{"id":"https://openalex.org/W3192050161","doi":"https://doi.org/10.1007/978-3-030-84245-1_12","title":"Efficient Information-Theoretic Multi-party Computation over Non-commutative Rings","display_name":"Efficient Information-Theoretic Multi-party Computation over Non-commutative Rings","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3192050161","doi":"https://doi.org/10.1007/978-3-030-84245-1_12","mag":"3192050161"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-84245-1_12","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-84245-1_12","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://pure.au.dk/portal/en/publications/3f91c03d-57b8-49b6-b4b6-1a8d4a016805","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033020836","display_name":"Daniel Escudero","orcid":"https://orcid.org/0000-0003-2375-0034"},"institutions":[{"id":"https://openalex.org/I204337017","display_name":"Aarhus University","ror":"https://ror.org/01aj84f44","country_code":"DK","type":"education","lineage":["https://openalex.org/I204337017"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Daniel Escudero","raw_affiliation_strings":["Department of Computer Science, Aarhus University, Aarhus, Denmark"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Aarhus University, Aarhus, Denmark","institution_ids":["https://openalex.org/I204337017"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064057263","display_name":"Eduardo Soria-V\u00e1zquez","orcid":"https://orcid.org/0000-0002-4882-0230"},"institutions":[{"id":"https://openalex.org/I4210087059","display_name":"Technology Innovation Institute","ror":"https://ror.org/001kv2y39","country_code":"AE","type":"facility","lineage":["https://openalex.org/I4210087059"]}],"countries":["AE"],"is_corresponding":true,"raw_author_name":"Eduardo Soria-Vazquez","raw_affiliation_strings":["Cryptography Research Centre, Technology Innovation Institute, Abu Dhabi, UAE"],"affiliations":[{"raw_affiliation_string":"Cryptography Research Centre, Technology Innovation Institute, Abu Dhabi, UAE","institution_ids":["https://openalex.org/I4210087059"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5033020836","https://openalex.org/A5064057263"],"corresponding_institution_ids":["https://openalex.org/I204337017","https://openalex.org/I4210087059"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":3.7842,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.94598815,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"335","last_page":"364"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","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/T10237","display_name":"Cryptography and Data Security","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/T11130","display_name":"Coding theory and cryptography","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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9882000088691711,"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/multiplicative-function","display_name":"Multiplicative function","score":0.6732187271118164},{"id":"https://openalex.org/keywords/secret-sharing","display_name":"Secret sharing","score":0.6118023991584778},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.49787139892578125},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.49700406193733215},{"id":"https://openalex.org/keywords/secure-multi-party-computation","display_name":"Secure multi-party computation","score":0.4768204092979431},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46358513832092285},{"id":"https://openalex.org/keywords/access-structure","display_name":"Access structure","score":0.4474470913410187},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.44576936960220337},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43503570556640625},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.41163530945777893},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3898910880088806},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.3568630814552307},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35054969787597656},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23566797375679016},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.11590549349784851},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.11101728677749634}],"concepts":[{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6732187271118164},{"id":"https://openalex.org/C3087436","wikidata":"https://www.wikidata.org/wiki/Q1386603","display_name":"Secret sharing","level":3,"score":0.6118023991584778},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.49787139892578125},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.49700406193733215},{"id":"https://openalex.org/C18396474","wikidata":"https://www.wikidata.org/wiki/Q2465888","display_name":"Secure multi-party computation","level":3,"score":0.4768204092979431},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46358513832092285},{"id":"https://openalex.org/C2778950925","wikidata":"https://www.wikidata.org/wiki/Q4672474","display_name":"Access structure","level":4,"score":0.4474470913410187},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.44576936960220337},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43503570556640625},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.41163530945777893},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3898910880088806},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3568630814552307},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35054969787597656},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23566797375679016},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.11590549349784851},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.11101728677749634},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-030-84245-1_12","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-84245-1_12","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:pure.atira.dk:openaire/3f91c03d-57b8-49b6-b4b6-1a8d4a016805","is_oa":true,"landing_page_url":"https://pure.au.dk/portal/en/publications/3f91c03d-57b8-49b6-b4b6-1a8d4a016805","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Escudero Ospina, D E & Soria Vazquez, E 2021, Efficient Information-Theoretic Multi-Party Computation over Non-Commutative Rings. in Advances in Cryptology \u2013 CRYPTO 2021 - 41st Annual International Cryptology Conference, CRYPTO 2021, Proceedings : Proceedings. Springer, pp. 335-364, Annual International Cryptology Conference, 16/08/2021. https://doi.org/10.1007/978-3-030-84245-1_12","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:openaire/3f91c03d-57b8-49b6-b4b6-1a8d4a016805","is_oa":true,"landing_page_url":"https://pure.au.dk/portal/en/publications/3f91c03d-57b8-49b6-b4b6-1a8d4a016805","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Escudero Ospina, D E & Soria Vazquez, E 2021, Efficient Information-Theoretic Multi-Party Computation over Non-Commutative Rings. in Advances in Cryptology \u2013 CRYPTO 2021 - 41st Annual International Cryptology Conference, CRYPTO 2021, Proceedings : Proceedings. Springer, pp. 335-364, Annual International Cryptology Conference, 16/08/2021. https://doi.org/10.1007/978-3-030-84245-1_12","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[{"score":0.8500000238418579,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W48039395","https://openalex.org/W147290027","https://openalex.org/W1499934958","https://openalex.org/W1528693676","https://openalex.org/W1556155774","https://openalex.org/W1590063586","https://openalex.org/W1964571330","https://openalex.org/W1999121964","https://openalex.org/W2006453614","https://openalex.org/W2015676876","https://openalex.org/W2113136973","https://openalex.org/W2113241723","https://openalex.org/W2141420453","https://openalex.org/W2322288390","https://openalex.org/W2761587086","https://openalex.org/W2810304253","https://openalex.org/W2947456252","https://openalex.org/W2991155000","https://openalex.org/W3091480782","https://openalex.org/W3103648976","https://openalex.org/W3118096690","https://openalex.org/W3137092842","https://openalex.org/W3160700308","https://openalex.org/W3187633241","https://openalex.org/W3208971183","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1601320192","https://openalex.org/W2950578674","https://openalex.org/W1426154471","https://openalex.org/W1660794319","https://openalex.org/W2366423588","https://openalex.org/W2534775105","https://openalex.org/W2969683082","https://openalex.org/W1995566873","https://openalex.org/W2907243341","https://openalex.org/W2223862429"],"abstract_inverted_index":{"We":[0,275],"construct":[1],"the":[2,22,60,78,81,108,135,138,159,200,236,239,294,297],"first":[3],"efficient,":[4],"unconditionally":[5],"secure":[6],"MPC":[7,182],"protocol":[8,241],"that":[9,95,219,292],"only":[10,27],"requires":[11],"black-box":[12,191,263],"access":[13,192],"to":[14,53,134,180,193],"a":[15,30,47,84,185,258,267],"non-commutative":[16,54],"ring":[17,82,201],"R.":[18,194],"Previous":[19],"results":[20],"in":[21],"same":[23],"setting":[24,256],"were":[25],"efficient":[26,187,283],"either":[28],"for":[29,208,286],"constant":[31],"number":[32],"of":[33,49,80,129,140,147,238,271,296],"corruptions":[34],"or":[35],"when":[36,210],"computing":[37],"branching":[38],"programs":[39],"and":[40,69,116,169,190,228,250],"formulas.":[41],"Our":[42],"techniques":[43],"are":[44,177],"based":[45,242],"on":[46,62,73,243],"generalization":[48],"Shamir\u2019s":[50],"secret":[51,110,160],"sharing":[52,111,161],"rings,":[55,158],"which":[56,209],"we":[57,117,176,198,216],"derive":[58],"from":[59],"work":[61,131],"Reed":[63],"Solomon":[64],"codes":[65],"by":[66,278],"Quintin,":[67],"Barbier":[68],"Chabot":[70],"(IEEE":[71],"Transactions":[72],"Information":[74],"Theory,":[75],"2013).":[76],"When":[77],"center":[79],"contains":[83],"set":[85],"$$A":[86],"=":[87],"\\{\\alpha":[88],"_0,":[89],"\\ldots":[90],",":[91,107,207,215],"\\alpha":[92,100,103],"_n\\}$$":[93],"such":[94,157],"$$\\forall":[96],"i":[97],"\\ne":[98],"j,":[99],"_i":[101],"\\,-\\,":[102],"_j":[104],"\\in":[105],"R^*$$":[106],"resulting":[109],"scheme":[112,162],"is":[113,132,172],"strongly":[114],"multiplicative":[115],"can":[118],"generalize":[119],"existing":[120],"constructions":[121],"over":[122],"finite":[123],"fields":[124],"without":[125],"much":[126],"trouble.":[127],"Most":[128],"our":[130,262],"devoted":[133],"case":[136],"where":[137],"elements":[139],"A":[141],"do":[142],"not":[143,173],"commute":[144,152],"with":[145,153,184,257],"all":[146],"R,":[148],"but":[149],"they":[150],"just":[151],"each":[154],"other.":[155],"For":[156],"cannot":[163],"be":[164],"linear":[165],"\u201con":[166],"both":[167],"sides\u201d":[168],"furthermore":[170],"it":[171],"multiplicative.":[174],"Nevertheless,":[175],"still":[178],"able":[179],"build":[181],"protocols":[183,218,285],"concretely":[186,282],"online":[188],"phase":[189,265],"As":[195],"an":[196],"example":[197],"consider":[199],"$$\\mathcal":[202,287],"{M}_{m\\times":[203,288],"m}(\\mathbb":[204,289],"{Z}/2^k\\mathbb":[205,290],"{Z})$$":[206,291],"$$m":[211],">":[212],"\\log":[213,223,230],"(n+1)$$":[214],"obtain":[217],"require":[220],"around":[221],"$$\\lceil":[222],"(n+1)\\rceil":[224,231],"/2$$":[225],"less":[226,233,268],"communication":[227],"$$2\\lceil":[229],"$$":[232],"computation":[234],"than":[235],"state":[237],"art":[240],"Circuit":[244],"Amortization":[245],"Friendly":[246],"Encodings":[247],"(Dalskov,":[248],"Lee":[249],"Soria-Vazquez,":[251],"ASIACRYPT":[252],"2020).":[253],"In":[254],"this":[255,277],"\u201cless":[259],"commutative\u201d":[260],"A,":[261],"preprocessing":[264,284],"has":[266],"practical":[269],"complexity":[270],"$$\\mathsf":[272],"{poly}(n)$$":[273],".":[274],"fix":[276],"additionally":[279],"providing":[280],"specialized,":[281],"exploit":[293],"structure":[295],"matrix":[298],"ring.":[299]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2021-08-16T00:00:00"}
