96,98,118,121,140,144,172,212],"equations":[6,81,123,145],"is":[7,53,161],"one":[8],"most":[11,28],"fundamental":[12],"problems":[13],"both":[14],"in":[15,125,156],"theory":[16],"and":[17,84,169,180,216],"practice.":[18],"However":[19],"this":[20,102,157,188,192,213],"problem":[21],"requires":[22],"too":[23],"much":[24],"computational":[25],"resource":[26],"for":[27,115],"users":[29,41],"to":[30,43,48,176,194,219],"solve":[31],"it.":[32],"With":[33],"rapid":[35],"development":[36],"cloud":[38,50,65,132,178],"services,":[39],"many":[40,89],"tend":[42],"outsource":[44],"expensive":[46],"computing":[47],"server,":[51,179],"which":[52,151,165,200],"regarded":[54],"as":[55],"an":[56],"efficient":[57],"way":[58],"solving":[60],"such":[61],"problem.":[62],"Nevertheless,":[63],"server":[66,133],"can":[67,134,201],"not":[68,184],"protect":[69,195,202],"data":[71,171],"privacy":[72,108,181,205],"well,":[73],"especially":[74],"when":[75],"user's":[77],"contain":[82],"private":[83,168],"sensitive":[85,170],"data.":[86],"There":[87],"are":[88],"previous":[90],"research":[91],"works":[92],"on":[93],"secure":[94,116],"outsourcing":[95,117],"systems":[97,120],"equations.":[100],"In":[101],"paper":[103],"we":[104,190],"first":[105],"analyze":[106],"a":[107,162],"preserving":[109,182],"CGM":[110],"(conjugate":[111],"gradient":[112],"method)":[113],"algorithm":[114,193],"proposed":[124],"[1]":[126],".":[127],"We":[128,207],"find":[129],"that":[130],"recover":[135],"protected":[137],"coefficient":[138],"matrix":[139],"from":[146,198],"message":[148,197],"it":[149],"receives,":[150],"makes":[152,166],"security":[154,211],"method":[155],"scheme":[158,215],"fails.":[159],"This":[160],"serious":[163],"problem,":[164,189],"user":[174],"leak":[175],"does":[183],"exist.":[185],"To":[186],"overcome":[187],"modified":[191],"leaking,":[199],"users'":[204],"well.":[206],"also":[208],"show":[209,220],"new":[214],"do":[217],"experiments":[218],"its":[221],"efficiency.":[222]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
