{"id":"https://openalex.org/W2181456612","doi":"https://doi.org/10.1109/ssd.2015.7348106","title":"Chaos-based designing of a highly nonlinear S-box using Boolean functions","display_name":"Chaos-based designing of a highly nonlinear S-box using Boolean functions","publication_year":2015,"publication_date":"2015-03-01","ids":{"openalex":"https://openalex.org/W2181456612","doi":"https://doi.org/10.1109/ssd.2015.7348106","mag":"2181456612"},"language":"en","primary_location":{"id":"doi:10.1109/ssd.2015.7348106","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ssd.2015.7348106","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE 12th International Multi-Conference on Systems, Signals & Devices (SSD15)","raw_type":"proceedings-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/A5045754914","display_name":"Ramzi Guesmi","orcid":"https://orcid.org/0000-0001-8759-0151"},"institutions":[{"id":"https://openalex.org/I142899784","display_name":"University of Sfax","ror":"https://ror.org/04d4sd432","country_code":"TN","type":"education","lineage":["https://openalex.org/I142899784"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Ramzi Guesmi","raw_affiliation_strings":["Laboratory of Electronics and Information Technology, Sfax University, Sfax, B.P.W., Tunisia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Electronics and Information Technology, Sfax University, Sfax, B.P.W., Tunisia","institution_ids":["https://openalex.org/I142899784"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061834318","display_name":"Mohamed Amine Ben Farah","orcid":"https://orcid.org/0000-0002-0135-9942"},"institutions":[{"id":"https://openalex.org/I142899784","display_name":"University of Sfax","ror":"https://ror.org/04d4sd432","country_code":"TN","type":"education","lineage":["https://openalex.org/I142899784"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Mohamed Amine Ben Farah","raw_affiliation_strings":["Laboratory of Electronics and Information Technology, Sfax University, Sfax, B.P.W., Tunisia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Electronics and Information Technology, Sfax University, Sfax, B.P.W., Tunisia","institution_ids":["https://openalex.org/I142899784"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003921571","display_name":"Abdennaceur Kachouri","orcid":"https://orcid.org/0000-0003-3357-2569"},"institutions":[{"id":"https://openalex.org/I142899784","display_name":"University of Sfax","ror":"https://ror.org/04d4sd432","country_code":"TN","type":"education","lineage":["https://openalex.org/I142899784"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Abdennaceur Kachouri","raw_affiliation_strings":["Laboratory of Electronics and Information Technology, Sfax University, Sfax, B.P.W., Tunisia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Electronics and Information Technology, Sfax University, Sfax, B.P.W., Tunisia","institution_ids":["https://openalex.org/I142899784"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114032623","display_name":"Mounir Samet","orcid":null},"institutions":[{"id":"https://openalex.org/I142899784","display_name":"University of Sfax","ror":"https://ror.org/04d4sd432","country_code":"TN","type":"education","lineage":["https://openalex.org/I142899784"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Mounir Samet","raw_affiliation_strings":["Laboratory of Electronics and Information Technology, Sfax University, Sfax, B.P.W., Tunisia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Electronics and Information Technology, Sfax University, Sfax, B.P.W., Tunisia","institution_ids":["https://openalex.org/I142899784"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I142899784"],"apc_list":null,"apc_paid":null,"fwci":0.3673,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.68804998,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9998999834060669,"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":0.9998999834060669,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9994999766349792,"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/T11130","display_name":"Coding theory and cryptography","score":0.9987000226974487,"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/boolean-function","display_name":"Boolean function","score":0.8310117125511169},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.7642573118209839},{"id":"https://openalex.org/keywords/s-box","display_name":"S-box","score":0.7309807538986206},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.6395652294158936},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6114211678504944},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5691128373146057},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5442396402359009},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.48613211512565613},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.47393304109573364},{"id":"https://openalex.org/keywords/circuit-minimization-for-boolean-functions","display_name":"Circuit minimization for Boolean functions","score":0.47204455733299255},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4554942548274994},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4341009557247162},{"id":"https://openalex.org/keywords/substitution","display_name":"Substitution (logic)","score":0.42827308177948},{"id":"https://openalex.org/keywords/chaos","display_name":"CHAOS (operating system)","score":0.4269689917564392},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4179397225379944},{"id":"https://openalex.org/keywords/boolean-network","display_name":"Boolean network","score":0.41633865237236023},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3318067789077759},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2962077558040619},{"id":"https://openalex.org/keywords/block-cipher","display_name":"Block cipher","score":0.23581776022911072},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09854191541671753}],"concepts":[{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.8310117125511169},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.7642573118209839},{"id":"https://openalex.org/C45737032","wikidata":"https://www.wikidata.org/wiki/Q748364","display_name":"S-box","level":4,"score":0.7309807538986206},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.6395652294158936},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6114211678504944},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5691128373146057},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5442396402359009},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.48613211512565613},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.47393304109573364},{"id":"https://openalex.org/C94992772","wikidata":"https://www.wikidata.org/wiki/Q6667469","display_name":"Circuit minimization for Boolean functions","level":4,"score":0.47204455733299255},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4554942548274994},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4341009557247162},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.42827308177948},{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.4269689917564392},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4179397225379944},{"id":"https://openalex.org/C134444547","wikidata":"https://www.wikidata.org/wiki/Q585230","display_name":"Boolean network","level":3,"score":0.41633865237236023},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3318067789077759},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2962077558040619},{"id":"https://openalex.org/C106544461","wikidata":"https://www.wikidata.org/wiki/Q543151","display_name":"Block cipher","level":3,"score":0.23581776022911072},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09854191541671753},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ssd.2015.7348106","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ssd.2015.7348106","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE 12th International Multi-Conference on Systems, Signals & Devices (SSD15)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1499093303","https://openalex.org/W1629301835","https://openalex.org/W1670558497","https://openalex.org/W1980279697","https://openalex.org/W1991643601","https://openalex.org/W1996552840","https://openalex.org/W2023892116","https://openalex.org/W2036691397","https://openalex.org/W2040505942","https://openalex.org/W2088148276","https://openalex.org/W2109394932","https://openalex.org/W2120706888","https://openalex.org/W2173356534","https://openalex.org/W6629792826"],"related_works":["https://openalex.org/W2143645888","https://openalex.org/W2114952989","https://openalex.org/W2148068842","https://openalex.org/W2289022454","https://openalex.org/W1593463844","https://openalex.org/W2109259936","https://openalex.org/W2141243770","https://openalex.org/W1990123009","https://openalex.org/W194961446","https://openalex.org/W2295716705"],"abstract_inverted_index":{"In":[0],"this":[1],"manuscript":[2],"we":[3,41,64],"present":[4],"a":[5,10,35,67],"novel":[6],"method":[7,19],"to":[8,52],"design":[9],"strong":[11],"substitution":[12],"box":[13],"having":[14],"important":[15,109],"cryptographic":[16,110],"properties.":[17,111],"Our":[18],"is":[20,75],"based":[21],"on":[22],"chaos":[23],"and":[24,77,93,100],"take":[25,43],"into":[26],"account":[27],"that":[28,104],"an":[29],"S-box":[30,107],"can":[31,65],"be":[32],"viewed":[33],"as":[34],"set":[36],"of":[37,45,49],"Boolean":[38,55,62],"functions.":[39],"Therefore,":[40],"will":[42],"advantage":[44],"the":[46,72,80,105],"different":[47],"characteristics":[48],"chaotic":[50],"functions":[51,56],"generate":[53],"random":[54],"with":[57],"high":[58],"nonlinearity.":[59],"Using":[60],"these":[61],"functions,":[63],"create":[66],"highly":[68],"nonlinear":[69],"S-box.":[70],"Afterwards,":[71],"proposed":[73,106],"methodology":[74],"analyzed":[76],"tested":[78],"for":[79],"following":[81],"criteria:":[82],"bijective":[83],"property,":[84],"nonlinearity,":[85],"strict":[86],"avalanche":[87],"criterion,":[88],"output":[89],"bits":[90],"independence":[91],"criterion":[92],"equiprobable":[94],"input/output":[95],"XOR":[96],"distribution.":[97],"Numerical":[98],"simulation":[99],"security":[101],"analysis":[102],"demonstrate":[103],"has":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}