{"id":"https://openalex.org/W4327737970","doi":"https://doi.org/10.3390/axioms12030304","title":"An IND-CPA Analysis of a Cryptosystem Based on Bivariate Polynomial Reconstruction Problem","display_name":"An IND-CPA Analysis of a Cryptosystem Based on Bivariate Polynomial Reconstruction Problem","publication_year":2023,"publication_date":"2023-03-17","ids":{"openalex":"https://openalex.org/W4327737970","doi":"https://doi.org/10.3390/axioms12030304"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12030304","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12030304","pdf_url":"https://www.mdpi.com/2075-1680/12/3/304/pdf?version=1679032119","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/3/304/pdf?version=1679032119","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055166362","display_name":"Siti Nabilah Yusof","orcid":"https://orcid.org/0009-0007-7564-9516"},"institutions":[{"id":"https://openalex.org/I130343225","display_name":"Universiti Putra Malaysia","ror":"https://ror.org/02e91jd64","country_code":"MY","type":"education","lineage":["https://openalex.org/I130343225"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Siti Nabilah Yusof","raw_affiliation_strings":["Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia"],"raw_orcid":"https://orcid.org/0009-0007-7564-9516","affiliations":[{"raw_affiliation_string":"Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia","institution_ids":["https://openalex.org/I130343225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071414544","display_name":"Muhammad Rezal Kamel Ariffin","orcid":"https://orcid.org/0000-0001-5000-354X"},"institutions":[{"id":"https://openalex.org/I130343225","display_name":"Universiti Putra Malaysia","ror":"https://ror.org/02e91jd64","country_code":"MY","type":"education","lineage":["https://openalex.org/I130343225"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"Muhammad Rezal Kamel Ariffin","raw_affiliation_strings":["Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia","Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia","institution_ids":["https://openalex.org/I130343225"]},{"raw_affiliation_string":"Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia","institution_ids":["https://openalex.org/I130343225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058176227","display_name":"Terry Shue Chien Lau","orcid":"https://orcid.org/0000-0002-1218-9133"},"institutions":[{"id":"https://openalex.org/I173029219","display_name":"Multimedia University","ror":"https://ror.org/04zrbnc33","country_code":"MY","type":"education","lineage":["https://openalex.org/I173029219"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Terry Shue Chien Lau","raw_affiliation_strings":["Faculty of Computing and Informatics, Multimedia University, Cyberjaya 63100, Selangor, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Computing and Informatics, Multimedia University, Cyberjaya 63100, Selangor, Malaysia","institution_ids":["https://openalex.org/I173029219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004960425","display_name":"Nur Raidah Salim","orcid":"https://orcid.org/0000-0002-7941-1878"},"institutions":[{"id":"https://openalex.org/I130343225","display_name":"Universiti Putra Malaysia","ror":"https://ror.org/02e91jd64","country_code":"MY","type":"education","lineage":["https://openalex.org/I130343225"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Nur Raidah Salim","raw_affiliation_strings":["Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia"],"raw_orcid":"https://orcid.org/0000-0002-7941-1878","affiliations":[{"raw_affiliation_string":"Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia","institution_ids":["https://openalex.org/I130343225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079411335","display_name":"Sook-Chin Yip","orcid":"https://orcid.org/0000-0002-8575-4244"},"institutions":[{"id":"https://openalex.org/I173029219","display_name":"Multimedia University","ror":"https://ror.org/04zrbnc33","country_code":"MY","type":"education","lineage":["https://openalex.org/I173029219"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"Sook-Chin Yip","raw_affiliation_strings":["Faculty of Engineering, Multimedia University, Cyberjaya 63100, Selangor, Malaysia"],"raw_orcid":"https://orcid.org/0000-0002-8575-4244","affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Multimedia University, Cyberjaya 63100, Selangor, Malaysia","institution_ids":["https://openalex.org/I173029219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070838486","display_name":"Timothy Tzen Vun Yap","orcid":"https://orcid.org/0000-0003-1277-1710"},"institutions":[{"id":"https://openalex.org/I173029219","display_name":"Multimedia University","ror":"https://ror.org/04zrbnc33","country_code":"MY","type":"education","lineage":["https://openalex.org/I173029219"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Timothy Tzen Vun Yap","raw_affiliation_strings":["Faculty of Computing and Informatics, Multimedia University, Cyberjaya 63100, Selangor, Malaysia"],"raw_orcid":"https://orcid.org/0000-0003-1277-1710","affiliations":[{"raw_affiliation_string":"Faculty of Computing and Informatics, Multimedia University, Cyberjaya 63100, Selangor, Malaysia","institution_ids":["https://openalex.org/I173029219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5071414544","https://openalex.org/A5079411335"],"corresponding_institution_ids":["https://openalex.org/I130343225","https://openalex.org/I173029219"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.8425,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.77469205,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"12","issue":"3","first_page":"304","last_page":"304"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","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/T11130","display_name":"Coding theory and cryptography","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/T10951","display_name":"Cryptographic Implementations and 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/T11797","display_name":"graph theory and CDMA systems","score":0.9991999864578247,"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/bivariate-analysis","display_name":"Bivariate analysis","score":0.786271870136261},{"id":"https://openalex.org/keywords/cryptosystem","display_name":"Cryptosystem","score":0.646578311920166},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5983816385269165},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.583779513835907},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46694791316986084},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4638146758079529},{"id":"https://openalex.org/keywords/plaintext","display_name":"Plaintext","score":0.44993993639945984},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3919031023979187},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35710588097572327},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30825307965278625},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.19530212879180908},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1566622257232666},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.1492878794670105},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.11356410384178162}],"concepts":[{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.786271870136261},{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.646578311920166},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5983816385269165},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.583779513835907},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46694791316986084},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4638146758079529},{"id":"https://openalex.org/C92717368","wikidata":"https://www.wikidata.org/wiki/Q1162538","display_name":"Plaintext","level":3,"score":0.44993993639945984},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3919031023979187},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35710588097572327},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30825307965278625},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.19530212879180908},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1566622257232666},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.1492878794670105},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.11356410384178162},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/axioms12030304","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12030304","pdf_url":"https://www.mdpi.com/2075-1680/12/3/304/pdf?version=1679032119","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:shdl.mmu.edu.my:11368","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196753","display_name":"Siti Hasmah Digital Library-MMU Institutiona Repository (Multimedia University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I173029219","host_organization_name":"Multimedia University","host_organization_lineage":["https://openalex.org/I173029219"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"NonPeerReviewed"},{"id":"pmh:oai:doaj.org/article:5deb407a58a04eaab4d1fea16d60461b","is_oa":true,"landing_page_url":"https://doaj.org/article/5deb407a58a04eaab4d1fea16d60461b","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 3, p 304 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/3/304/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12030304","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 12; Issue 3; Pages: 304","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12030304","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12030304","pdf_url":"https://www.mdpi.com/2075-1680/12/3/304/pdf?version=1679032119","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3743872278","display_name":null,"funder_award_id":"FRGS/1/2019/STG06/UPM/02/8","funder_id":"https://openalex.org/F4320321709","funder_display_name":"Ministry of Higher Education, Malaysia"},{"id":"https://openalex.org/G7018233427","display_name":null,"funder_award_id":"UPM/INSPEM/ 700-3/1/GERAN ANTARABANGSA/6380071\u201310065","funder_id":"https://openalex.org/F4320321709","funder_display_name":"Ministry of Higher Education, Malaysia"},{"id":"https://openalex.org/G7077195140","display_name":null,"funder_award_id":"MMUI/220141","funder_id":"https://openalex.org/F4320321709","funder_display_name":"Ministry of Higher Education, Malaysia"}],"funders":[{"id":"https://openalex.org/F4320321709","display_name":"Ministry of Higher Education, Malaysia","ror":"https://ror.org/05mcs2t73"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4327737970.pdf"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1511374591","https://openalex.org/W1519763659","https://openalex.org/W1570727527","https://openalex.org/W1576797337","https://openalex.org/W1583396709","https://openalex.org/W1608796955","https://openalex.org/W2017464959","https://openalex.org/W2032431003","https://openalex.org/W2096050004","https://openalex.org/W2110775981","https://openalex.org/W2168676717","https://openalex.org/W2312628401","https://openalex.org/W2343426927","https://openalex.org/W2400680388","https://openalex.org/W2747598286","https://openalex.org/W2951898221","https://openalex.org/W2963026014","https://openalex.org/W3005494689","https://openalex.org/W3027098926","https://openalex.org/W3100599485","https://openalex.org/W3130043982","https://openalex.org/W3195347196","https://openalex.org/W3213492606","https://openalex.org/W6634792585","https://openalex.org/W6704450298"],"related_works":["https://openalex.org/W4394590985","https://openalex.org/W2348840575","https://openalex.org/W2030498341","https://openalex.org/W3122841410","https://openalex.org/W2046205453","https://openalex.org/W2770017172","https://openalex.org/W89977309","https://openalex.org/W2183901182","https://openalex.org/W2030930882","https://openalex.org/W4300013323"],"abstract_inverted_index":{"The":[0,51],"Polynomial":[1],"Reconstruction":[2],"Problem":[3],"(PRP)":[4],"was":[5,34,40,49],"introduced":[6],"in":[7,14,42,87],"1999":[8],"as":[9],"a":[10,25,30,46,54],"new":[11],"hard":[12],"problem":[13],"post-quantum":[15],"cryptography.":[16],"Augot":[17,58],"and":[18,39,59,70],"Finiasz":[19],"were":[20],"the":[21,66,81,91],"first":[22],"to":[23,75],"design":[24,52],"cryptographic":[26],"system":[27],"based":[28],"on":[29],"univariate":[31],"PRP,":[32],"which":[33],"published":[35],"at":[36],"Eurocrypt":[37],"2003":[38],"broken":[41],"2004.":[43],"In":[44],"2013,":[45],"bivariate":[47,82,92],"PRP":[48,93],"proposed.":[50],"is":[53,94],"modified":[55,67],"version":[56],"of":[57,80],"Finiasz\u2019s":[60],"design.":[61],"Our":[62],"strategic":[63],"method,":[64],"comprising":[65],"Berlekamp\u2013Welch":[68],"algorithm":[69],"Coron":[71],"strategies,":[72],"allowed":[73],"us":[74,88],"obtain":[76],"certain":[77],"secret":[78],"parameters":[79],"PRP.":[83],"This":[84],"finding":[85],"resulted":[86],"concluding":[89],"that":[90],"not":[95],"secure":[96],"against":[97],"Indistinguishable":[98],"Chosen-Plaintext":[99],"Attack":[100],"(IND-CPA).":[101]},"counts_by_year":[{"year":2024,"cited_by_count":5}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2023-03-18T00:00:00"}