{"id":"https://openalex.org/W4200425123","doi":"https://doi.org/10.3390/info12120509","title":"Probabilistic Evaluation of the Exploration\u2013Exploitation Balance during the Search, Using the Swap Operator, for Nonlinear Bijective S-Boxes, Resistant to Power Attacks","display_name":"Probabilistic Evaluation of the Exploration\u2013Exploitation Balance during the Search, Using the Swap Operator, for Nonlinear Bijective S-Boxes, Resistant to Power Attacks","publication_year":2021,"publication_date":"2021-12-08","ids":{"openalex":"https://openalex.org/W4200425123","doi":"https://doi.org/10.3390/info12120509"},"language":"en","primary_location":{"id":"doi:10.3390/info12120509","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info12120509","pdf_url":"https://www.mdpi.com/2078-2489/12/12/509/pdf?version=1638949869","source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"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":"Information","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2078-2489/12/12/509/pdf?version=1638949869","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054641143","display_name":"Carlos Miguel Leg\u00f3n-P\u00e9rez","orcid":"https://orcid.org/0000-0002-6104-9671"},"institutions":[{"id":"https://openalex.org/I2656126","display_name":"University of Havana","ror":"https://ror.org/04204gr61","country_code":"CU","type":"education","lineage":["https://openalex.org/I2656126"]}],"countries":["CU"],"is_corresponding":false,"raw_author_name":"Carlos Miguel Leg\u00f3n-P\u00e9rez","raw_affiliation_strings":["Institute of Cryptography, University of Havana, Havana 10400, Cuba"],"raw_orcid":"https://orcid.org/0000-0002-6104-9671","affiliations":[{"raw_affiliation_string":"Institute of Cryptography, University of Havana, Havana 10400, Cuba","institution_ids":["https://openalex.org/I2656126"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074278424","display_name":"Jorge Ariel Men\u00e9ndez-Verdec\u00eda","orcid":"https://orcid.org/0000-0002-5829-3817"},"institutions":[{"id":"https://openalex.org/I4210137344","display_name":"Escuela Superior Polit\u00e9cnica del Chimborazo","ror":"https://ror.org/02zyw2q61","country_code":"EC","type":"education","lineage":["https://openalex.org/I4210137344"]}],"countries":["EC"],"is_corresponding":false,"raw_author_name":"Jorge Ariel Men\u00e9ndez-Verdec\u00eda","raw_affiliation_strings":["Facultad de Inform\u00e1tica y Electr\u00f3nica, Escuela Superior Polit\u00e9cnica de Chimborazo, Riobamba 060155, Ecuador"],"raw_orcid":"https://orcid.org/0000-0002-5829-3817","affiliations":[{"raw_affiliation_string":"Facultad de Inform\u00e1tica y Electr\u00f3nica, Escuela Superior Polit\u00e9cnica de Chimborazo, Riobamba 060155, Ecuador","institution_ids":["https://openalex.org/I4210137344"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038566084","display_name":"Ismel Mart\u00ednez-D\u00edaz","orcid":"https://orcid.org/0000-0002-7064-232X"},"institutions":[{"id":"https://openalex.org/I2656126","display_name":"University of Havana","ror":"https://ror.org/04204gr61","country_code":"CU","type":"education","lineage":["https://openalex.org/I2656126"]}],"countries":["CU"],"is_corresponding":false,"raw_author_name":"Ismel Mart\u00ednez-D\u00edaz","raw_affiliation_strings":["Institute of Cryptography, University of Havana, Havana 10400, Cuba"],"raw_orcid":"https://orcid.org/0000-0002-7064-232X","affiliations":[{"raw_affiliation_string":"Institute of Cryptography, University of Havana, Havana 10400, Cuba","institution_ids":["https://openalex.org/I2656126"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006503010","display_name":"Guillermo Sosa-G\u00f3mez","orcid":"https://orcid.org/0000-0001-7793-896X"},"institutions":[{"id":"https://openalex.org/I86613570","display_name":"Universidad Panamericana","ror":"https://ror.org/01n1q0h77","country_code":"MX","type":"education","lineage":["https://openalex.org/I86613570"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Guillermo Sosa-G\u00f3mez","raw_affiliation_strings":["Facultad de Ciencias Econ\u00f3micas y Empresariales, Universidad Panamericana, \u00c1lvaro del Portillo 49, Zapopan 45010, Mexico"],"raw_orcid":"https://orcid.org/0000-0001-7793-896X","affiliations":[{"raw_affiliation_string":"Facultad de Ciencias Econ\u00f3micas y Empresariales, Universidad Panamericana, \u00c1lvaro del Portillo 49, Zapopan 45010, Mexico","institution_ids":["https://openalex.org/I86613570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082236115","display_name":"Omar Rojas","orcid":"https://orcid.org/0000-0002-0681-3833"},"institutions":[{"id":"https://openalex.org/I205133468","display_name":"Airlangga University","ror":"https://ror.org/04ctejd88","country_code":"ID","type":"education","lineage":["https://openalex.org/I205133468"]},{"id":"https://openalex.org/I86613570","display_name":"Universidad Panamericana","ror":"https://ror.org/01n1q0h77","country_code":"MX","type":"education","lineage":["https://openalex.org/I86613570"]}],"countries":["ID","MX"],"is_corresponding":false,"raw_author_name":"Omar Rojas","raw_affiliation_strings":["Facultad de Ciencias Econ\u00f3micas y Empresariales, Universidad Panamericana, \u00c1lvaro del Portillo 49, Zapopan 45010, Mexico","Faculty of Economics and Business, Universitas Airlangga, Surabaya 60286, Indonesia"],"raw_orcid":"https://orcid.org/0000-0002-0681-3833","affiliations":[{"raw_affiliation_string":"Facultad de Ciencias Econ\u00f3micas y Empresariales, Universidad Panamericana, \u00c1lvaro del Portillo 49, Zapopan 45010, Mexico","institution_ids":["https://openalex.org/I86613570"]},{"raw_affiliation_string":"Faculty of Economics and Business, Universitas Airlangga, Surabaya 60286, Indonesia","institution_ids":["https://openalex.org/I205133468"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087191697","display_name":"Germania del Roci\u00f3 Veloz-Remache","orcid":"https://orcid.org/0000-0003-2865-8181"},"institutions":[{"id":"https://openalex.org/I4210137344","display_name":"Escuela Superior Polit\u00e9cnica del Chimborazo","ror":"https://ror.org/02zyw2q61","country_code":"EC","type":"education","lineage":["https://openalex.org/I4210137344"]}],"countries":["EC"],"is_corresponding":false,"raw_author_name":"Germania del Roci\u00f3 Veloz-Remache","raw_affiliation_strings":["Facultad de Inform\u00e1tica y Electr\u00f3nica, Escuela Superior Polit\u00e9cnica de Chimborazo, Riobamba 060155, Ecuador"],"raw_orcid":"https://orcid.org/0000-0003-2865-8181","affiliations":[{"raw_affiliation_string":"Facultad de Inform\u00e1tica y Electr\u00f3nica, Escuela Superior Polit\u00e9cnica de Chimborazo, Riobamba 060155, Ecuador","institution_ids":["https://openalex.org/I4210137344"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5006503010"],"corresponding_institution_ids":["https://openalex.org/I86613570"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.1399,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58673994,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"12","issue":"12","first_page":"509","last_page":"509"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9997000098228455,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9997000098228455,"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":0.9954000115394592,"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/T11130","display_name":"Coding theory and cryptography","score":0.9902999997138977,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6280686259269714},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.5875951051712036},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4961746633052826},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4562176465988159},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.4488789737224579},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41949141025543213},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3814389407634735},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3625871539115906},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32988232374191284},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2830808162689209}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6280686259269714},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.5875951051712036},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4961746633052826},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4562176465988159},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.4488789737224579},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41949141025543213},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3814389407634735},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3625871539115906},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32988232374191284},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2830808162689209},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/info12120509","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info12120509","pdf_url":"https://www.mdpi.com/2078-2489/12/12/509/pdf?version=1638949869","source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"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":"Information","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:89c7b3324cc0488b95bb6eb18c5c7064","is_oa":true,"landing_page_url":"https://doaj.org/article/89c7b3324cc0488b95bb6eb18c5c7064","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":"Information, Vol 12, Iss 12, p 509 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2078-2489/12/12/509/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/info12120509","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":"Information; Volume 12; Issue 12; Pages: 509","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/info12120509","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info12120509","pdf_url":"https://www.mdpi.com/2078-2489/12/12/509/pdf?version=1638949869","source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"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":"Information","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4200425123.pdf"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W110767368","https://openalex.org/W781006782","https://openalex.org/W1595334710","https://openalex.org/W1967766138","https://openalex.org/W2043325537","https://openalex.org/W2096094378","https://openalex.org/W2144420897","https://openalex.org/W2166531223","https://openalex.org/W2294812025","https://openalex.org/W2499186340","https://openalex.org/W2735385767","https://openalex.org/W2994539035","https://openalex.org/W3008439737","https://openalex.org/W3009979760","https://openalex.org/W3012385585","https://openalex.org/W3040330020","https://openalex.org/W3092205448","https://openalex.org/W3096977645","https://openalex.org/W3106674947","https://openalex.org/W3119771803","https://openalex.org/W3120067464","https://openalex.org/W3157858770","https://openalex.org/W3164382787","https://openalex.org/W3184277961","https://openalex.org/W4245524709","https://openalex.org/W4246565613","https://openalex.org/W6631450893","https://openalex.org/W6877020638"],"related_works":["https://openalex.org/W4287020903","https://openalex.org/W2952259524","https://openalex.org/W2279732055","https://openalex.org/W2995857455","https://openalex.org/W4288805235","https://openalex.org/W2998840281","https://openalex.org/W2027277382","https://openalex.org/W1508013399","https://openalex.org/W3181135859","https://openalex.org/W2055712922"],"abstract_inverted_index":{"During":[0],"the":[1,9,29,33,41,44,67,76,81,120,123,133,143,148,167,170,178,182,192,203,207,213,223,229,248,256,262,272,293,296,300,304,313,327],"search":[2,45,214,243,305],"for":[3,39,215,244,277,306],"S-boxes":[4,128,217,246,279,307],"resistant":[5,218,232,308],"to":[6,21,25,61,165,184,219,233,242,270,309,326,330],"Power":[7,220,235,310],"Attacks,":[8],"S-box":[10,77],"space":[11,129],"has":[12],"recently":[13],"been":[14],"divided":[15],"into":[16],"Hamming":[17,72,124,314],"Weight":[18,73,125,315],"classes,":[19],"according":[20],"its":[22,174],"theoretical":[23,68,290],"resistance":[24],"these":[26,93,160],"attacks":[27],"using":[28],"metric":[30],"variance":[31],"of":[32,43,59,70,75,92,122,127,145,169,181,191,206,258,274,295,323],"confusion":[34],"coefficient.":[35],"This":[36,250],"partition":[37],"allows":[38,188],"reducing":[40],"size":[42],"space.":[46,317],"The":[47,90,198,318],"swap":[48,82,171,208,297,328],"operator":[49,83,112,209,260,298,329],"is":[50,78,84,95,108,151,163,210,231],"frequently":[51],"used":[52],"when":[53,80,228],"searching":[54,278],"with":[55,115,177,280],"a":[56,88,101,267,285],"random":[57,175,204],"selection":[58,180],"items":[60],"be":[62,185,226,239],"exchanged.":[63],"In":[64,284],"this":[65,111,259,332],"work,":[66],"probability":[69,144],"changing":[71],"class":[74,126,150,230,316],"calculated":[79,199],"applied":[85],"randomly":[86],"in":[87,261,299,312],"permutation.":[89],"precision":[91],"probabilities":[94,200],"confirmed":[96],"experimentally.":[97],"Its":[98],"limit":[99],"and":[100,196],"recursive":[102],"formula":[103],"are":[104,139],"theoretically":[105],"proved.":[106],"It":[107,237,265],"shown":[109],"that":[110,142,202],"changes":[113],"classes":[114],"high":[116],"probability,":[117],"which":[118,187],"favors":[119],"exploration":[121,195,224],"but":[130],"dramatically":[131],"reduces":[132],"exploitation":[134],"within":[135,147,247],"classes.":[136],"These":[137],"results":[138],"generalized,":[140],"showing":[141],"moving":[146],"same":[149],"substantially":[152],"reduced":[153],"by":[154],"applying":[155],"two":[156],"swaps.":[157],"Based":[158],"on":[159],"results,":[161],"it":[162],"proposed":[164],"modify/improve":[166],"use":[168],"operator,":[172],"replacing":[173],"application":[176,205],"appropriate":[179],"elements":[183],"exchanged,":[186],"taking":[189],"control":[190,331],"balance":[193,263,302,333],"between":[194],"exploitation.":[197],"show":[201],"inappropriate":[211,227],"during":[212,303],"nonlinear":[216,245],"Attacks":[221,311],"since":[222],"may":[225],"Differential":[234],"Attack.":[236],"would":[238],"more":[240],"convenient":[241],"class.":[249],"result":[251,291],"provides":[252],"new":[253],"knowledge":[254],"about":[255],"influence":[257,294],"exploration\u2013exploitation.":[264],"constitutes":[266],"valuable":[268],"tool":[269],"improve":[271],"design":[273],"future":[275],"algorithms":[276],"good":[281],"cryptography":[282],"properties.":[283],"probabilistic":[286],"way,":[287],"our":[288],"main":[289,319],"characterizes":[292],"exploration\u2013exploitation":[301],"practical":[320],"contribution":[321],"consists":[322],"proposing":[324],"modifications":[325],"better.":[334]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
