{"id":"https://openalex.org/W3025809365","doi":"https://doi.org/10.3390/sym12050829","title":"A Two-Parameter Modified Logistic Map and Its Application to Random Bit Generation","display_name":"A Two-Parameter Modified Logistic Map and Its Application to Random Bit Generation","publication_year":2020,"publication_date":"2020-05-18","ids":{"openalex":"https://openalex.org/W3025809365","doi":"https://doi.org/10.3390/sym12050829","mag":"3025809365"},"language":"en","primary_location":{"id":"doi:10.3390/sym12050829","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12050829","pdf_url":null,"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,"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"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/sym12050829","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055872900","display_name":"Lazaros Moysis","orcid":"https://orcid.org/0000-0002-5652-2532"},"institutions":[{"id":"https://openalex.org/I21370196","display_name":"Aristotle University of Thessaloniki","ror":"https://ror.org/02j61yw88","country_code":"GR","type":"education","lineage":["https://openalex.org/I21370196"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Lazaros Moysis","raw_affiliation_strings":["Laboratory of Nonlinear Systems, Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece"],"raw_orcid":"https://orcid.org/0000-0002-5652-2532","affiliations":[{"raw_affiliation_string":"Laboratory of Nonlinear Systems, Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece","institution_ids":["https://openalex.org/I21370196"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076771418","display_name":"\u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440\u0430 \u0422\u0443\u0442\u0443\u0435\u0432\u0430","orcid":"https://orcid.org/0000-0002-9747-1962"},"institutions":[{"id":"https://openalex.org/I41518628","display_name":"Saint Petersburg State Electrotechnical University","ror":"https://ror.org/023bq8521","country_code":"RU","type":"education","lineage":["https://openalex.org/I41518628"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Aleksandra Tutueva","raw_affiliation_strings":["Department of Computer-Aided Design, Saint Petersburg Electrotechnical University \u201cLETI\u201d, 5, Professora Popova st., 197376 Saint Petersburg, Russia","Department of Computer-Aided Design, Saint Petersburg Electrotechnical University \"LETI\", 5, Professora Popova st., 197376 Saint Petersburg, Russia"],"raw_orcid":"https://orcid.org/0000-0002-9747-1962","affiliations":[{"raw_affiliation_string":"Department of Computer-Aided Design, Saint Petersburg Electrotechnical University \u201cLETI\u201d, 5, Professora Popova st., 197376 Saint Petersburg, Russia","institution_ids":["https://openalex.org/I41518628"]},{"raw_affiliation_string":"Department of Computer-Aided Design, Saint Petersburg Electrotechnical University \"LETI\", 5, Professora Popova st., 197376 Saint Petersburg, Russia","institution_ids":["https://openalex.org/I41518628"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061639181","display_name":"Christos Volos","orcid":"https://orcid.org/0000-0001-8763-7255"},"institutions":[{"id":"https://openalex.org/I21370196","display_name":"Aristotle University of Thessaloniki","ror":"https://ror.org/02j61yw88","country_code":"GR","type":"education","lineage":["https://openalex.org/I21370196"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Christos Volos","raw_affiliation_strings":["Laboratory of Nonlinear Systems, Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece"],"raw_orcid":"https://orcid.org/0000-0001-8763-7255","affiliations":[{"raw_affiliation_string":"Laboratory of Nonlinear Systems, Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece","institution_ids":["https://openalex.org/I21370196"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075024454","display_name":"\u0414\u0435\u043d\u0438\u0441 \u0411\u0443\u0442\u0443\u0441\u043e\u0432","orcid":"https://orcid.org/0000-0002-8941-4220"},"institutions":[{"id":"https://openalex.org/I41518628","display_name":"Saint Petersburg State Electrotechnical University","ror":"https://ror.org/023bq8521","country_code":"RU","type":"education","lineage":["https://openalex.org/I41518628"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Denis Butusov","raw_affiliation_strings":["Youth Research Institute, Saint-Petersburg Electrotechnical University \u201cLETI\u201d, 5, Professora Popova st., 197376 Saint Petersburg, Russia","Youth Research Institute, Saint-Petersburg Electrotechnical University \"LETI\", 5, Professora Popova st., 197376 Saint Petersburg, Russia"],"raw_orcid":"https://orcid.org/0000-0002-8941-4220","affiliations":[{"raw_affiliation_string":"Youth Research Institute, Saint-Petersburg Electrotechnical University \u201cLETI\u201d, 5, Professora Popova st., 197376 Saint Petersburg, Russia","institution_ids":["https://openalex.org/I41518628"]},{"raw_affiliation_string":"Youth Research Institute, Saint-Petersburg Electrotechnical University \"LETI\", 5, Professora Popova st., 197376 Saint Petersburg, Russia","institution_ids":["https://openalex.org/I41518628"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029391974","display_name":"Jes\u00fas M. Mu\u00f1oz\u2010Pacheco","orcid":"https://orcid.org/0000-0002-9106-6982"},"institutions":[{"id":"https://openalex.org/I721619","display_name":"Benem\u00e9rita Universidad Aut\u00f3noma de Puebla","ror":"https://ror.org/03p2z7827","country_code":"MX","type":"education","lineage":["https://openalex.org/I721619"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Jesus M. Munoz-Pacheco","raw_affiliation_strings":["Faculty of Electronics Sciences, Autonomous University of Puebla, Puebla 72000, Mexico"],"raw_orcid":"https://orcid.org/0000-0002-9106-6982","affiliations":[{"raw_affiliation_string":"Faculty of Electronics Sciences, Autonomous University of Puebla, Puebla 72000, Mexico","institution_ids":["https://openalex.org/I721619"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035617385","display_name":"Hector E. Nistazakis","orcid":"https://orcid.org/0000-0002-9301-0691"},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Hector Nistazakis","raw_affiliation_strings":["Section of Electronic Physics, Department of Physics, National and Kapodistrian University of Athens, 15784 Athens, Greece"],"raw_orcid":"https://orcid.org/0000-0002-9301-0691","affiliations":[{"raw_affiliation_string":"Section of Electronic Physics, Department of Physics, National and Kapodistrian University of Athens, 15784 Athens, Greece","institution_ids":["https://openalex.org/I200777214"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5061639181"],"corresponding_institution_ids":["https://openalex.org/I21370196"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":3.1733,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.9272756,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"12","issue":"5","first_page":"829","last_page":"829"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9994999766349792,"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":0.9994999766349792,"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/T10244","display_name":"Chaos control and synchronization","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/logistic-map","display_name":"Logistic map","score":0.902908444404602},{"id":"https://openalex.org/keywords/nist","display_name":"NIST","score":0.7635700106620789},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.7014798521995544},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.6275429725646973},{"id":"https://openalex.org/keywords/chaotic-map","display_name":"Chaotic map","score":0.6054384708404541},{"id":"https://openalex.org/keywords/bit","display_name":"Bit (key)","score":0.542962908744812},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49674636125564575},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4819759726524353},{"id":"https://openalex.org/keywords/chaos","display_name":"CHAOS (operating system)","score":0.4719972610473633},{"id":"https://openalex.org/keywords/tent-map","display_name":"Tent map","score":0.4706788659095764},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.46618080139160156},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4081270098686218},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.30342572927474976},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.28523293137550354},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07300582528114319}],"concepts":[{"id":"https://openalex.org/C205330730","wikidata":"https://www.wikidata.org/wiki/Q587182","display_name":"Logistic map","level":3,"score":0.902908444404602},{"id":"https://openalex.org/C111219384","wikidata":"https://www.wikidata.org/wiki/Q6954384","display_name":"NIST","level":2,"score":0.7635700106620789},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.7014798521995544},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6275429725646973},{"id":"https://openalex.org/C2983793180","wikidata":"https://www.wikidata.org/wiki/Q166314","display_name":"Chaotic map","level":3,"score":0.6054384708404541},{"id":"https://openalex.org/C117011727","wikidata":"https://www.wikidata.org/wiki/Q1278488","display_name":"Bit (key)","level":2,"score":0.542962908744812},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49674636125564575},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4819759726524353},{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.4719972610473633},{"id":"https://openalex.org/C15998118","wikidata":"https://www.wikidata.org/wiki/Q11319849","display_name":"Tent map","level":3,"score":0.4706788659095764},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.46618080139160156},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4081270098686218},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.30342572927474976},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28523293137550354},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07300582528114319},{"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/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12050829","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12050829","pdf_url":null,"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,"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:ff38de35378d409a80fdc5853eba7768","is_oa":true,"landing_page_url":"https://doaj.org/article/ff38de35378d409a80fdc5853eba7768","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":"Symmetry, Vol 12, Iss 5, p 829 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/5/829/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12050829","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12050829","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12050829","pdf_url":null,"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,"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1529513229","https://openalex.org/W1568276820","https://openalex.org/W2000232527","https://openalex.org/W2001032007","https://openalex.org/W2036655098","https://openalex.org/W2041330138","https://openalex.org/W2065540272","https://openalex.org/W2066208760","https://openalex.org/W2081024858","https://openalex.org/W2082425750","https://openalex.org/W2094177410","https://openalex.org/W2102892532","https://openalex.org/W2105145864","https://openalex.org/W2113005260","https://openalex.org/W2122271717","https://openalex.org/W2165983133","https://openalex.org/W2176627963","https://openalex.org/W2183918150","https://openalex.org/W2204310803","https://openalex.org/W2278852559","https://openalex.org/W2293161194","https://openalex.org/W2497629929","https://openalex.org/W2516950210","https://openalex.org/W2627122219","https://openalex.org/W2808720755","https://openalex.org/W2900721467","https://openalex.org/W2908420681","https://openalex.org/W2911365385","https://openalex.org/W2914369222","https://openalex.org/W2945388785","https://openalex.org/W2949485390","https://openalex.org/W2952469659","https://openalex.org/W2956215630","https://openalex.org/W2976764752","https://openalex.org/W2985012163","https://openalex.org/W2989930392","https://openalex.org/W2998636469","https://openalex.org/W3003027562","https://openalex.org/W3083393508","https://openalex.org/W4243494487","https://openalex.org/W4250883246","https://openalex.org/W6633907081","https://openalex.org/W6739666421","https://openalex.org/W7027811205"],"related_works":["https://openalex.org/W2587616480","https://openalex.org/W2061342071","https://openalex.org/W2182116519","https://openalex.org/W2372883970","https://openalex.org/W2057446926","https://openalex.org/W2393587766","https://openalex.org/W2359175050","https://openalex.org/W4210931300","https://openalex.org/W2140640830","https://openalex.org/W2360233907"],"abstract_inverted_index":{"This":[0],"work":[1],"proposes":[2],"a":[3,99],"modified":[4],"logistic":[5],"map":[6,19,38,49,59],"based":[7],"on":[8],"the":[9,33,37,44,47,56,65,74,90],"system":[10],"previously":[11],"proposed":[12,48,86],"by":[13],"Han":[14],"in":[15],"2019.":[16],"The":[17,58,85],"constructed":[18],"exhibits":[20],"interesting":[21],"chaos":[22],"related":[23],"phenomena":[24],"like":[25,73],"antimonotonicity,":[26],"crisis,":[27],"and":[28,82,97],"coexisting":[29],"attractors.":[30],"In":[31],"addition,":[32],"Lyapunov":[34],"exponent":[35],"of":[36,46,67],"can":[39],"achieve":[40],"higher":[41],"values,":[42],"so":[43],"behavior":[45],"is":[50,60],"overall":[51],"more":[52],"complex":[53],"compared":[54],"to":[55,64],"original.":[57],"then":[61],"successfully":[62],"applied":[63],"problem":[66],"random":[68],"bit":[69,83],"generation":[70],"using":[71],"techniques":[72],"comparison":[75],"between":[76],"maps,":[77],"X":[78],"O":[79],"R":[80],",":[81],"reversal.":[84],"algorithm":[87],"passes":[88],"all":[89],"NIST":[91],"tests,":[92],"shows":[93],"good":[94],"correlation":[95],"characteristics,":[96],"has":[98],"high":[100],"key":[101],"space.":[102]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":4}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}