{"id":"https://openalex.org/W4392016994","doi":"https://doi.org/10.3390/sym16030263","title":"An Improved Public Key Cryptographic Algorithm Based on Chebyshev Polynomials and RSA","display_name":"An Improved Public Key Cryptographic Algorithm Based on Chebyshev Polynomials and RSA","publication_year":2024,"publication_date":"2024-02-21","ids":{"openalex":"https://openalex.org/W4392016994","doi":"https://doi.org/10.3390/sym16030263"},"language":"en","primary_location":{"id":"doi:10.3390/sym16030263","doi":"https://doi.org/10.3390/sym16030263","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16030263","pdf_url":"https://www.mdpi.com/2073-8994/16/3/263/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","norway-1","poland-70","russia-white-list-1","vabb-shw"],"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":"Symmetry","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/16/3/263/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101830346","display_name":"Chunfu Zhang","orcid":"https://orcid.org/0000-0003-2867-9652","observed_orcids":["https://orcid.org/0000-0003-2867-9652"]},"institutions":[{"id":"https://openalex.org/I4405281264","display_name":"Zhuhai College of Science and Technology","ror":"https://ror.org/0440ra149","country_code":"CN","type":"education","lineage":["https://openalex.org/I4405281264"]},{"id":"https://openalex.org/I99682543","display_name":"University of Minho","ror":"https://ror.org/037wpkx04","country_code":"PT","type":"education","lineage":["https://openalex.org/I99682543"]}],"countries":["CN","PT"],"is_corresponding":false,"raw_author_name":"Chunfu Zhang","raw_affiliation_strings":["Department of Industrial Electronics, University of Minho, 4800-058 Guimaraes, Portugal","School of Statistics and Data Science, Zhuhai College of Science and Technology, Zhuhai 519041, China"],"raw_orcid":"https://orcid.org/0000-0003-2867-9652","affiliations":[{"raw_affiliation_string":"Department of Industrial Electronics, University of Minho, 4800-058 Guimaraes, Portugal","institution_ids":["https://openalex.org/I99682543"]},{"raw_affiliation_string":"School of Statistics and Data Science, Zhuhai College of Science and Technology, Zhuhai 519041, China","institution_ids":["https://openalex.org/I4405281264"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076665413","display_name":"Yanchun Liang","orcid":"https://orcid.org/0000-0002-1147-3968","observed_orcids":["https://orcid.org/0000-0002-1147-3968"]},"institutions":[{"id":"https://openalex.org/I4405281264","display_name":"Zhuhai College of Science and Technology","ror":"https://ror.org/0440ra149","country_code":"CN","type":"education","lineage":["https://openalex.org/I4405281264"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanchun Liang","raw_affiliation_strings":["School of Computer Science, Zhuhai College of Science and Technology, Zhuhai 519041, China","of , of , - , ;"],"raw_orcid":"https://orcid.org/0000-0002-1147-3968","affiliations":[{"raw_affiliation_string":"School of Computer Science, Zhuhai College of Science and Technology, Zhuhai 519041, China","institution_ids":["https://openalex.org/I4405281264"]},{"raw_affiliation_string":"of , of , - , ;","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063889753","display_name":"Adriano Tavares","orcid":"https://orcid.org/0000-0001-8316-6927","observed_orcids":["https://orcid.org/0000-0001-8316-6927"]},"institutions":[{"id":"https://openalex.org/I99682543","display_name":"University of Minho","ror":"https://ror.org/037wpkx04","country_code":"PT","type":"education","lineage":["https://openalex.org/I99682543"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Adriano Tavares","raw_affiliation_strings":["Department of Industrial Electronics, University of Minho, 4800-058 Guimaraes, Portugal","of , of , - , ;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Electronics, University of Minho, 4800-058 Guimaraes, Portugal","institution_ids":["https://openalex.org/I99682543"]},{"raw_affiliation_string":"of , of , - , ;","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100424668","display_name":"Lidong Wang","orcid":"https://orcid.org/0000-0003-1462-9443","observed_orcids":["https://orcid.org/0000-0003-1462-9443","https://orcid.org/0009-0004-1905-0320","https://orcid.org/0009-0006-1792-9176"]},"institutions":[{"id":"https://openalex.org/I4405281264","display_name":"Zhuhai College of Science and Technology","ror":"https://ror.org/0440ra149","country_code":"CN","type":"education","lineage":["https://openalex.org/I4405281264"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lidong Wang","raw_affiliation_strings":["School of Statistics and Data Science, Zhuhai College of Science and Technology, Zhuhai 519041, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Statistics and Data Science, Zhuhai College of Science and Technology, Zhuhai 519041, China","institution_ids":["https://openalex.org/I4405281264"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064098327","display_name":"Tiago Gomes","orcid":"https://orcid.org/0000-0002-4071-9015","observed_orcids":["https://orcid.org/0000-0002-4071-9015"]},"institutions":[{"id":"https://openalex.org/I99682543","display_name":"University of Minho","ror":"https://ror.org/037wpkx04","country_code":"PT","type":"education","lineage":["https://openalex.org/I99682543"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Tiago Gomes","raw_affiliation_strings":["Department of Industrial Electronics, University of Minho, 4800-058 Guimaraes, Portugal","of , of , - , ;"],"raw_orcid":"https://orcid.org/0000-0002-4071-9015","affiliations":[{"raw_affiliation_string":"Department of Industrial Electronics, University of Minho, 4800-058 Guimaraes, Portugal","institution_ids":["https://openalex.org/I99682543"]},{"raw_affiliation_string":"of , of , - , ;","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058864507","display_name":"Sandro Pinto","orcid":"https://orcid.org/0000-0003-4580-7484","observed_orcids":["https://orcid.org/0000-0003-4580-7484"]},"institutions":[{"id":"https://openalex.org/I99682543","display_name":"University of Minho","ror":"https://ror.org/037wpkx04","country_code":"PT","type":"education","lineage":["https://openalex.org/I99682543"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Sandro Pinto","raw_affiliation_strings":["Department of Industrial Electronics, University of Minho, 4800-058 Guimaraes, Portugal","of , of , - , ;"],"raw_orcid":"https://orcid.org/0000-0003-4580-7484","affiliations":[{"raw_affiliation_string":"Department of Industrial Electronics, University of Minho, 4800-058 Guimaraes, Portugal","institution_ids":["https://openalex.org/I99682543"]},{"raw_affiliation_string":"of , of , - , ;","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2400,"currency":"CHF","value_usd":2728},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2728},"fwci":2.5589,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.90966712,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"16","issue":"3","first_page":"263","last_page":"263"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.8848000168800354,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.8848000168800354,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10237","display_name":"Cryptography and Data Security","score":0.05620000138878822,"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"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.04450000077486038,"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/public-key-cryptography","display_name":"public-key cryptography","score":0.8899999856948853},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.996999979019165},{"id":"https://openalex.org/keywords/hybrid-encryption","display_name":"hybrid encryption","score":0.5490000247955322},{"id":"https://openalex.org/keywords/key-generation","display_name":"key generation","score":0.6119999885559082},{"id":"https://openalex.org/keywords/encryption-and-decryption","display_name":"encryption and decryption","score":0.7570000290870667},{"id":"https://openalex.org/keywords/attack-resistance","display_name":"attack resistance","score":0.5149999856948853}],"concepts":[{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.7283703088760376},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6344090700149536},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.6185745596885681},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.5922383069992065},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5653631687164307},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.5497865080833435},{"id":"https://openalex.org/C47750902","wikidata":"https://www.wikidata.org/wiki/Q1557574","display_name":"Key size","level":4,"score":0.542707085609436},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.5397911667823792},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49700191617012024},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45053526759147644},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.4361081123352051},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.4204345941543579},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3701860308647156},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.06691807508468628},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"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/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym16030263","doi":"https://doi.org/10.3390/sym16030263","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16030263","pdf_url":"https://www.mdpi.com/2073-8994/16/3/263/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","norway-1","poland-70","russia-white-list-1","vabb-shw"],"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:19386891d0ab4584bdf6a10b317bd9ef","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/19386891d0ab4584bdf6a10b317bd9ef","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,"listed_in":[],"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":"Symmetry, Vol 16, Iss 3, p 263 (2024)","raw_type":"article"},{"id":"pmh:oai:repositorium.sdum.uminho.pt:1822/89878","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/1822/89878","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"journal article"},{"id":"pmh:oai:repositorium.uminho.pt:1822/89878","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/1822/89878","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"}],"best_oa_location":{"id":"doi:10.3390/sym16030263","doi":"https://doi.org/10.3390/sym16030263","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16030263","pdf_url":"https://www.mdpi.com/2073-8994/16/3/263/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","norway-1","poland-70","russia-white-list-1","vabb-shw"],"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G106173642","display_name":null,"funder_award_id":"2021KCXTD015","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1955255439","display_name":null,"funder_award_id":"2019XJCQ001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3095911524","display_name":null,"funder_award_id":"62372494","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5736914374","display_name":null,"funder_award_id":"2021ZDJS138","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7302766455","display_name":null,"funder_award_id":"2023KQNCX132","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4392016994.pdf","grobid_xml":"https://content.openalex.org/works/W4392016994.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W1849280677","https://openalex.org/W1989266974","https://openalex.org/W2003234415","https://openalex.org/W2085837398","https://openalex.org/W2090396608","https://openalex.org/W2105709923","https://openalex.org/W2109394932","https://openalex.org/W2154466273","https://openalex.org/W2156186849","https://openalex.org/W2318801069","https://openalex.org/W2327503495","https://openalex.org/W2604682599","https://openalex.org/W2735253746","https://openalex.org/W2750426476","https://openalex.org/W2755444697","https://openalex.org/W2768334467","https://openalex.org/W2790150847","https://openalex.org/W2920524007","https://openalex.org/W2968183237","https://openalex.org/W2969904548","https://openalex.org/W3028165933","https://openalex.org/W3136646738","https://openalex.org/W3161457301","https://openalex.org/W3198500300","https://openalex.org/W3216657397","https://openalex.org/W4200233568","https://openalex.org/W4210503308","https://openalex.org/W4210778337","https://openalex.org/W4210835755","https://openalex.org/W4213326178","https://openalex.org/W4232836212","https://openalex.org/W4283258646","https://openalex.org/W4296019566","https://openalex.org/W4361274621","https://openalex.org/W4366983421","https://openalex.org/W4366988295","https://openalex.org/W4385372708","https://openalex.org/W4387385726","https://openalex.org/W6983633736"],"related_works":["https://openalex.org/W4402129425","https://openalex.org/W2033240897","https://openalex.org/W4406985890","https://openalex.org/W145770041","https://openalex.org/W2966470738","https://openalex.org/W2090396608","https://openalex.org/W7005271042","https://openalex.org/W2387552756","https://openalex.org/W2607008924","https://openalex.org/W2139877067"],"abstract_inverted_index":{"Due":[0],"to":[1,98,120],"its":[2,122],"very":[3],"desirable":[4],"properties,":[5],"Chebyshev":[6,23,29,41],"polynomials":[7],"are":[8,74,96],"often":[9],"used":[10,97],"in":[11,124],"the":[12,22,26,55,62,69,80,86,104],"design":[13],"of":[14,28,57,64,82,126],"public":[15,35],"key":[16,36,87],"cryptographic":[17],"systems.":[18],"This":[19,48],"paper":[20],"discretizes":[21],"mapping,":[24],"generalizes":[25],"properties":[27],"polynomials,":[30],"and":[31,44,68,89,128],"proposes":[32],"an":[33],"improved":[34],"encryption":[37],"algorithm":[38,49,101,105,112],"based":[39],"on":[40],"chaotic":[42],"mapping":[43],"RSA,":[45],"i.e.,":[46],"CRPKC\u2212Ki.":[47],"introduces":[50],"alternative":[51],"multiplication":[52],"coefficients":[53],"Ki,":[54],"selection":[56,72],"which":[58],"is":[59,113],"determined":[60],"by":[61],"size":[63],"TrTdxmod":[65],"N=TdTrxmod":[66],"N,":[67],"specific":[70],"value":[71],"rules":[73],"shared":[75],"secrets":[76],"among":[77],"participants,":[78],"overcoming":[79],"shortcomings":[81],"previous":[83],"schemes.":[84],"In":[85],"generation":[88],"encryption/decryption":[90],"stages,":[91],"more":[92,106],"complex":[93],"intermediate":[94],"processes":[95],"achieve":[99],"higher":[100],"complexity,":[102],"making":[103],"robust":[107],"against":[108],"ordinary":[109],"attacks.":[110],"The":[111],"also":[114],"compared":[115],"with":[116],"other":[117],"RSA-based":[118],"algorithms":[119],"demonstrate":[121],"effectiveness":[123],"terms":[125],"performance":[127],"security.":[129]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":8}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2024-02-22T00:00:00"}