{"id":"https://openalex.org/W2618795523","doi":"https://doi.org/10.1155/2017/5207386","title":"Efficient Solutions to Two-Party and Multiparty Millionaires\u2019 Problem","display_name":"Efficient Solutions to Two-Party and Multiparty Millionaires\u2019 Problem","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2618795523","doi":"https://doi.org/10.1155/2017/5207386","mag":"2618795523"},"language":"en","primary_location":{"id":"doi:10.1155/2017/5207386","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2017/5207386","pdf_url":"http://downloads.hindawi.com/journals/scn/2017/5207386.pdf","source":{"id":"https://openalex.org/S120683614","display_name":"Security and Communication Networks","issn_l":"1939-0114","issn":["1939-0114","1939-0122"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Security and Communication Networks","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"http://downloads.hindawi.com/journals/scn/2017/5207386.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100352218","display_name":"Xin Liu","orcid":"https://orcid.org/0000-0002-3450-3808"},"institutions":[{"id":"https://openalex.org/I31637741","display_name":"Inner Mongolia University of Science and Technology","ror":"https://ror.org/044rgx723","country_code":"CN","type":"education","lineage":["https://openalex.org/I31637741"]},{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xin Liu","raw_affiliation_strings":["School of Computer Science, Shaanxi Normal University, Xi\u2019an 710062, China","School of Information Engineering, Inner Mongolia University of Science and Technology, Baotou 014010, China"],"raw_orcid":"https://orcid.org/0000-0002-3450-3808","affiliations":[{"raw_affiliation_string":"School of Computer Science, Shaanxi Normal University, Xi\u2019an 710062, China","institution_ids":["https://openalex.org/I88830068"]},{"raw_affiliation_string":"School of Information Engineering, Inner Mongolia University of Science and Technology, Baotou 014010, China","institution_ids":["https://openalex.org/I31637741"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101844423","display_name":"Shundong Li","orcid":"https://orcid.org/0000-0002-8345-2955"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shundong Li","raw_affiliation_strings":["School of Computer Science, Shaanxi Normal University, Xi\u2019an 710062, China"],"raw_orcid":"https://orcid.org/0000-0002-8345-2955","affiliations":[{"raw_affiliation_string":"School of Computer Science, Shaanxi Normal University, Xi\u2019an 710062, China","institution_ids":["https://openalex.org/I88830068"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005902299","display_name":"Xiu\u2010Bo Chen","orcid":"https://orcid.org/0000-0002-9761-3414"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"XiuBo Chen","raw_affiliation_strings":["Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China","institution_ids":["https://openalex.org/I139759216"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045319978","display_name":"Gang Xu","orcid":"https://orcid.org/0000-0002-1409-252X"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gang Xu","raw_affiliation_strings":["School of Software Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Software Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China","institution_ids":["https://openalex.org/I139759216"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101755023","display_name":"Xiaolin Zhang","orcid":"https://orcid.org/0000-0003-0962-4007"},"institutions":[{"id":"https://openalex.org/I31637741","display_name":"Inner Mongolia University of Science and Technology","ror":"https://ror.org/044rgx723","country_code":"CN","type":"education","lineage":["https://openalex.org/I31637741"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaolin Zhang","raw_affiliation_strings":["School of Information Engineering, Inner Mongolia University of Science and Technology, Baotou 014010, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Engineering, Inner Mongolia University of Science and Technology, Baotou 014010, China","institution_ids":["https://openalex.org/I31637741"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101984501","display_name":"Yong Zhou","orcid":"https://orcid.org/0000-0003-2924-7341"},"institutions":[{"id":"https://openalex.org/I49420792","display_name":"Northwest University of Politics and Law","ror":"https://ror.org/05008jp45","country_code":"CN","type":"education","lineage":["https://openalex.org/I49420792"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong Zhou","raw_affiliation_strings":["Information and Network Center, Northwest University of Politics and Law, Xi\u2019an 710061, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information and Network Center, Northwest University of Politics and Law, Xi\u2019an 710061, China","institution_ids":["https://openalex.org/I49420792"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101844423"],"corresponding_institution_ids":["https://openalex.org/I88830068"],"apc_list":{"value":2550,"currency":"USD","value_usd":2550},"apc_paid":{"value":2550,"currency":"USD","value_usd":2550},"fwci":3.3951,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.93657605,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"2017","issue":null,"first_page":"1","last_page":"11"},"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":0.9972000122070312,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9876000285148621,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.8145924210548401},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6700961589813232},{"id":"https://openalex.org/keywords/vectorization","display_name":"Vectorization (mathematics)","score":0.5700389742851257},{"id":"https://openalex.org/keywords/protocol","display_name":"Protocol (science)","score":0.4248772859573364},{"id":"https://openalex.org/keywords/database","display_name":"Database","score":0.388444721698761},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33699938654899597},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.08376258611679077}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8145924210548401},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6700961589813232},{"id":"https://openalex.org/C41681595","wikidata":"https://www.wikidata.org/wiki/Q7917855","display_name":"Vectorization (mathematics)","level":2,"score":0.5700389742851257},{"id":"https://openalex.org/C2780385302","wikidata":"https://www.wikidata.org/wiki/Q367158","display_name":"Protocol (science)","level":3,"score":0.4248772859573364},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.388444721698761},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33699938654899597},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.08376258611679077},{"id":"https://openalex.org/C142724271","wikidata":"https://www.wikidata.org/wiki/Q7208","display_name":"Pathology","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C204787440","wikidata":"https://www.wikidata.org/wiki/Q188504","display_name":"Alternative medicine","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2017/5207386","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2017/5207386","pdf_url":"http://downloads.hindawi.com/journals/scn/2017/5207386.pdf","source":{"id":"https://openalex.org/S120683614","display_name":"Security and Communication Networks","issn_l":"1939-0114","issn":["1939-0114","1939-0122"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Security and Communication Networks","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3f38f9298a5e4f0e95ca654e6c415585","is_oa":false,"landing_page_url":"https://doaj.org/article/3f38f9298a5e4f0e95ca654e6c415585","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":"Security and Communication Networks, Vol 2017 (2017)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2017/5207386","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2017/5207386","pdf_url":"http://downloads.hindawi.com/journals/scn/2017/5207386.pdf","source":{"id":"https://openalex.org/S120683614","display_name":"Security and Communication Networks","issn_l":"1939-0114","issn":["1939-0114","1939-0122"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Security and Communication Networks","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1360124390","display_name":null,"funder_award_id":"61272514","funder_id":"https://openalex.org/F4320322868","funder_display_name":"Natural Science Foundation of Inner Mongolia"},{"id":"https://openalex.org/G2544931309","display_name":"\u4e91\u8ba1\u7b97\u4e0e\u4e91\u5b58\u50a8\u82e5\u5e72\u5173\u952e\u5b89\u5168\u95ee\u9898\u7814\u7a76","funder_award_id":"61272435","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2655324589","display_name":null,"funder_award_id":"61562065","funder_id":"https://openalex.org/F4320322868","funder_display_name":"Natural Science Foundation of Inner Mongolia"},{"id":"https://openalex.org/G3660487942","display_name":"\u91cf\u5b50\u7f51\u7edc\u7f16\u7801\u7406\u8bba\u53ca\u5176\u5e94\u7528\u7814\u7a76","funder_award_id":"61272514","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3675151945","display_name":"\u9762\u5411\u4e91\u8ba1\u7b97\u73af\u5883\u7684\u5927\u89c4\u6a21\u793e\u4f1a\u7f51\u7edc\u9690\u79c1\u4fdd\u62a4\u6280\u672f\u7814\u7a76","funder_award_id":"61562065","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4265678875","display_name":"\u57fa\u4e8eDLPCNN\u7684\u5e73\u7a33Contourlet\u57df\u8111\u90e8\u591a\u6a21\u533b\u5b66\u56fe\u50cf\u878d\u5408\u7b97\u6cd5\u7814\u7a76","funder_award_id":"61261028","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4609257124","display_name":null,"funder_award_id":"2017MS0602","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G5607258921","display_name":null,"funder_award_id":"2016TS061","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5812720534","display_name":null,"funder_award_id":"NJZY17166","funder_id":"https://openalex.org/F4320322868","funder_display_name":"Natural Science Foundation of Inner Mongolia"},{"id":"https://openalex.org/G583900899","display_name":null,"funder_award_id":"61261028","funder_id":"https://openalex.org/F4320322868","funder_display_name":"Natural Science Foundation of Inner Mongolia"},{"id":"https://openalex.org/G6928307067","display_name":null,"funder_award_id":"2017MS0602","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6973118068","display_name":null,"funder_award_id":"61562065","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G7098127779","display_name":null,"funder_award_id":"61272514","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G7306847709","display_name":null,"funder_award_id":"61272435","funder_id":"https://openalex.org/F4320322868","funder_display_name":"Natural Science Foundation of Inner Mongolia"},{"id":"https://openalex.org/G7310288184","display_name":null,"funder_award_id":"61261028","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G7653024909","display_name":null,"funder_award_id":"2016TS061","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G7920039346","display_name":null,"funder_award_id":"NJZY17166","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8344597904","display_name":null,"funder_award_id":"2017MS0602","funder_id":"https://openalex.org/F4320322868","funder_display_name":"Natural Science Foundation of Inner Mongolia"},{"id":"https://openalex.org/G835740452","display_name":null,"funder_award_id":"2016TS061","funder_id":"https://openalex.org/F4320322868","funder_display_name":"Natural Science Foundation of Inner Mongolia"},{"id":"https://openalex.org/G8508988952","display_name":null,"funder_award_id":"61272435","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G8655764600","display_name":null,"funder_award_id":"NJZY17166","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322868","display_name":"Natural Science Foundation of Inner Mongolia","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2618795523.pdf","grobid_xml":"https://content.openalex.org/works/W2618795523.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1548880861","https://openalex.org/W1562018356","https://openalex.org/W1966637168","https://openalex.org/W1979493600","https://openalex.org/W1987706396","https://openalex.org/W2003668524","https://openalex.org/W2007877577","https://openalex.org/W2027154656","https://openalex.org/W2061879449","https://openalex.org/W2077456032","https://openalex.org/W2087504901","https://openalex.org/W2130901615","https://openalex.org/W2138684280","https://openalex.org/W2196528695","https://openalex.org/W2321155245","https://openalex.org/W2469486851","https://openalex.org/W2470666398","https://openalex.org/W2516684370","https://openalex.org/W2556752342","https://openalex.org/W2963325634"],"related_works":["https://openalex.org/W2762467749","https://openalex.org/W2374048355","https://openalex.org/W2161584192","https://openalex.org/W3024308452","https://openalex.org/W2359910081","https://openalex.org/W2381929598","https://openalex.org/W2383797864","https://openalex.org/W2364351544","https://openalex.org/W2385460613","https://openalex.org/W2115712375"],"abstract_inverted_index":{"The":[0],"millionaires\u2019":[1,32,67],"problem":[2,68],"is":[3],"the":[4,19,31,51,65,82,90,95,101,105],"basis":[5],"of":[6,86],"secure":[7,27,61,70],"multiparty":[8,66],"computation":[9],"and":[10,18,53,73,84,93,97,104],"has":[11],"many":[12],"applications.":[13],"Using":[14],"a":[15,26],"vectorization":[16,52],"method":[17],"Paillier":[20],"encryption":[21],"scheme,":[22],"we":[23,57],"first":[24],"propose":[25,58],"two-party":[28],"solution":[29],"to":[30,63],"problem,":[33],"which":[34],"can":[35,76],"determine":[36],"<mml:math":[37,43],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[38,44],"id=\"M1\"><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mo>":[39],"</mml:mo><mml:mo>":[40],"</mml:mo><mml:mi>x</mml:mi><mml:mo>&lt;</mml:mo><mml:mi>y</mml:mi></mml:math>,":[41],"or":[42],"id=\"M2\"><mml:mi>x</mml:mi><mml:mo>&gt;</mml:mo><mml:mi>y</mml:mi></mml:math>":[45],"in":[46,89],"one":[47],"execution.":[48],"Subsequently,":[49],"using":[50],"secret":[54],"splitting":[55],"methods,":[56],"an":[59],"information-theoretically":[60],"protocol":[62,75],"solve":[64],"(a.k.a.":[69],"sorting":[71],"problem),":[72],"this":[74],"resist":[77],"collusion":[78],"attacks.":[79],"We":[80],"analyze":[81],"accuracy":[83],"security":[85],"our":[87],"protocols":[88,103],"semihonest":[91],"model":[92],"compare":[94],"computational":[96],"communication":[98],"complexities":[99],"between":[100],"proposed":[102],"existing":[106],"ones.":[107]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":6}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}