{"id":"https://openalex.org/W2041223547","doi":"https://doi.org/10.1145/2016567.2016585","title":"Cheater identification on a secret sharing scheme using GCD","display_name":"Cheater identification on a secret sharing scheme using GCD","publication_year":2011,"publication_date":"2011-07-25","ids":{"openalex":"https://openalex.org/W2041223547","doi":"https://doi.org/10.1145/2016567.2016585","mag":"2041223547"},"language":"en","primary_location":{"id":"doi:10.1145/2016567.2016585","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2016567.2016585","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","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/A5100994048","display_name":"Hiroshi Kai","orcid":null},"institutions":[{"id":"https://openalex.org/I43545212","display_name":"Ehime University","ror":"https://ror.org/017hkng22","country_code":"JP","type":"education","lineage":["https://openalex.org/I43545212"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Hiroshi Kai","raw_affiliation_strings":["Ehime University, Matsuyama, Japan",", Ehime University, Matsuyama, Japan"],"affiliations":[{"raw_affiliation_string":"Ehime University, Matsuyama, Japan","institution_ids":["https://openalex.org/I43545212"]},{"raw_affiliation_string":", Ehime University, Matsuyama, Japan","institution_ids":["https://openalex.org/I43545212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055454635","display_name":"Shigenobu Inoue","orcid":null},"institutions":[{"id":"https://openalex.org/I43545212","display_name":"Ehime University","ror":"https://ror.org/017hkng22","country_code":"JP","type":"education","lineage":["https://openalex.org/I43545212"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Shigenobu Inoue","raw_affiliation_strings":["Ehime University, Matsuyama, Japan",", Ehime University, Matsuyama, Japan"],"affiliations":[{"raw_affiliation_string":"Ehime University, Matsuyama, Japan","institution_ids":["https://openalex.org/I43545212"]},{"raw_affiliation_string":", Ehime University, Matsuyama, Japan","institution_ids":["https://openalex.org/I43545212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100994048"],"corresponding_institution_ids":["https://openalex.org/I43545212"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.09367589,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"45","issue":"1/2","first_page":"119","last_page":"120"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9995999932289124,"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":0.9995999932289124,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9993000030517578,"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":0.9983000159263611,"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/secret-sharing","display_name":"Secret sharing","score":0.7540769577026367},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.6664855480194092},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.6345180869102478},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6043571829795837},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5152011513710022},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5137108564376831},{"id":"https://openalex.org/keywords/rational-number","display_name":"Rational number","score":0.49797964096069336},{"id":"https://openalex.org/keywords/identification","display_name":"Identification (biology)","score":0.492135226726532},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4678298532962799},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.4549401104450226},{"id":"https://openalex.org/keywords/shamirs-secret-sharing","display_name":"Shamir's Secret Sharing","score":0.4337441921234131},{"id":"https://openalex.org/keywords/identification-scheme","display_name":"Identification scheme","score":0.410469651222229},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3796420395374298},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2944679260253906},{"id":"https://openalex.org/keywords/homomorphic-secret-sharing","display_name":"Homomorphic secret sharing","score":0.2543637156486511},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2198811173439026},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.16032198071479797},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.13527020812034607},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06391221284866333},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.06098359823226929},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.04720929265022278}],"concepts":[{"id":"https://openalex.org/C3087436","wikidata":"https://www.wikidata.org/wiki/Q1386603","display_name":"Secret sharing","level":3,"score":0.7540769577026367},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6664855480194092},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.6345180869102478},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6043571829795837},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5152011513710022},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5137108564376831},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.49797964096069336},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.492135226726532},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4678298532962799},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.4549401104450226},{"id":"https://openalex.org/C131755552","wikidata":"https://www.wikidata.org/wiki/Q935125","display_name":"Shamir's Secret Sharing","level":5,"score":0.4337441921234131},{"id":"https://openalex.org/C2778922385","wikidata":"https://www.wikidata.org/wiki/Q3475620","display_name":"Identification scheme","level":3,"score":0.410469651222229},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3796420395374298},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2944679260253906},{"id":"https://openalex.org/C132161212","wikidata":"https://www.wikidata.org/wiki/Q5891458","display_name":"Homomorphic secret sharing","level":4,"score":0.2543637156486511},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2198811173439026},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.16032198071479797},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.13527020812034607},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06391221284866333},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.06098359823226929},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.04720929265022278},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2016567.2016585","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2016567.2016585","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","score":0.5899999737739563,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1990304797","https://openalex.org/W2018562795","https://openalex.org/W2023398101","https://openalex.org/W2062046804","https://openalex.org/W2129289679","https://openalex.org/W2141420453"],"related_works":["https://openalex.org/W2391956792","https://openalex.org/W1504170878","https://openalex.org/W2186273494","https://openalex.org/W2368879407","https://openalex.org/W1983660604","https://openalex.org/W2382300719","https://openalex.org/W2766276905","https://openalex.org/W2265876396","https://openalex.org/W2063166432","https://openalex.org/W2041223547"],"abstract_inverted_index":{"A":[0],"method":[1],"to":[2],"identify":[3,52],"cheaters":[4,56],"on":[5],"the":[6,48,63,67],"Shamir's":[7],"(":[8],"k,":[9],"n":[10],")":[11],"threshold":[12],"secret":[13],"sharing":[14],"scheme":[15],"is":[16,25],"proposed":[17],"using":[18],"rational":[19,23,49],"interpolation.":[20],"When":[21],"a":[22],"interpolant":[24,50],"computed":[26,59],"for":[27],"l":[28,38],"shares":[29],"Di,":[30],"i":[31],"=":[32,39],"1,":[33],"...":[34],",":[35],"l,":[36],"where":[37],"k":[40],"+":[41],"2s,":[42],"then":[43],"s":[44,53],"unattainable":[45],"points":[46],"of":[47,62],"may":[51],"cheaters.":[54],"The":[55],"can":[57],"be":[58],"by":[60],"GCD":[61],"numerator":[64],"polynomial":[65],"and":[66],"denominator":[68],"polynomial.":[69]},"counts_by_year":[{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}