{"id":"https://openalex.org/W7134887372","doi":"https://doi.org/10.48550/arxiv.2603.08944","title":"Differentially Private Secure Multiplication: Beyond Two Multiplicands","display_name":"Differentially Private Secure Multiplication: Beyond Two Multiplicands","publication_year":2026,"publication_date":"2026-03-09","ids":{"openalex":"https://openalex.org/W7134887372","doi":"https://doi.org/10.48550/arxiv.2603.08944"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.08944","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08944","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.08944","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128714940","display_name":"Haoyang Hu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hu, Haoyang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5008627075","display_name":"Viveck R. Cadambe","orcid":"https://orcid.org/0000-0001-6786-8785"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cadambe, Viveck R.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.26030001044273376,"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":0.26030001044273376,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.20499999821186066,"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"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.20090000331401825,"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/converse","display_name":"Converse","score":0.8295000195503235},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6578999757766724},{"id":"https://openalex.org/keywords/collusion","display_name":"Collusion","score":0.5467000007629395},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.49300000071525574},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.4255000054836273},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.39750000834465027}],"concepts":[{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.8295000195503235},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6578999757766724},{"id":"https://openalex.org/C2781198186","wikidata":"https://www.wikidata.org/wiki/Q701521","display_name":"Collusion","level":2,"score":0.5467000007629395},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.49300000071525574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.453000009059906},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.45170000195503235},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4440000057220459},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4429999887943268},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.4255000054836273},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.39750000834465027},{"id":"https://openalex.org/C23130292","wikidata":"https://www.wikidata.org/wiki/Q5275358","display_name":"Differential privacy","level":2,"score":0.3336000144481659},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.29420000314712524},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.2897999882698059},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2851000130176544}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.08944","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08944","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.08944","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08944","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/17","display_name":"Partnerships for the goals","score":0.402913898229599}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,86,123],"study":[1],"the":[2,32,53,58,71,77,111,144,164],"problem":[3],"of":[4,34,44,60,75,79,84,114],"differentially":[5],"private":[6,36],"(DP)":[7],"secure":[8,89],"multiplication":[9,59,90],"in":[10,163],"distributed":[11],"computing":[12,76],"systems,":[13],"focusing":[14],"on":[15,93],"regimes":[16],"where":[17],"perfect":[18,21],"privacy":[19],"and":[20,109,132,156],"accuracy":[22],"cannot":[23],"be":[24],"simultaneously":[25],"achieved.":[26],"Specifically,":[27],"N":[28,129,133,139,149],"nodes":[29],"collaboratively":[30],"compute":[31],"product":[33,78],"M":[35,83],"inputs":[37],"while":[38],"guaranteeing":[39],"epsilon-DP":[40],"against":[41],"any":[42],"collusion":[43],"up":[45],"to":[46,70,119],"T":[47],"nodes.":[48],"Prior":[49],"work":[50],"has":[51],"characterized":[52],"fundamental":[54],"privacy-accuracy":[55],"trade-off":[56],"for":[57],"two":[61,125],"multiplicands.":[62,85],"In":[63],"this":[64],"paper,":[65],"we":[66,142,152],"extend":[67],"these":[68],"results":[69],"more":[72],"general":[73],"setting":[74],"an":[80],"arbitrary":[81],"number":[82],"propose":[87],"a":[88],"framework":[91],"based":[92],"carefully":[94],"designed":[95],"encoding":[96],"polynomials":[97],"combined":[98],"with":[99],"layered":[100],"noise":[101,116],"injection.":[102],"The":[103],"proposed":[104],"construction":[105],"generalizes":[106],"existing":[107],"schemes":[108],"enables":[110],"systematic":[112],"cancellation":[113],"lower-order":[115],"terms,":[117],"leading":[118],"improved":[120],"estimation":[121],"accuracy.":[122],"explore":[124],"regimes:":[126],"(M-1)T+1":[127,137],"&lt;=":[128,130,138,140],"MT":[131],"=":[134,150],"T+1.":[135],"For":[136],"MT,":[141],"characterize":[143],"optimal":[145],"privacy--accuracy":[146],"trade-off.":[147],"When":[148],"T+1,":[151],"derive":[153],"nontrivial":[154],"achievability":[155],"converse":[157],"bounds":[158],"that":[159],"are":[160],"asymptotically":[161],"tight":[162],"high-privacy":[165],"regime.":[166]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-03-12T00:00:00"}
