{"id":"https://openalex.org/W2402235285","doi":"https://doi.org/10.1007/978-3-642-32009-5_38","title":"Multiparty Computation from Somewhat Homomorphic Encryption","display_name":"Multiparty Computation from Somewhat Homomorphic Encryption","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2402235285","doi":"https://doi.org/10.1007/978-3-642-32009-5_38","mag":"2402235285"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-32009-5_38","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-32009-5_38","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/e887dd2f-6f29-4be5-8163-d10efae562ad","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079826922","display_name":"Ivan Damg\u00e5rd","orcid":"https://orcid.org/0009-0003-6164-0896"},"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":false,"raw_author_name":"Ivan Damg\u00e5rd","raw_affiliation_strings":["Department of Computer Science, Aarhus University, Aarhus, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Aarhus University, Aarhus, Denmark","institution_ids":["https://openalex.org/I204337017"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022196371","display_name":"Valerio Pastro","orcid":null},"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":false,"raw_author_name":"Valerio Pastro","raw_affiliation_strings":["Department of Computer Science, Aarhus University, Aarhus, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Aarhus University, Aarhus, Denmark","institution_ids":["https://openalex.org/I204337017"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013420832","display_name":"Nigel P. Smart","orcid":"https://orcid.org/0000-0003-3567-3304"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Nigel Smart","raw_affiliation_strings":["Department of Computer Science, Bristol University, Bristol, England"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Bristol University, Bristol, England","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001901089","display_name":"Sarah Zakarias","orcid":null},"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":false,"raw_author_name":"Sarah Zakarias","raw_affiliation_strings":["Department of Computer Science, Aarhus University, Aarhus, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Aarhus University, Aarhus, Denmark","institution_ids":["https://openalex.org/I204337017"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":65.0408,"has_fulltext":true,"cited_by_count":1296,"citation_normalized_percentile":{"value":0.99987085,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"643","last_page":"662"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":1.0,"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":1.0,"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":0.9936000108718872,"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"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9933000206947327,"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/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.8415618538856506},{"id":"https://openalex.org/keywords/cryptosystem","display_name":"Cryptosystem","score":0.7602128386497498},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.732787013053894},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6545219421386719},{"id":"https://openalex.org/keywords/security-parameter","display_name":"Security parameter","score":0.5979559421539307},{"id":"https://openalex.org/keywords/ciphertext","display_name":"Ciphertext","score":0.5646487474441528},{"id":"https://openalex.org/keywords/secure-multi-party-computation","display_name":"Secure multi-party computation","score":0.5309664011001587},{"id":"https://openalex.org/keywords/oblivious-transfer","display_name":"Oblivious transfer","score":0.5199210047721863},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5040820837020874},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.4685662090778351},{"id":"https://openalex.org/keywords/commitment-scheme","display_name":"Commitment scheme","score":0.4465027451515198},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4445118010044098},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.43923425674438477},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.42597317695617676},{"id":"https://openalex.org/keywords/secure-two-party-computation","display_name":"Secure two-party computation","score":0.424093097448349},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.3728100061416626},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3338685631752014},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.24124404788017273},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20949572324752808},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.1090516448020935},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07923242449760437}],"concepts":[{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.8415618538856506},{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.7602128386497498},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.732787013053894},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6545219421386719},{"id":"https://openalex.org/C2776711565","wikidata":"https://www.wikidata.org/wiki/Q7445058","display_name":"Security parameter","level":3,"score":0.5979559421539307},{"id":"https://openalex.org/C93974786","wikidata":"https://www.wikidata.org/wiki/Q1589480","display_name":"Ciphertext","level":3,"score":0.5646487474441528},{"id":"https://openalex.org/C18396474","wikidata":"https://www.wikidata.org/wiki/Q2465888","display_name":"Secure multi-party computation","level":3,"score":0.5309664011001587},{"id":"https://openalex.org/C53076038","wikidata":"https://www.wikidata.org/wiki/Q2915383","display_name":"Oblivious transfer","level":3,"score":0.5199210047721863},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5040820837020874},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.4685662090778351},{"id":"https://openalex.org/C91399829","wikidata":"https://www.wikidata.org/wiki/Q1115684","display_name":"Commitment scheme","level":3,"score":0.4465027451515198},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4445118010044098},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.43923425674438477},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.42597317695617676},{"id":"https://openalex.org/C13652956","wikidata":"https://www.wikidata.org/wiki/Q7444883","display_name":"Secure two-party computation","level":4,"score":0.424093097448349},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.3728100061416626},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3338685631752014},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.24124404788017273},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20949572324752808},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.1090516448020935},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07923242449760437}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/978-3-642-32009-5_38","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-32009-5_38","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:publications/78061ff9-a3b6-4d7e-9f14-302f945dac9b","is_oa":false,"landing_page_url":"https://pure.au.dk/portal/en/publications/78061ff9-a3b6-4d7e-9f14-302f945dac9b","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Damg\u00e5rd, I B, Pastro, V, Smart, N & Zakarias, S N H 2012, 'Multiparty computation from somewhat homomorphic encryption', Lecture Notes in Computer Science, vol. 7417, pp. 643-662. https://doi.org/10.1007/978-3-642-32009-5_38","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.atira.dk:publications/e887dd2f-6f29-4be5-8163-d10efae562ad","is_oa":true,"landing_page_url":"https://pure.au.dk/portal/en/publications/e887dd2f-6f29-4be5-8163-d10efae562ad","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Damg\u00e5rd, I B, Pastro, V, Smart, N & Zakarias, S N H 2011 'Multiparty Computation from Somewhat Homomorphic Encryption'. < http://eprint.iacr.org/2011/535 >","raw_type":"info:eu-repo/semantics/workingPaper"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/c90b36af-c496-4594-b984-60c2e8c9b828","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/c90b36af-c496-4594-b984-60c2e8c9b828","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Damg\u00e5rd, I, Pastro, V, Smart, N P & Zakarias, S 2012, Multiparty Computation from Somewhat Homomorphic Encryption. in R Safavi-Naini & R Canetti (eds), Advances in Cryptology - CRYPTO 2012. vol. 7417, Springer Berlin Heidelberg, pp. 643-662.","raw_type":"contributionToPeriodical"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:publications/e887dd2f-6f29-4be5-8163-d10efae562ad","is_oa":true,"landing_page_url":"https://pure.au.dk/portal/en/publications/e887dd2f-6f29-4be5-8163-d10efae562ad","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Damg\u00e5rd, I B, Pastro, V, Smart, N & Zakarias, S N H 2011 'Multiparty Computation from Somewhat Homomorphic Encryption'. < http://eprint.iacr.org/2011/535 >","raw_type":"info:eu-repo/semantics/workingPaper"},"sustainable_development_goals":[{"score":0.7200000286102295,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G2575519571","display_name":null,"funder_award_id":"EP/I03126X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W80562455","https://openalex.org/W147235090","https://openalex.org/W198033559","https://openalex.org/W1494049356","https://openalex.org/W1494774797","https://openalex.org/W1505629034","https://openalex.org/W1506156414","https://openalex.org/W1507124880","https://openalex.org/W1521893691","https://openalex.org/W1524288918","https://openalex.org/W1527450129","https://openalex.org/W1560201081","https://openalex.org/W1576843907","https://openalex.org/W1755636270","https://openalex.org/W1760474993","https://openalex.org/W1761303171","https://openalex.org/W1766548092","https://openalex.org/W1884982511","https://openalex.org/W1966731635","https://openalex.org/W1980227445","https://openalex.org/W2016443801","https://openalex.org/W2031533839","https://openalex.org/W2096218735","https://openalex.org/W2098290658","https://openalex.org/W2106970188","https://openalex.org/W2108603643","https://openalex.org/W2113085788","https://openalex.org/W2114118999","https://openalex.org/W2120033653","https://openalex.org/W2126484007","https://openalex.org/W2147436724","https://openalex.org/W2152926062","https://openalex.org/W2398715209","https://openalex.org/W2403288623","https://openalex.org/W2475786860","https://openalex.org/W2479682916","https://openalex.org/W2497843319","https://openalex.org/W3030551544"],"related_works":["https://openalex.org/W2952477979","https://openalex.org/W4293056000","https://openalex.org/W2952662274","https://openalex.org/W2987358745","https://openalex.org/W2949728854","https://openalex.org/W2886283651","https://openalex.org/W2587122949","https://openalex.org/W2979421064","https://openalex.org/W2899423027","https://openalex.org/W2120315802"],"abstract_inverted_index":{"We":[0,124,158],"propose":[1],"a":[2,41,59,107,139,154,160,205,230],"general":[3],"multiparty":[4],"computation":[5,68,130],"protocol":[6,21,38],"secure":[7,76,140,200,231],"against":[8],"an":[9],"active":[10],"adversary":[11],"corrupting":[12],"up":[13],"to":[14,25,51,117],"$$n-1$$":[15],"of":[16,40,48,55,89,185,213],"the":[17,49,56,66,87,99,119,122,192,210,214,227],"n":[18],"players.":[19],"The":[20,71,182],"may":[22],"be":[23,52,144],"used":[24],"compute":[26,118],"securely":[27],"arithmetic":[28],"circuits":[29],"over":[30],"any":[31],"finite":[32],"field":[33],"$$\\mathbb":[34],"{F}_{p^k}$$":[35],".":[36],"Our":[37,149],"consists":[39],"preprocessing":[42,150,187,228],"phase":[43,64,73,188],"that":[44,167,207],"is":[45,74,105,127,151,189,204],"both":[46],"independent":[47],"function":[50],"computed":[53],"and":[54,58,77,173],"inputs,":[57],"much":[60],"more":[61],"efficient":[62],"online":[63,72],"where":[65,91,202],"actual":[67],"takes":[69],"place.":[70],"unconditionally":[75],"has":[78],"total":[79],"computational":[80,183],"(and":[81],"communication)":[82],"complexity":[83,184],"linear":[84],"in":[85,96,121,131,146,177,179,218,237],"n,":[86],"number":[88],"players,":[90,138],"earlier":[92],"work":[93,100,217],"was":[94],"quadratic":[95],"n.":[97],"Moreover,":[98],"done":[101,145],"by":[102,162,191],"each":[103],"player":[104],"only":[106],"small":[108],"constant":[109],"factor":[110],"larger":[111],"than":[112],"what":[113],"one":[114,180],"would":[115],"need":[116,196],"circuit":[120],"clear.":[123],"show":[125],"this":[126,219],"optimal":[128],"for":[129,136,234],"large":[132],"fields.":[133],"In":[134,225],"practice,":[135,226],"3":[137,235],"64-bit":[141,232],"multiplication":[142,201,233],"can":[143,169],"0.05":[147],"ms.":[148,240],"based":[152],"on":[153],"somewhat":[155],"homomorphic":[156],"cryptosystem.":[157,215],"extend":[159],"scheme":[161],"Brakerski":[163],"et":[164],"al.,":[165],"so":[166],"we":[168,195],"perform":[170],"distributed":[171],"decryption":[172],"handle":[174],"many":[175],"values":[176],"parallel":[178],"ciphertext.":[181],"our":[186],"dominated":[190],"public-key":[193],"operations,":[194],"$$O(n^2/s)$$":[197],"operations":[198],"per":[199],"s":[203],"parameter":[206,212],"increases":[208],"with":[209],"security":[211],"Earlier":[216],"model":[220],"needed":[221],"$$\\varOmega":[222],"(n^2)$$":[223],"operations.":[224],"prepares":[229],"players":[236],"about":[238],"13":[239]},"counts_by_year":[{"year":2026,"cited_by_count":21},{"year":2025,"cited_by_count":121},{"year":2024,"cited_by_count":114},{"year":2023,"cited_by_count":127},{"year":2022,"cited_by_count":116},{"year":2021,"cited_by_count":146},{"year":2020,"cited_by_count":134},{"year":2019,"cited_by_count":89},{"year":2018,"cited_by_count":84},{"year":2017,"cited_by_count":81},{"year":2016,"cited_by_count":55},{"year":2015,"cited_by_count":68},{"year":2014,"cited_by_count":69},{"year":2013,"cited_by_count":48},{"year":2012,"cited_by_count":20}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}