{"id":"https://openalex.org/W3089062277","doi":"https://doi.org/10.1155/2020/8883884","title":"The Effect of the Primitive Irreducible Polynomial on the Quality of Cryptographic Properties of Block Ciphers","display_name":"The Effect of the Primitive Irreducible Polynomial on the Quality of Cryptographic Properties of Block Ciphers","publication_year":2020,"publication_date":"2020-09-24","ids":{"openalex":"https://openalex.org/W3089062277","doi":"https://doi.org/10.1155/2020/8883884","mag":"3089062277"},"language":"en","primary_location":{"id":"doi:10.1155/2020/8883884","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/8883884","pdf_url":"https://downloads.hindawi.com/journals/scn/2020/8883884.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":"https://downloads.hindawi.com/journals/scn/2020/8883884.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054500045","display_name":"Sajjad Shaukat Jamal","orcid":"https://orcid.org/0000-0002-5852-1955"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Sajjad Shaukat Jamal","raw_affiliation_strings":["Department of Mathematics, College of Science, King Khalid University, P. O. Box 9004, Abha, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Khalid University, P. O. Box 9004, Abha, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047819360","display_name":"Dawood Shah","orcid":"https://orcid.org/0000-0001-9589-5991"},"institutions":[{"id":"https://openalex.org/I12469534","display_name":"Quaid-i-Azam University","ror":"https://ror.org/04s9hft57","country_code":"PK","type":"education","lineage":["https://openalex.org/I12469534"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Dawood Shah","raw_affiliation_strings":["Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan","institution_ids":["https://openalex.org/I12469534"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006451276","display_name":"Abdulaziz Deajim","orcid":"https://orcid.org/0000-0002-0630-1280"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Abdulaziz Deajim","raw_affiliation_strings":["Department of Mathematics, College of Science, King Khalid University, P. O. Box 9004, Abha, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Khalid University, P. O. Box 9004, Abha, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059990662","display_name":"Tariq Shah","orcid":"https://orcid.org/0000-0002-6587-1638"},"institutions":[{"id":"https://openalex.org/I12469534","display_name":"Quaid-i-Azam University","ror":"https://ror.org/04s9hft57","country_code":"PK","type":"education","lineage":["https://openalex.org/I12469534"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Tariq Shah","raw_affiliation_strings":["Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan","institution_ids":["https://openalex.org/I12469534"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5054500045"],"corresponding_institution_ids":["https://openalex.org/I82952536"],"apc_list":{"value":2100,"currency":"USD","value_usd":2100},"apc_paid":{"value":2100,"currency":"USD","value_usd":2100},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.11646778,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"14"},"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":0.9998000264167786,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9990000128746033,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.684544563293457},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5856465101242065},{"id":"https://openalex.org/keywords/irreducible-polynomial","display_name":"Irreducible polynomial","score":0.5370378494262695},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4410616457462311},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.3242941200733185},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.271005779504776},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08531403541564941}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.684544563293457},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5856465101242065},{"id":"https://openalex.org/C165030954","wikidata":"https://www.wikidata.org/wiki/Q1476663","display_name":"Irreducible polynomial","level":4,"score":0.5370378494262695},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4410616457462311},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3242941200733185},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.271005779504776},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08531403541564941},{"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/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2020/8883884","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/8883884","pdf_url":"https://downloads.hindawi.com/journals/scn/2020/8883884.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:b2b3615e5b2f41c98705a69035a4568c","is_oa":true,"landing_page_url":"https://doaj.org/article/b2b3615e5b2f41c98705a69035a4568c","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Security and Communication Networks, Vol 2020 (2020)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/2020/8883884","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/8883884","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"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":"","raw_type":"Research Article"}],"best_oa_location":{"id":"doi:10.1155/2020/8883884","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/8883884","pdf_url":"https://downloads.hindawi.com/journals/scn/2020/8883884.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/G1380584810","display_name":null,"funder_award_id":"R.G.P","funder_id":"https://openalex.org/F4320324433","funder_display_name":"King Khalid University"},{"id":"https://openalex.org/G6429626434","display_name":null,"funder_award_id":"R.G.P. 1/234/41","funder_id":"https://openalex.org/F4320324433","funder_display_name":"King Khalid University"}],"funders":[{"id":"https://openalex.org/F4320324433","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3089062277.pdf","grobid_xml":"https://content.openalex.org/works/W3089062277.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1629301835","https://openalex.org/W1965864407","https://openalex.org/W1971515204","https://openalex.org/W2016280276","https://openalex.org/W2018406493","https://openalex.org/W2018856610","https://openalex.org/W2094557114","https://openalex.org/W2118702985","https://openalex.org/W2264272837","https://openalex.org/W2750385101","https://openalex.org/W2797813330","https://openalex.org/W2808755199","https://openalex.org/W2903665442","https://openalex.org/W2970987811","https://openalex.org/W2987515729","https://openalex.org/W2996163077","https://openalex.org/W3036836497"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W4302229733","https://openalex.org/W2108824846","https://openalex.org/W40530611"],"abstract_inverted_index":{"Substitution":[0],"boxes":[1,36,185,228],"are":[2,57,186,229],"the":[3,8,18,23,34,49,121,189,209,215,225,233],"only":[4],"nonlinear":[5],"component":[6],"of":[7,33,63,76,81,91,183,191,214,235],"symmetric":[9],"key":[10,15],"cryptography":[11],"and":[12,27,43,66,178,200,202,211],"play":[13],"a":[14,96],"role":[16],"in":[17],"cryptosystem.":[19],"In":[20,110],"block":[21],"ciphers,":[22],"S-boxes":[24,118,171],"create":[25],"confusion":[26],"add":[28],"valuable":[29],"strength.":[30],"The":[31],"majority":[32],"substitution":[35,145,217,227],"algorithms":[37],"focus":[38],"on":[39,88,95],"bijective":[40],"Boolean":[41],"functions":[42],"primitive":[44,60,102,130,175],"irreducible":[45,61,103,131,176],"polynomial":[46,104],"that":[47,224],"generates":[48],"Galois":[50,73,89],"field.":[51],"For":[52],"binary":[53],"field":[54,74,90],"F2,":[55],"there":[56],"exactly":[58],"16":[59,72,140,153,164],"polynomials":[62,132,177],"degree":[64,98,126],"8":[65],"it":[67],"prompts":[68],"us":[69],"to":[70,138,207],"construct":[71],"extensions":[75],"order":[77,92],"256.":[78],"Conventionally,":[79],"construction":[80],"affine":[82,84,115,117,154,156],"power":[83,116,155],"S-box":[85],"is":[86],"based":[87],"256,":[93],"depending":[94],"single":[97],"<mml:math":[99,106,122,127,134,142],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[100,107,123,128,135,143],"id=\"M1\"><mml:mn>8</mml:mn></mml:math>":[101],"over":[105,133],"id=\"M2\"><mml:msub><mml:mrow><mml:mi":[108],"mathvariant=\"normal\">\u2124</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>.":[109],"this":[111,149],"manuscript,":[112],"we":[113,151,162,168],"study":[114,170],"for":[119,159,232],"all":[120,173],"id=\"M3\"><mml:mn>16</mml:mn></mml:math>":[124],"distinct":[125,165],"id=\"M4\"><mml:mn>8</mml:mn></mml:math>":[129],"id=\"M5\"><mml:msub><mml:mrow><mml:mi":[136],"mathvariant=\"normal\">\u2124</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>":[137],"propose":[139],"different":[141],"id=\"M6\"><mml:mn>8</mml:mn><mml:mo>\u00d7</mml:mo><mml:mn>8</mml:mn></mml:math>":[144],"boxes.":[146,218],"To":[147],"perform":[148],"idea,":[150],"introduce":[152],"transformations":[157],"and,":[158],"fixed":[160],"parameters,":[161],"obtained":[163],"S-boxes.":[166],"Here,":[167],"thoroughly":[169],"with":[172,188],"possible":[174],"their":[179],"algebraic":[180,210],"properties.":[181],"All":[182],"these":[184],"evaluated":[187],"help":[190],"nonlinearity":[192],"test,":[193],"strict":[194],"avalanche":[195],"criterion,":[196,199],"bit":[197],"independent":[198],"linear":[201],"differential":[203],"approximation":[204],"probability":[205],"analyses":[206],"measure":[208],"statistical":[212],"strength":[213],"proposed":[216,226],"Majority":[219],"logic":[220],"criterion":[221],"results":[222],"indicate":[223],"well":[230],"suited":[231],"techniques":[234],"secure":[236],"communication.":[237]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
