{"id":"https://openalex.org/W2937874745","doi":"https://doi.org/10.1007/s10586-019-02930-4","title":"Verifiable outsourcing computation for modular exponentiation from shareable functions","display_name":"Verifiable outsourcing computation for modular exponentiation from shareable functions","publication_year":2019,"publication_date":"2019-04-16","ids":{"openalex":"https://openalex.org/W2937874745","doi":"https://doi.org/10.1007/s10586-019-02930-4","mag":"2937874745"},"language":"en","primary_location":{"id":"doi:10.1007/s10586-019-02930-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10586-019-02930-4","pdf_url":null,"source":{"id":"https://openalex.org/S106148199","display_name":"Cluster Computing","issn_l":"1386-7857","issn":["1386-7857","1573-7543"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cluster 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/A5101676982","display_name":"Muhua Liu","orcid":"https://orcid.org/0000-0002-9967-8545"},"institutions":[{"id":"https://openalex.org/I167383011","display_name":"Henan University of Science and Technology","ror":"https://ror.org/05d80kz58","country_code":"CN","type":"education","lineage":["https://openalex.org/I167383011"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Muhua Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471000, People\u2019s Republic of China"],"raw_orcid":"https://orcid.org/0000-0002-9967-8545","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471000, People\u2019s Republic of China","institution_ids":["https://openalex.org/I167383011"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042765290","display_name":"Ying Wu","orcid":"https://orcid.org/0000-0001-8029-3664"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I37448385","display_name":"China People's Public Security University","ror":"https://ror.org/05twya590","country_code":"CN","type":"education","lineage":["https://openalex.org/I37448385"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ying Wu","raw_affiliation_strings":["School of Cyber Security, University of Chinese Academy of Sciences, Beijing, 100049, People\u2019s Republic of China","State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100049, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing, 100049, People\u2019s Republic of China","institution_ids":["https://openalex.org/I37448385","https://openalex.org/I4210165038"]},{"raw_affiliation_string":"State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100049, People\u2019s Republic of China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079155690","display_name":"Rui Xue","orcid":"https://orcid.org/0000-0001-6024-3635"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I37448385","display_name":"China People's Public Security University","ror":"https://ror.org/05twya590","country_code":"CN","type":"education","lineage":["https://openalex.org/I37448385"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rui Xue","raw_affiliation_strings":["School of Cyber Security, University of Chinese Academy of Sciences, Beijing, 100049, People\u2019s Republic of China","State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100049, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing, 100049, People\u2019s Republic of China","institution_ids":["https://openalex.org/I37448385","https://openalex.org/I4210165038"]},{"raw_affiliation_string":"State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100049, People\u2019s Republic of China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100422048","display_name":"Rui Zhang","orcid":"https://orcid.org/0000-0002-4221-1311"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I37448385","display_name":"China People's Public Security University","ror":"https://ror.org/05twya590","country_code":"CN","type":"education","lineage":["https://openalex.org/I37448385"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rui Zhang","raw_affiliation_strings":["School of Cyber Security, University of Chinese Academy of Sciences, Beijing, 100049, People\u2019s Republic of China","State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100049, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing, 100049, People\u2019s Republic of China","institution_ids":["https://openalex.org/I37448385","https://openalex.org/I4210165038"]},{"raw_affiliation_string":"State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100049, People\u2019s Republic of China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5101676982"],"corresponding_institution_ids":["https://openalex.org/I167383011"],"apc_list":{"value":2790,"currency":"USD","value_usd":2790},"apc_paid":null,"fwci":1.109,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.8315935,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":"1","first_page":"43","last_page":"55"},"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/T11614","display_name":"Cloud Data Security Solutions","score":0.9948999881744385,"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/T11181","display_name":"Advanced Data Storage Technologies","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/computer-science","display_name":"Computer science","score":0.8895574808120728},{"id":"https://openalex.org/keywords/modular-exponentiation","display_name":"Modular exponentiation","score":0.8453320860862732},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.6818670630455017},{"id":"https://openalex.org/keywords/exponentiation","display_name":"Exponentiation","score":0.6542502045631409},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6363551020622253},{"id":"https://openalex.org/keywords/outsourcing","display_name":"Outsourcing","score":0.6284670829772949},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.6017688512802124},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.45141908526420593},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4280288815498352},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.375559538602829},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.3493335247039795},{"id":"https://openalex.org/keywords/distributed-computing","display_name":"Distributed computing","score":0.33076393604278564},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3081676959991455},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.12948501110076904},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.10362812876701355},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.08068522810935974}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8895574808120728},{"id":"https://openalex.org/C152763109","wikidata":"https://www.wikidata.org/wiki/Q1228841","display_name":"Modular exponentiation","level":4,"score":0.8453320860862732},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.6818670630455017},{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.6542502045631409},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6363551020622253},{"id":"https://openalex.org/C46934059","wikidata":"https://www.wikidata.org/wiki/Q61515","display_name":"Outsourcing","level":2,"score":0.6284670829772949},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.6017688512802124},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.45141908526420593},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4280288815498352},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.375559538602829},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.3493335247039795},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.33076393604278564},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3081676959991455},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.12948501110076904},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.10362812876701355},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.08068522810935974},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10586-019-02930-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10586-019-02930-4","pdf_url":null,"source":{"id":"https://openalex.org/S106148199","display_name":"Cluster Computing","issn_l":"1386-7857","issn":["1386-7857","1573-7543"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cluster Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1977279789","display_name":null,"funder_award_id":"61402471","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G271907962","display_name":"\u7b26\u53f7\u5316\u901a\u7528\u590d\u5408\u7684\u5bc6\u7801\u534f\u8bae\u5206\u6790\u65b9\u6cd5\u7814\u7a76","funder_award_id":"61170280","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8638297732","display_name":"\u5bf9\u4f9d\u8d56\u5bc6\u94a5\u7684\u660e\u6587\u8fdb\u884c\u5b89\u5168\u52a0\u5bc6\u7684\u6027\u8d28\u7814\u7a76","funder_award_id":"61472414","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W9326323","https://openalex.org/W22402230","https://openalex.org/W24999078","https://openalex.org/W110839122","https://openalex.org/W154795652","https://openalex.org/W167928972","https://openalex.org/W174039250","https://openalex.org/W231770548","https://openalex.org/W654550811","https://openalex.org/W1484276943","https://openalex.org/W1557386445","https://openalex.org/W1561511342","https://openalex.org/W1581161155","https://openalex.org/W1855553159","https://openalex.org/W1873037073","https://openalex.org/W1970606468","https://openalex.org/W1974267799","https://openalex.org/W1980516015","https://openalex.org/W1988007981","https://openalex.org/W2009432965","https://openalex.org/W2010094835","https://openalex.org/W2053086236","https://openalex.org/W2058701727","https://openalex.org/W2096390054","https://openalex.org/W2101687784","https://openalex.org/W2114486350","https://openalex.org/W2116653107","https://openalex.org/W2121423622","https://openalex.org/W2136936712","https://openalex.org/W2138736975","https://openalex.org/W2146099890","https://openalex.org/W2153478646","https://openalex.org/W2161508639","https://openalex.org/W2239212099","https://openalex.org/W2304212389","https://openalex.org/W2520288416","https://openalex.org/W2561675875","https://openalex.org/W3030771120","https://openalex.org/W3141585064"],"related_works":["https://openalex.org/W4235485585","https://openalex.org/W670148","https://openalex.org/W1507420113","https://openalex.org/W4242613270","https://openalex.org/W2107014706","https://openalex.org/W28274153","https://openalex.org/W2736837562","https://openalex.org/W2020808628","https://openalex.org/W2113040119","https://openalex.org/W2767903583"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}