{"id":"https://openalex.org/W2005900892","doi":"https://doi.org/10.1137/s0097539797321742","title":"Reducibility and Completeness in Private Computations","display_name":"Reducibility and Completeness in Private Computations","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2005900892","doi":"https://doi.org/10.1137/s0097539797321742","mag":"2005900892"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539797321742","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539797321742","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on 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/A5037463975","display_name":"Joe Kilian","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Joe Kilian","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036104549","display_name":"Eyal Kushilevitz","orcid":"https://orcid.org/0009-0009-9277-3863"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eyal Kushilevitz","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030198184","display_name":"Silvio Micali","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Silvio Micali","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5020375635","display_name":"Rafail Ostrovsky","orcid":"https://orcid.org/0000-0002-1501-1330"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rafail Ostrovsky","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5037463975"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.3676,"has_fulltext":false,"cited_by_count":62,"citation_normalized_percentile":{"value":0.96316854,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"29","issue":"4","first_page":"1189","last_page":"1208"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9939000010490417,"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/T11598","display_name":"Internet Traffic Analysis and Secure E-voting","score":0.9927999973297119,"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/completeness","display_name":"Completeness (order theory)","score":0.8540358543395996},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.7547755241394043},{"id":"https://openalex.org/keywords/argument","display_name":"Argument (complex analysis)","score":0.6254794597625732},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.6071360111236572},{"id":"https://openalex.org/keywords/black-box","display_name":"Black box","score":0.5960386991500854},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5892901420593262},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5465230941772461},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5383004546165466},{"id":"https://openalex.org/keywords/parity-function","display_name":"Parity function","score":0.43215981125831604},{"id":"https://openalex.org/keywords/boolean-data-type","display_name":"Boolean data type","score":0.42950063943862915},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.42842045426368713},{"id":"https://openalex.org/keywords/one-way-function","display_name":"One-way function","score":0.42832961678504944},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.41493797302246094},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3723253309726715},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3210684657096863},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15354669094085693},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.12365657091140747},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05880081653594971}],"concepts":[{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.8540358543395996},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.7547755241394043},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.6254794597625732},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6071360111236572},{"id":"https://openalex.org/C94966114","wikidata":"https://www.wikidata.org/wiki/Q29256","display_name":"Black box","level":2,"score":0.5960386991500854},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5892901420593262},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5465230941772461},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5383004546165466},{"id":"https://openalex.org/C188183281","wikidata":"https://www.wikidata.org/wiki/Q2898309","display_name":"Parity function","level":4,"score":0.43215981125831604},{"id":"https://openalex.org/C7342684","wikidata":"https://www.wikidata.org/wiki/Q520777","display_name":"Boolean data type","level":2,"score":0.42950063943862915},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.42842045426368713},{"id":"https://openalex.org/C105355099","wikidata":"https://www.wikidata.org/wiki/Q720931","display_name":"One-way function","level":3,"score":0.42832961678504944},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.41493797302246094},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3723253309726715},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3210684657096863},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15354669094085693},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.12365657091140747},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05880081653594971},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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:10.1137/s0097539797321742","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539797321742","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.44.6800","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.6800","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.argreenhouse.com/papers/rafail/21.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.550000011920929,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1603973540","https://openalex.org/W1607225066","https://openalex.org/W1974751157","https://openalex.org/W1984332407","https://openalex.org/W1987667503","https://openalex.org/W1988394435","https://openalex.org/W2006453614","https://openalex.org/W2013784340","https://openalex.org/W2020316223","https://openalex.org/W2027471022","https://openalex.org/W2032956091","https://openalex.org/W2035912926","https://openalex.org/W2039320535","https://openalex.org/W2047539027","https://openalex.org/W2052193425","https://openalex.org/W2074423381","https://openalex.org/W2077315235","https://openalex.org/W2080911030","https://openalex.org/W2088492763","https://openalex.org/W2092422002","https://openalex.org/W2096430557","https://openalex.org/W2144752539","https://openalex.org/W2147263373","https://openalex.org/W2151433956","https://openalex.org/W2153708829","https://openalex.org/W2161670619","https://openalex.org/W2336770924"],"related_works":["https://openalex.org/W1597080238","https://openalex.org/W2234833091","https://openalex.org/W2011469629","https://openalex.org/W2487593933","https://openalex.org/W2106622045","https://openalex.org/W59031104","https://openalex.org/W2061512596","https://openalex.org/W3141532631","https://openalex.org/W2131164334","https://openalex.org/W2121507897"],"abstract_inverted_index":{"We":[0,20,64],"define":[1],"the":[2,38,56,86,121,155],"notions":[3,122,166],"of":[4,58,123,135],"reducibility":[5],"and":[6,10,54,100,125],"completeness":[7,124],"in":[8,151],"(two-party":[9],"multiparty)":[11],"private":[12,71],"computations.":[13],"Let":[14],"g":[15,31,47,60,67,96,103],"be":[16,106],"an":[17],"n-argument":[18,118],"function.":[19],"say":[21,65],"that":[22,66,92,147,163],"a":[23,29,43,93,132],"function":[24,30,39,75,95],"f":[25,76],"is":[26,68,77,97,111],"reducible":[27,78],"to":[28,79,143],"if":[32,73,99,102],"n":[33],"honest-but-curious":[34],"players":[35],"can":[36],"compute":[37],"fn":[40],"-privately,":[41],"given":[42,149],"black":[44,113],"box":[45,114],"for":[46,117,158],"(for":[48,70],"which":[49],"they":[50],"secretly":[51],"give":[52],"inputs":[53],"get":[55],"result":[57],"operating":[59],"on":[61],"these":[62,164],"inputs).":[63],"complete":[69,87,98,136],"computations)":[72],"every":[74],"g.":[80],"In":[81],"this":[82],"paper,":[83],"we":[84,90,161],"characterize":[85],"boolean":[88,94,119,140],"functions:":[89],"show":[91,162],"only":[101],"itself":[104],"cannot":[105],"computed":[107],"n-privately":[108],"(when":[109],"there":[110],"no":[112],"available).":[115],"Namely,":[116],"functions,":[120,160],"n-privacy":[126],"are":[127,167],"complementary.":[128,169],"This":[129],"characterization":[130],"provides":[131],"huge":[133],"collection":[134],"functions":[137],"any":[138],"nonprivate":[139],"function!)":[141],"compared":[142],"very":[144],"few":[145],"examples":[146],"were":[148],"(implicitly)":[150],"previous":[152],"work.":[153],"On":[154],"other":[156],"hand,":[157],"nonboolean":[159],"two":[165],"not":[168]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
