{"id":"https://openalex.org/W4292402685","doi":"https://doi.org/10.1109/tim.2022.3197774","title":"Pseudo-Chaotic Sequences Generated by the Discrete Arnold\u2019s Map Over Z<sub>2<sup><i>m</i></sup></sub>: Period Analysis and FPGA Implementation","display_name":"Pseudo-Chaotic Sequences Generated by the Discrete Arnold\u2019s Map Over Z<sub>2<sup><i>m</i></sup></sub>: Period Analysis and FPGA Implementation","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4292402685","doi":"https://doi.org/10.1109/tim.2022.3197774"},"language":"en","primary_location":{"id":"doi:10.1109/tim.2022.3197774","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tim.2022.3197774","pdf_url":null,"source":{"id":"https://openalex.org/S10892749","display_name":"IEEE Transactions on Instrumentation and Measurement","issn_l":"0018-9456","issn":["0018-9456","1557-9662"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Instrumentation and Measurement","raw_type":"journal-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/A5029683443","display_name":"Carlos E. C. Souza","orcid":"https://orcid.org/0000-0001-6006-0900"},"institutions":[{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Carlos E. C. Souza","raw_affiliation_strings":["Department of Electronics and Systems, Federal University of Pernambuco, Recife, Brazil","Department of Electronics and Systems, Federal University of Pernambuco, Recife-PE, Brazil"],"raw_orcid":"https://orcid.org/0000-0001-6006-0900","affiliations":[{"raw_affiliation_string":"Department of Electronics and Systems, Federal University of Pernambuco, Recife, Brazil","institution_ids":["https://openalex.org/I25112270"]},{"raw_affiliation_string":"Department of Electronics and Systems, Federal University of Pernambuco, Recife-PE, Brazil","institution_ids":["https://openalex.org/I25112270"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082647793","display_name":"Davi Moreno","orcid":"https://orcid.org/0000-0002-6878-0600"},"institutions":[{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Davi Moreno","raw_affiliation_strings":["Department of Electronics and Systems, Federal University of Pernambuco, Recife, Brazil","Department of Electronics and Systems, Federal University of Pernambuco, Recife-PE, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-6878-0600","affiliations":[{"raw_affiliation_string":"Department of Electronics and Systems, Federal University of Pernambuco, Recife, Brazil","institution_ids":["https://openalex.org/I25112270"]},{"raw_affiliation_string":"Department of Electronics and Systems, Federal University of Pernambuco, Recife-PE, Brazil","institution_ids":["https://openalex.org/I25112270"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081177321","display_name":"Daniel P. B. Chaves","orcid":"https://orcid.org/0000-0003-4345-4320"},"institutions":[{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Daniel P. B. Chaves","raw_affiliation_strings":["Department of Electronics and Systems, Federal University of Pernambuco, Recife, Brazil","Department of Electronics and Systems, Federal University of Pernambuco, Recife-PE, Brazil"],"raw_orcid":"https://orcid.org/0000-0003-4345-4320","affiliations":[{"raw_affiliation_string":"Department of Electronics and Systems, Federal University of Pernambuco, Recife, Brazil","institution_ids":["https://openalex.org/I25112270"]},{"raw_affiliation_string":"Department of Electronics and Systems, Federal University of Pernambuco, Recife-PE, Brazil","institution_ids":["https://openalex.org/I25112270"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044717316","display_name":"Cec\u00edlio Pimentel","orcid":"https://orcid.org/0000-0003-2632-919X"},"institutions":[{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Cecilio Pimentel","raw_affiliation_strings":["Department of Electronics and Systems, Federal University of Pernambuco, Recife, Brazil","Department of Electronics and Systems, Federal University of Pernambuco, Recife-PE, Brazil"],"raw_orcid":"https://orcid.org/0000-0003-2632-919X","affiliations":[{"raw_affiliation_string":"Department of Electronics and Systems, Federal University of Pernambuco, Recife, Brazil","institution_ids":["https://openalex.org/I25112270"]},{"raw_affiliation_string":"Department of Electronics and Systems, Federal University of Pernambuco, Recife-PE, Brazil","institution_ids":["https://openalex.org/I25112270"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I25112270"],"apc_list":null,"apc_paid":null,"fwci":1.4214,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.8269434,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"71","issue":null,"first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":1.0,"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":1.0,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9918000102043152,"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":0.9894000291824341,"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/pseudorandom-number-generator","display_name":"Pseudorandom number generator","score":0.7265002727508545},{"id":"https://openalex.org/keywords/fibonacci-number","display_name":"Fibonacci number","score":0.5851055383682251},{"id":"https://openalex.org/keywords/nist","display_name":"NIST","score":0.5816164016723633},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5353833436965942},{"id":"https://openalex.org/keywords/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.5244156122207642},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4693789482116699},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.4181726574897766},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.390358030796051},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3811323046684265},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35070061683654785},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3023267090320587},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.250548392534256},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.2146427035331726},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10409817099571228}],"concepts":[{"id":"https://openalex.org/C140642157","wikidata":"https://www.wikidata.org/wiki/Q1623338","display_name":"Pseudorandom number generator","level":2,"score":0.7265002727508545},{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.5851055383682251},{"id":"https://openalex.org/C111219384","wikidata":"https://www.wikidata.org/wiki/Q6954384","display_name":"NIST","level":2,"score":0.5816164016723633},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5353833436965942},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.5244156122207642},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4693789482116699},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.4181726574897766},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.390358030796051},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3811323046684265},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35070061683654785},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3023267090320587},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.250548392534256},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.2146427035331726},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10409817099571228},{"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/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"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":1,"locations":[{"id":"doi:10.1109/tim.2022.3197774","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tim.2022.3197774","pdf_url":null,"source":{"id":"https://openalex.org/S10892749","display_name":"IEEE Transactions on Instrumentation and Measurement","issn_l":"0018-9456","issn":["0018-9456","1557-9662"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Instrumentation and Measurement","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.41999998688697815}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W565312106","https://openalex.org/W1517403092","https://openalex.org/W1991560324","https://openalex.org/W2001633993","https://openalex.org/W2019409703","https://openalex.org/W2102688401","https://openalex.org/W2161397732","https://openalex.org/W2605543710","https://openalex.org/W2790225553","https://openalex.org/W2885590378","https://openalex.org/W2900684459","https://openalex.org/W2901050362","https://openalex.org/W2903241858","https://openalex.org/W2916817737","https://openalex.org/W2918846722","https://openalex.org/W2945388785","https://openalex.org/W2968111791","https://openalex.org/W2980608281","https://openalex.org/W2994775901","https://openalex.org/W3010109072","https://openalex.org/W3013098700","https://openalex.org/W3022677734","https://openalex.org/W3029897761","https://openalex.org/W3045032477","https://openalex.org/W3094060727","https://openalex.org/W3095288157","https://openalex.org/W3110374082","https://openalex.org/W3123229602","https://openalex.org/W3129397526","https://openalex.org/W3168397396","https://openalex.org/W3211439587","https://openalex.org/W4246704875","https://openalex.org/W4388288416"],"related_works":["https://openalex.org/W2158491338","https://openalex.org/W2807901368","https://openalex.org/W2133733652","https://openalex.org/W2072658171","https://openalex.org/W2606392311","https://openalex.org/W2320042380","https://openalex.org/W4385956668","https://openalex.org/W2900895161","https://openalex.org/W4380838366","https://openalex.org/W2626887348"],"abstract_inverted_index":{"In":[0],"this":[1,57],"work,":[2],"we":[3],"propose":[4],"a":[5,47,73],"method":[6],"to":[7,45,120],"generate":[8],"one-dimensional":[9],"pseudo-chaotic":[10,41],"sequences":[11,29,42,93,104],"based":[12],"on":[13],"the":[14,20,27,35,53,62,69,87,92,124],"discrete":[15],"Arnold&#x2019;s":[16],"map":[17],"defined":[18,94,105],"over":[19,38,95,106],"integer":[21],"ring":[22],"Z<sub>2<sup><i>m</i></sup></sub>.":[23,39],"The":[24,40,108],"period":[25],"of":[26,34,56],"generated":[28],"is":[30],"investigated":[31],"using":[32],"properties":[33,55],"Fibonacci":[36],"sequence":[37],"are":[43,59],"employed":[44],"design":[46],"pseudo-random":[48],"number":[49],"generator":[50],"(PRNG),":[51],"and":[52,79,114],"statistical":[54,64],"PRNG":[58,71,110],"analyzed":[60],"by":[61],"NIST":[63],"test":[65],"suite.":[66],"We":[67],"implement":[68],"proposed":[70,103,109],"in":[72,123],"field":[74],"programmable":[75],"gate":[76],"array":[77],"(FPGA)":[78],"investigate":[80],"its":[81],"hardware":[82,99],"requirements.We":[83],"show":[84],"that":[85],"for":[86],"same":[88],"bit":[89],"generation":[90],"rate,":[91],"Z<sub>2<sup><i>m</i></sup></sub>":[96],"require":[97],"fewer":[98],"units":[100],"than":[101],"recently":[102],"Z<sub>3<sup><i>m</i></sup></sub>.":[107],"has":[111],"higher":[112],"throughput":[113],"competitive":[115],"hard-ware":[116],"consumption":[117],"when":[118],"compared":[119],"other":[121],"architectures":[122],"literature.":[125]},"counts_by_year":[{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}