{"id":"https://openalex.org/W3182014825","doi":"https://doi.org/10.3390/e23070904","title":"Secret Communication Systems Using Chaotic Wave Equations with Neural Network Boundary Conditions","display_name":"Secret Communication Systems Using Chaotic Wave Equations with Neural Network Boundary Conditions","publication_year":2021,"publication_date":"2021-07-16","ids":{"openalex":"https://openalex.org/W3182014825","doi":"https://doi.org/10.3390/e23070904","mag":"3182014825","pmid":"https://pubmed.ncbi.nlm.nih.gov/34356445"},"language":"en","primary_location":{"id":"doi:10.3390/e23070904","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23070904","pdf_url":"https://www.mdpi.com/1099-4300/23/7/904/pdf?version=1626415763","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/23/7/904/pdf?version=1626415763","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102759770","display_name":"Yuhan Chen","orcid":"https://orcid.org/0000-0001-8485-4713"},"institutions":[{"id":"https://openalex.org/I65837984","display_name":"Kobe University","ror":"https://ror.org/03tgsfw79","country_code":"JP","type":"education","lineage":["https://openalex.org/I65837984"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yuhan Chen","raw_affiliation_strings":["Graduate School of System Informatics, Kobe University, Kobe 657-8501, Japan"],"raw_orcid":"https://orcid.org/0000-0001-8485-4713","affiliations":[{"raw_affiliation_string":"Graduate School of System Informatics, Kobe University, Kobe 657-8501, Japan","institution_ids":["https://openalex.org/I65837984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101890858","display_name":"Hideki Sano","orcid":"https://orcid.org/0000-0003-1053-1078"},"institutions":[{"id":"https://openalex.org/I65837984","display_name":"Kobe University","ror":"https://ror.org/03tgsfw79","country_code":"JP","type":"education","lineage":["https://openalex.org/I65837984"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hideki Sano","raw_affiliation_strings":["Graduate School of System Informatics, Kobe University, Kobe 657-8501, Japan"],"raw_orcid":"https://orcid.org/0000-0003-1053-1078","affiliations":[{"raw_affiliation_string":"Graduate School of System Informatics, Kobe University, Kobe 657-8501, Japan","institution_ids":["https://openalex.org/I65837984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066708711","display_name":"Masashi Wakaiki","orcid":"https://orcid.org/0000-0002-0905-6268"},"institutions":[{"id":"https://openalex.org/I65837984","display_name":"Kobe University","ror":"https://ror.org/03tgsfw79","country_code":"JP","type":"education","lineage":["https://openalex.org/I65837984"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masashi Wakaiki","raw_affiliation_strings":["Graduate School of System Informatics, Kobe University, Kobe 657-8501, Japan"],"raw_orcid":"https://orcid.org/0000-0002-0905-6268","affiliations":[{"raw_affiliation_string":"Graduate School of System Informatics, Kobe University, Kobe 657-8501, Japan","institution_ids":["https://openalex.org/I65837984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004524501","display_name":"Takaharu Yaguchi","orcid":"https://orcid.org/0000-0001-9025-6015"},"institutions":[{"id":"https://openalex.org/I65837984","display_name":"Kobe University","ror":"https://ror.org/03tgsfw79","country_code":"JP","type":"education","lineage":["https://openalex.org/I65837984"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takaharu Yaguchi","raw_affiliation_strings":["Graduate School of System Informatics, Kobe University, Kobe 657-8501, Japan"],"raw_orcid":"https://orcid.org/0000-0001-9025-6015","affiliations":[{"raw_affiliation_string":"Graduate School of System Informatics, Kobe University, Kobe 657-8501, Japan","institution_ids":["https://openalex.org/I65837984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5102759770"],"corresponding_institution_ids":["https://openalex.org/I65837984"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.8728,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.75674629,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"23","issue":"7","first_page":"904","last_page":"904"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9940000176429749,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9754999876022339,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.7041525840759277},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6414484977722168},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.5902079939842224},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.587712287902832},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.5634427070617676},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5328092575073242},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5183371305465698},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.42522573471069336},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.42359331250190735},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3783953785896301},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32831889390945435},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22527781128883362},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09422048926353455}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7041525840759277},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6414484977722168},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.5902079939842224},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.587712287902832},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5634427070617676},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5328092575073242},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5183371305465698},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.42522573471069336},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.42359331250190735},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3783953785896301},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32831889390945435},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22527781128883362},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09422048926353455},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e23070904","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23070904","pdf_url":"https://www.mdpi.com/1099-4300/23/7/904/pdf?version=1626415763","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:34356445","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34356445","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:irdb.nii.ac.jp:01257:0005619049","is_oa":true,"landing_page_url":"https://hdl.handle.net/20.500.14094/90008524","pdf_url":"https://da.lib.kobe-u.ac.jp/da/kernel/90008524/90008524.pdf","source":{"id":"https://openalex.org/S7407056385","display_name":"Institutional Repositories DataBase (IRDB)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184597095","host_organization_name":"National Institute of Informatics","host_organization_lineage":["https://openalex.org/I184597095"],"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":"Entropy","raw_type":"journal article"},{"id":"pmh:oai:doaj.org/article:39498a02f77940948cd132f67b950a75","is_oa":true,"landing_page_url":"https://doaj.org/article/39498a02f77940948cd132f67b950a75","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":"Entropy, Vol 23, Iss 7, p 904 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/23/7/904/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e23070904","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":"Entropy; Volume 23; Issue 7; Pages: 904","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8306622","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8306622","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e23070904","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23070904","pdf_url":"https://www.mdpi.com/1099-4300/23/7/904/pdf?version=1626415763","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.6000000238418579,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G4028502120","display_name":"\u5e7e\u4f55\u5b66\u7684\u96e2\u6563\u529b\u5b66\u3092\u6838\u3068\u3059\u308b\u69cb\u9020\u4fdd\u5b58\u7684\u30b7\u30b9\u30c6\u30e0\u30e2\u30c7\u30ea\u30f3\u30b0\u30fb\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u57fa\u76e4","funder_award_id":"JPMJCR1914","funder_id":"https://openalex.org/F4320334789","funder_display_name":"Japan Science and Technology Agency"},{"id":"https://openalex.org/G443570101","display_name":null,"funder_award_id":"JP 21K03370","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"},{"id":"https://openalex.org/F4320334789","display_name":"Japan Science and Technology Agency","ror":"https://ror.org/00097mb19"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3182014825.pdf","grobid_xml":"https://content.openalex.org/works/W3182014825.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1641808155","https://openalex.org/W1855169650","https://openalex.org/W1903823580","https://openalex.org/W1966242839","https://openalex.org/W1973202362","https://openalex.org/W1982207894","https://openalex.org/W2001065713","https://openalex.org/W2002131976","https://openalex.org/W2003645334","https://openalex.org/W2018839322","https://openalex.org/W2024710783","https://openalex.org/W2060759080","https://openalex.org/W2062019423","https://openalex.org/W2068262191","https://openalex.org/W2085648684","https://openalex.org/W2112647358","https://openalex.org/W2425286230","https://openalex.org/W2500739439","https://openalex.org/W2590132587","https://openalex.org/W2743028355","https://openalex.org/W2790225553","https://openalex.org/W2944785541","https://openalex.org/W2955017137","https://openalex.org/W3037686808","https://openalex.org/W3088547738","https://openalex.org/W3120899908","https://openalex.org/W3127303671","https://openalex.org/W3130148533","https://openalex.org/W4231424545","https://openalex.org/W4285719527","https://openalex.org/W6645890879","https://openalex.org/W6717539790","https://openalex.org/W6783843635"],"related_works":["https://openalex.org/W1979229270","https://openalex.org/W2374600121","https://openalex.org/W125502673","https://openalex.org/W2384948345","https://openalex.org/W2361515791","https://openalex.org/W2375956839","https://openalex.org/W1982767765","https://openalex.org/W2376048186","https://openalex.org/W2133690079","https://openalex.org/W2111215486"],"abstract_inverted_index":{"In":[0,30,68,147],"a":[1,14,31,34,224,281],"secret":[2],"communication":[3,9],"system":[4,37],"using":[5],"chaotic":[6,35,186],"synchronization,":[7],"the":[8,24,28,42,46,54,57,73,84,98,104,109,113,121,126,134,144,153,161,168,180,192,201,208,227,240,245,253,262,265,284,297,302,310,319,322],"information":[10,86,190,243,300],"is":[11,21,63,93,101,116,150,171,195,220,277],"embedded":[12],"in":[13,191,222,279],"signal":[15],"that":[16,119,152,179,226,252,283,309],"behaves":[17],"as":[18,103,118],"chaos":[19],"and":[20,112,139,142],"sent":[22],"to":[23,26,88],"receiver":[25],"retrieve":[27],"information.":[29],"previous":[32],"study,":[33,70],"synchronous":[36],"was":[38],"developed":[39],"by":[40,207],"integrating":[41],"wave":[43,110],"equation":[44,111],"with":[45,77],"van":[47],"der":[48],"Pol":[49],"boundary":[50,75,106,129],"condition,":[51],"of":[52,56,108,160,167,236,242,264,293,299,321],"which":[53,62,260,317],"number":[55],"parameters":[58],"are":[59,156,214,230,256,271,287,313],"only":[60],"three,":[61],"not":[64],"enough":[65],"for":[66,136],"security.":[67],"this":[69],"we":[71],"replace":[72],"nonlinear":[74,128],"condition":[76,107],"an":[78],"artificial":[79],"neural":[80,91,169,182],"network,":[81],"thereby":[82,238,295],"making":[83],"transmitted":[85,228,285],"difficult":[87],"leak.":[89],"The":[90,164,174,189,217,248,274,305],"network":[92,170,183],"divided":[94],"into":[95,232,289],"two":[96],"parts;":[97],"first":[99],"half":[100,115],"used":[102,117],"left":[105],"second":[114],"on":[120],"right":[122],"boundary,":[123],"thus":[124],"replacing":[125],"original":[127,193,246,303],"condition.":[130],"We":[131],"also":[132,172,215,272],"show":[133,251,308],"results":[135,250,307],"both":[137],"monochrome":[138],"color":[140],"images":[141,155,229,235,255,286,292,312],"evaluate":[143],"security":[145,212,263,269,320],"performance.":[146],"particular,":[148],"it":[149],"shown":[151],"encrypted":[154,231,254,288,311],"almost":[157,233,258,290,315],"identical":[158,234,291],"regardless":[159],"input":[162],"images.":[163],"learning":[165],"performance":[166],"investigated.":[173],"calculated":[175],"Lyapunov":[176],"exponent":[177],"shows":[178],"learned":[181],"causes":[184],"some":[185],"vibration":[187],"effect.":[188],"image":[194,202],"completely":[196],"invisible":[197],"when":[198],"viewed":[199],"through":[200],"obtained":[203],"after":[204],"being":[205],"concealed":[206],"proposed":[209,218,266,275,323],"system.":[210],"Some":[211,268],"tests":[213,270],"performed.":[216,273],"method":[219,276],"designed":[221,278],"such":[223,280],"way":[225,282],"waves,":[237,294],"preventing":[239,296],"retrieval":[241,298],"from":[244,301],"image.":[247,304],"numerical":[249,306],"certainly":[257,314],"identical,":[259,316],"supports":[261,318],"method.":[267,324]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
