{"id":"https://openalex.org/W4414095746","doi":"https://doi.org/10.3389/fcomp.2025.1649256","title":"Brownian motion models: cryptographic applications, capabilities, and limitations","display_name":"Brownian motion models: cryptographic applications, capabilities, and limitations","publication_year":2025,"publication_date":"2025-09-10","ids":{"openalex":"https://openalex.org/W4414095746","doi":"https://doi.org/10.3389/fcomp.2025.1649256"},"language":"en","primary_location":{"id":"doi:10.3389/fcomp.2025.1649256","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fcomp.2025.1649256","pdf_url":"https://www.frontiersin.org/journals/computer-science/articles/10.3389/fcomp.2025.1649256/pdf","source":{"id":"https://openalex.org/S4210211086","display_name":"Frontiers in Computer Science","issn_l":"2624-9898","issn":["2624-9898"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.frontiersin.org/journals/computer-science/articles/10.3389/fcomp.2025.1649256/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119581201","display_name":"Abduljameel Zainalabideen","orcid":null},"institutions":[{"id":"https://openalex.org/I4210139873","display_name":"Arab Open University","ror":"https://ror.org/03vfnky71","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210093932","https://openalex.org/I4210139873"]},{"id":"https://openalex.org/I159247623","display_name":"Mansoura University","ror":"https://ror.org/01k8vtd75","country_code":"EG","type":"education","lineage":["https://openalex.org/I159247623"]}],"countries":["EG","SA"],"is_corresponding":false,"raw_author_name":"Abduljameel Zainalabideen","raw_affiliation_strings":["Faculty of Computer Studies, Arab Open University, Riyadh, Saudi Arabia","Faculty of Computers and Information, Mansoura University, Mansoura, Egypt"],"affiliations":[{"raw_affiliation_string":"Faculty of Computer Studies, Arab Open University, Riyadh, Saudi Arabia","institution_ids":["https://openalex.org/I4210139873"]},{"raw_affiliation_string":"Faculty of Computers and Information, Mansoura University, Mansoura, Egypt","institution_ids":["https://openalex.org/I159247623"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027108688","display_name":"Khaled Suwais","orcid":"https://orcid.org/0000-0001-6530-5022"},"institutions":[{"id":"https://openalex.org/I4210139873","display_name":"Arab Open University","ror":"https://ror.org/03vfnky71","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210093932","https://openalex.org/I4210139873"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Khaled Suwais","raw_affiliation_strings":["Faculty of Computer Studies, Arab Open University, Riyadh, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Faculty of Computer Studies, Arab Open University, Riyadh, Saudi Arabia","institution_ids":["https://openalex.org/I4210139873"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042916753","display_name":"Hazem M. El\u2010Bakry","orcid":"https://orcid.org/0000-0002-4798-0427"},"institutions":[{"id":"https://openalex.org/I159247623","display_name":"Mansoura University","ror":"https://ror.org/01k8vtd75","country_code":"EG","type":"education","lineage":["https://openalex.org/I159247623"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Hazem El-Bakry","raw_affiliation_strings":["Faculty of Computers and Information, Mansoura University, Mansoura, Egypt"],"affiliations":[{"raw_affiliation_string":"Faculty of Computers and Information, Mansoura University, Mansoura, Egypt","institution_ids":["https://openalex.org/I159247623"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053278966","display_name":"Islam R. Abdelmaksoud","orcid":"https://orcid.org/0000-0001-7260-8857"},"institutions":[{"id":"https://openalex.org/I159247623","display_name":"Mansoura University","ror":"https://ror.org/01k8vtd75","country_code":"EG","type":"education","lineage":["https://openalex.org/I159247623"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Islam Abdelmaksoud","raw_affiliation_strings":["Faculty of Computers and Information, Mansoura University, Mansoura, Egypt"],"affiliations":[{"raw_affiliation_string":"Faculty of Computers and Information, Mansoura University, Mansoura, Egypt","institution_ids":["https://openalex.org/I159247623"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5027108688"],"corresponding_institution_ids":["https://openalex.org/I4210139873"],"apc_list":{"value":1150,"currency":"USD","value_usd":1150},"apc_paid":{"value":1150,"currency":"USD","value_usd":1150},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24693882,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"7","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9975000023841858,"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":0.9975000023841858,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.6643999814987183},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.5040000081062317},{"id":"https://openalex.org/keywords/cryptographic-primitive","display_name":"Cryptographic primitive","score":0.44190001487731934},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.4115000069141388},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.3995000123977661},{"id":"https://openalex.org/keywords/geometric-brownian-motion","display_name":"Geometric Brownian motion","score":0.3682999908924103},{"id":"https://openalex.org/keywords/cryptographic-protocol","display_name":"Cryptographic protocol","score":0.34549999237060547}],"concepts":[{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.6643999814987183},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5044000148773193},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.5040000081062317},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4519999921321869},{"id":"https://openalex.org/C15927051","wikidata":"https://www.wikidata.org/wiki/Q246593","display_name":"Cryptographic primitive","level":4,"score":0.44190001487731934},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.4115000069141388},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.3995000123977661},{"id":"https://openalex.org/C101615488","wikidata":"https://www.wikidata.org/wiki/Q1503307","display_name":"Geometric Brownian motion","level":4,"score":0.3682999908924103},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3490999937057495},{"id":"https://openalex.org/C33884865","wikidata":"https://www.wikidata.org/wiki/Q1254335","display_name":"Cryptographic protocol","level":3,"score":0.34549999237060547},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.3215999901294708},{"id":"https://openalex.org/C60391097","wikidata":"https://www.wikidata.org/wiki/Q1056809","display_name":"Wiener process","level":2,"score":0.3100000023841858},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.30709999799728394},{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.30079999566078186},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.28600001335144043},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.28060001134872437},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.27070000767707825}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3389/fcomp.2025.1649256","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fcomp.2025.1649256","pdf_url":"https://www.frontiersin.org/journals/computer-science/articles/10.3389/fcomp.2025.1649256/pdf","source":{"id":"https://openalex.org/S4210211086","display_name":"Frontiers in Computer Science","issn_l":"2624-9898","issn":["2624-9898"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a38e22685ca54e12af530565a1430c3b","is_oa":true,"landing_page_url":"https://doaj.org/article/a38e22685ca54e12af530565a1430c3b","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Frontiers in Computer Science, Vol 7 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3389/fcomp.2025.1649256","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fcomp.2025.1649256","pdf_url":"https://www.frontiersin.org/journals/computer-science/articles/10.3389/fcomp.2025.1649256/pdf","source":{"id":"https://openalex.org/S4210211086","display_name":"Frontiers in Computer Science","issn_l":"2624-9898","issn":["2624-9898"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414095746.pdf","grobid_xml":"https://content.openalex.org/works/W4414095746.grobid-xml"},"referenced_works_count":58,"referenced_works":["https://openalex.org/W1571438983","https://openalex.org/W2065096983","https://openalex.org/W2076057077","https://openalex.org/W2892240799","https://openalex.org/W2996920534","https://openalex.org/W2997370046","https://openalex.org/W3012512120","https://openalex.org/W3021150914","https://openalex.org/W3022365464","https://openalex.org/W3032794338","https://openalex.org/W3045864679","https://openalex.org/W3094844849","https://openalex.org/W3102100346","https://openalex.org/W3112037995","https://openalex.org/W3120750439","https://openalex.org/W3125291817","https://openalex.org/W3152123222","https://openalex.org/W3164731060","https://openalex.org/W3175992021","https://openalex.org/W3181312683","https://openalex.org/W3203913749","https://openalex.org/W3209309129","https://openalex.org/W3213484912","https://openalex.org/W3214808675","https://openalex.org/W3216497253","https://openalex.org/W4200038482","https://openalex.org/W4206021469","https://openalex.org/W4206615766","https://openalex.org/W4210362950","https://openalex.org/W4211036842","https://openalex.org/W4211192810","https://openalex.org/W4214691409","https://openalex.org/W4220897115","https://openalex.org/W4221007546","https://openalex.org/W4221039760","https://openalex.org/W4238187298","https://openalex.org/W4285156045","https://openalex.org/W4286944836","https://openalex.org/W4311961481","https://openalex.org/W4312060683","https://openalex.org/W4313245892","https://openalex.org/W4315433321","https://openalex.org/W4327912932","https://openalex.org/W4361986752","https://openalex.org/W4362733592","https://openalex.org/W4382776170","https://openalex.org/W4384764205","https://openalex.org/W4388221301","https://openalex.org/W4388293385","https://openalex.org/W4389828020","https://openalex.org/W4390495432","https://openalex.org/W4391665206","https://openalex.org/W4397003344","https://openalex.org/W4399625431","https://openalex.org/W4399977797","https://openalex.org/W4400197072","https://openalex.org/W4401535166","https://openalex.org/W4406419746"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"Brownian":[0,137],"motion":[1],"(BM)":[2],"is":[3],"a":[4,29,125],"stochastic":[5,118],"model":[6],"that":[7,82],"has":[8],"been":[9],"extensively":[10],"studied":[11],"in":[12,21,114],"physics,":[13],"finance,":[14],"and":[15,36,55,69,94,104,123],"engineering.":[16],"However,":[17],"its":[18],"potential":[19,105],"use":[20],"cryptographic":[22,37,85,121],"applications":[23],"remains":[24],"underexplored.":[25],"This":[26,110],"paper":[27,111],"presents":[28],"comprehensive":[30],"review":[31],"of":[32,39,62,76,92,107,117,132],"the":[33,44,60,101,115,129],"capabilities,":[34],"limitations,":[35],"properties":[38],"various":[40],"BM":[41],"models,":[42,64],"including":[43,87],"Wiener":[45],"process,":[46,52],"geometric":[47],"BM,":[48,50,54],"fractional":[49],"Ornstein\u2013Uhlenbeck":[51],"multidimensional":[53,90],"reflected":[56],"BM.":[57],"We":[58,98],"reviewed":[59],"mathematics":[61],"these":[63,77],"simulate":[65],"their":[66,71],"random":[67],"evolutions,":[68],"compare":[70],"cryptanalytic":[72],"properties.":[73],"A":[74],"comparison":[75],"sources":[78],"highlights":[79],"unique":[80],"characteristics":[81],"can":[83],"provide":[84],"resilience,":[86],"long-range":[88],"dependence,":[89],"modeling":[91],"noise,":[93],"constraints":[95],"on":[96,136],"randomness.":[97],"also":[99],"describe":[100],"main":[102],"limitations":[103],"weaknesses":[106],"each":[108],"model.":[109],"addresses":[112],"gaps":[113],"application":[116],"process":[119],"to":[120],"design":[122],"provides":[124],"foundational":[126],"guideline":[127],"for":[128],"continued":[130],"development":[131],"secure":[133],"systems":[134],"based":[135],"dynamics.":[138]},"counts_by_year":[],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
