{"id":"https://openalex.org/W4402047554","doi":"https://doi.org/10.3390/e26090743","title":"A Communication-Efficient Distributed Matrix Multiplication Scheme with Privacy, Security, and Resiliency","display_name":"A Communication-Efficient Distributed Matrix Multiplication Scheme with Privacy, Security, and Resiliency","publication_year":2024,"publication_date":"2024-08-30","ids":{"openalex":"https://openalex.org/W4402047554","doi":"https://doi.org/10.3390/e26090743","pmid":"https://pubmed.ncbi.nlm.nih.gov/39330077"},"language":"en","primary_location":{"id":"doi:10.3390/e26090743","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26090743","pdf_url":"https://www.mdpi.com/1099-4300/26/9/743/pdf?version=1725019763","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://www.mdpi.com/1099-4300/26/9/743/pdf?version=1725019763","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107194352","display_name":"Tao Wang","orcid":"https://orcid.org/0009-0005-6640-7713"},"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":"Tao Wang","raw_affiliation_strings":["National Key Laboratory of Wireless Communications, University of Electronic Science and Technology of China, Chengdu 611731, China"],"raw_orcid":"https://orcid.org/0009-0005-6640-7713","affiliations":[{"raw_affiliation_string":"National Key Laboratory of Wireless Communications, University of Electronic Science and Technology of China, Chengdu 611731, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090439174","display_name":"Zhiping Shi","orcid":"https://orcid.org/0000-0002-9851-440X"},"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":true,"raw_author_name":"Zhiping Shi","raw_affiliation_strings":["National Key Laboratory of Wireless Communications, University of Electronic Science and Technology of China, Chengdu 611731, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Key Laboratory of Wireless Communications, University of Electronic Science and Technology of China, Chengdu 611731, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039216902","display_name":"Juan Yang","orcid":"https://orcid.org/0000-0001-5337-7707"},"institutions":[{"id":"https://openalex.org/I3129996945","display_name":"Guilin University of Aerospace Technology","ror":"https://ror.org/00h1gc758","country_code":"CN","type":"education","lineage":["https://openalex.org/I3129996945"]},{"id":"https://openalex.org/I5343935","display_name":"Guilin University of Electronic Technology","ror":"https://ror.org/05arjae42","country_code":"CN","type":"education","lineage":["https://openalex.org/I5343935"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Juan Yang","raw_affiliation_strings":["Guangxi Key Laboratory of Automatic Detecting Technology and Instruments, Guilin University of Electronic Technology, Guilin 541004, China","School of Electronic Information and Automation, Guilin University of Aerospace Technology, Guilin 541004, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guangxi Key Laboratory of Automatic Detecting Technology and Instruments, Guilin University of Electronic Technology, Guilin 541004, China","institution_ids":["https://openalex.org/I5343935"]},{"raw_affiliation_string":"School of Electronic Information and Automation, Guilin University of Aerospace Technology, Guilin 541004, China","institution_ids":["https://openalex.org/I3129996945"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040000905","display_name":"Sha Liu","orcid":"https://orcid.org/0000-0003-4705-6805"},"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":"Sha Liu","raw_affiliation_strings":["National Key Laboratory of Wireless Communications, University of Electronic Science and Technology of China, Chengdu 611731, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Key Laboratory of Wireless Communications, University of Electronic Science and Technology of China, Chengdu 611731, China","institution_ids":["https://openalex.org/I150229711"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5090439174"],"corresponding_institution_ids":["https://openalex.org/I150229711"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.3254,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.64874764,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"26","issue":"9","first_page":"743","last_page":"743"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9979000091552734,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9979000091552734,"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":0.9972000122070312,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9970999956130981,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.6809515357017517},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6730896830558777},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6091859340667725},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.5060335993766785},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4766298532485962},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.3890901207923889},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3556610345840454},{"id":"https://openalex.org/keywords/distributed-computing","display_name":"Distributed computing","score":0.32793980836868286},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1624005138874054},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.10465580224990845},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07233455777168274}],"concepts":[{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6809515357017517},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6730896830558777},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6091859340667725},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.5060335993766785},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4766298532485962},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.3890901207923889},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3556610345840454},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.32793980836868286},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1624005138874054},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.10465580224990845},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07233455777168274},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"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":5,"locations":[{"id":"doi:10.3390/e26090743","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26090743","pdf_url":"https://www.mdpi.com/1099-4300/26/9/743/pdf?version=1725019763","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:39330077","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39330077","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:pubmedcentral.nih.gov:11431245","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11431245","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11431245/pdf/entropy-26-00743.pdf","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"},{"id":"pmh:oai:doaj.org/article:1411d0ef31bc453bb2d64cf5181b3a9e","is_oa":false,"landing_page_url":"https://doaj.org/article/1411d0ef31bc453bb2d64cf5181b3a9e","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 26, Iss 9, p 743 (2024)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/26/9/743/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e26090743","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e26090743","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26090743","pdf_url":"https://www.mdpi.com/1099-4300/26/9/743/pdf?version=1725019763","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/G3613373733","display_name":null,"funder_award_id":"62371101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6056180275","display_name":null,"funder_award_id":"2022YFC3005072","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4402047554.pdf","grobid_xml":"https://content.openalex.org/works/W4402047554.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1471103927","https://openalex.org/W2617565736","https://openalex.org/W2806273311","https://openalex.org/W2808580034","https://openalex.org/W2898024058","https://openalex.org/W2929607020","https://openalex.org/W2962858508","https://openalex.org/W2963072024","https://openalex.org/W2963498933","https://openalex.org/W3007714448","https://openalex.org/W3041063634","https://openalex.org/W3047848333","https://openalex.org/W3080407940","https://openalex.org/W3195764561","https://openalex.org/W3214565882","https://openalex.org/W4310902946","https://openalex.org/W4318779501","https://openalex.org/W4386057552","https://openalex.org/W4391326610","https://openalex.org/W4391877662","https://openalex.org/W6638991018"],"related_works":["https://openalex.org/W3099313426","https://openalex.org/W4287593139","https://openalex.org/W752783541","https://openalex.org/W1506547947","https://openalex.org/W2995605830","https://openalex.org/W4206811032","https://openalex.org/W2086123442","https://openalex.org/W2596457687","https://openalex.org/W3212757063","https://openalex.org/W2093666864"],"abstract_inverted_index":{"Secure":[0],"distributed":[1,9,17,31],"matrix":[2],"multiplication":[3],"(SDMM)":[4],"schemes":[5,39,52,106],"are":[6,53,93],"crucial":[7],"for":[8,96,126],"learning":[10],"algorithms":[11],"where":[12],"extensive":[13],"data":[14],"computation":[15],"is":[16],"across":[18],"multiple":[19],"servers.":[20],"Inspired":[21],"by":[22],"the":[23,45,85,97,108,120,127],"application":[24],"of":[25,47,87,110],"repairing":[26],"Reed-Solomon":[27],"(RS)":[28],"codes":[29],"in":[30],"storage":[32],"and":[33,74,91,113,123],"secret":[34],"sharing,":[35],"we":[36],"propose":[37],"SDMM":[38],"with":[40],"reduced":[41,111],"communication":[42],"overhead":[43],"through":[44],"use":[46],"trace":[48,101],"polynomials.":[49],"Specifically,":[50],"these":[51],"designed":[54],"to":[55,80],"address":[56],"three":[57],"critical":[58],"concerns:":[59],"(i)":[60],"ensuring":[61],"information-theoretic":[62],"privacy":[63],"against":[64,71,78],"collusion":[65],"among":[66],"servers;":[67,73],"(ii)":[68],"providing":[69],"security":[70,90],"Byzantine":[72],"(iii)":[75],"offering":[76],"resiliency":[77,92],"stragglers":[79],"mitigate":[81],"computing":[82],"delays.":[83],"To":[84],"best":[86],"our":[88,105],"knowledge,":[89],"being":[94],"considered":[95],"first":[98],"time":[99],"within":[100],"polynomial-based":[102],"approaches.":[103],"Furthermore,":[104],"offer":[107],"advantage":[109],"sub-packetization":[112],"a":[114],"lower":[115],"server-count":[116],"requirement,":[117],"which":[118],"diminish":[119],"computational":[121],"complexity":[122],"download":[124],"cost":[125],"user.":[128]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}