{"id":"https://openalex.org/W7220963765","doi":"https://doi.org/10.1364/oe.615359","title":"Large key space and efficient hierarchical chaotic encryption for secure transmission of 65536-QAM via delta sigma modulation","display_name":"Large key space and efficient hierarchical chaotic encryption for secure transmission of 65536-QAM via delta sigma modulation","publication_year":2026,"publication_date":"2026-10-08","ids":{"openalex":"https://openalex.org/W7220963765","doi":"https://doi.org/10.1364/oe.615359","pmid":"https://pubmed.ncbi.nlm.nih.gov/42963705"},"language":"en","primary_location":{"id":"doi:10.1364/oe.615359","doi":"https://doi.org/10.1364/oe.615359","is_oa":true,"landing_page_url":"https://doi.org/10.1364/oe.615359","pdf_url":null,"source":{"id":"https://openalex.org/S178776955","display_name":"Optics Express","issn_l":"1094-4087","issn":["1094-4087"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-b","jufo-1","ki-jl-1","medline","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315679","host_organization_name":"Optica Publishing Group","host_organization_lineage":["https://openalex.org/P4310315679"],"host_organization_lineage_names":["Optica Publishing Group"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optics Express","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1364/oe.615359","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111267916","display_name":"Haolin Bai","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haolin Bai","raw_affiliation_strings":["School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101950162","display_name":"Jiahao Huo","orcid":"https://orcid.org/0000-0002-3181-2816","observed_orcids":["https://orcid.org/0000-0002-3181-2816"]},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiahao Huo","raw_affiliation_strings":["School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China"],"raw_orcid":"https://orcid.org/0000-0002-3181-2816","affiliations":[{"raw_affiliation_string":"School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129446770","display_name":"peng Qin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peng Qin","raw_affiliation_strings":["School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157918975","display_name":"Weizhang Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210098582","display_name":"ZTE (China)","ror":"https://ror.org/00rjhhq63","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210098582"]},{"id":"https://openalex.org/I75746372","display_name":"ZTE (United States)","ror":"https://ror.org/0518yg160","country_code":"US","type":"company","lineage":["https://openalex.org/I4210098582","https://openalex.org/I75746372"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Weizhang Chen","raw_affiliation_strings":["Wireline Product R&D Institute, ZTE Corporation"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wireline Product R&D Institute, ZTE Corporation","institution_ids":["https://openalex.org/I4210098582","https://openalex.org/I75746372"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157902851","display_name":"Ruihua Huang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruihua Huang","raw_affiliation_strings":["School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5141428096","display_name":"Wenhao Ma","orcid":"https://orcid.org/0009-0009-0770-2885","observed_orcids":["https://orcid.org/0009-0009-0770-2885","https://orcid.org/0000-0002-3150-3124","https://orcid.org/0009-0001-8707-1471"]},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenhao Ma","raw_affiliation_strings":["School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036091413","display_name":"\u9686\u514b\u5e73 LONG Ke-ping","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Keping Long","raw_affiliation_strings":["School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China","institution_ids":["https://openalex.org/I92403157"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2270,"currency":"USD","value_usd":2270},"apc_paid":{"value":2270,"currency":"USD","value_usd":2270},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.68682103,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":"21","first_page":"40296","last_page":"40296"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9541000127792358,"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":0.9541000127792358,"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/T10767","display_name":"Advanced Photonic Communication Systems","score":0.011599999852478504,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.006599999964237213,"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/sigma-delta-modulator","display_name":"sigma-delta modulator","score":0.8009999990463257},{"id":"https://openalex.org/keywords/physical-layer-security","display_name":"physical layer security","score":0.7870000004768372},{"id":"https://openalex.org/keywords/radio-over-fiber","display_name":"radio-over-fiber","score":0.9399999976158142},{"id":"https://openalex.org/keywords/discrete-multitone-modulation","display_name":"discrete multitone modulation","score":0.6570000052452087},{"id":"https://openalex.org/keywords/logistic-map","display_name":"logistic map","score":0.5740000009536743},{"id":"https://openalex.org/keywords/lorenz-system","display_name":"Lorenz system","score":0.9070000052452087},{"id":"https://openalex.org/keywords/chaotic-sequence-generation","display_name":"chaotic sequence generation","score":0.7020000219345093},{"id":"https://openalex.org/keywords/key-space","display_name":"key space","score":0.6439999938011169},{"id":"https://openalex.org/keywords/intensity-modulation-direct-detection","display_name":"intensity modulation and direct detection","score":0.8830000162124634},{"id":"https://openalex.org/keywords/mobile-fronthaul","display_name":"mobile fronthaul","score":0.7549999952316284}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.617900013923645},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.5871000289916992},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5611000061035156},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.5534999966621399},{"id":"https://openalex.org/C123079801","wikidata":"https://www.wikidata.org/wiki/Q750240","display_name":"Modulation (music)","level":2,"score":0.5376999974250793},{"id":"https://openalex.org/C2779814227","wikidata":"https://www.wikidata.org/wiki/Q7444882","display_name":"Secure transmission","level":3,"score":0.505299985408783},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4738999903202057},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.41519999504089355},{"id":"https://openalex.org/C96834759","wikidata":"https://www.wikidata.org/wiki/Q750463","display_name":"Phase modulation","level":3,"score":0.3874000012874603},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.38359999656677246},{"id":"https://openalex.org/C110558960","wikidata":"https://www.wikidata.org/wiki/Q163461","display_name":"Delta modulation","level":5,"score":0.3546000123023987},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.34540000557899475},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3409999907016754},{"id":"https://openalex.org/C197000039","wikidata":"https://www.wikidata.org/wiki/Q2027432","display_name":"Free-space optical communication","level":3,"score":0.33629998564720154},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3321000039577484},{"id":"https://openalex.org/C129404179","wikidata":"https://www.wikidata.org/wiki/Q1469765","display_name":"Optical communication","level":2,"score":0.3310999870300293},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.3174999952316284},{"id":"https://openalex.org/C68754193","wikidata":"https://www.wikidata.org/wiki/Q1184820","display_name":"Delta-sigma modulation","level":3,"score":0.2989000082015991},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.28870001435279846},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.27950000762939453},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26499998569488525},{"id":"https://openalex.org/C557945733","wikidata":"https://www.wikidata.org/wiki/Q389772","display_name":"Data transmission","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C55020928","wikidata":"https://www.wikidata.org/wiki/Q3813865","display_name":"Image quality","level":3,"score":0.2630000114440918},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.25780001282691956},{"id":"https://openalex.org/C160724564","wikidata":"https://www.wikidata.org/wiki/Q1620670","display_name":"Wavelength-division multiplexing","level":3,"score":0.2526000142097473}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1364/oe.615359","doi":"https://doi.org/10.1364/oe.615359","is_oa":true,"landing_page_url":"https://doi.org/10.1364/oe.615359","pdf_url":null,"source":{"id":"https://openalex.org/S178776955","display_name":"Optics Express","issn_l":"1094-4087","issn":["1094-4087"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-b","jufo-1","ki-jl-1","medline","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315679","host_organization_name":"Optica Publishing Group","host_organization_lineage":["https://openalex.org/P4310315679"],"host_organization_lineage_names":["Optica Publishing Group"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optics Express","raw_type":"journal-article"},{"id":"pmid:42963705","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42963705","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,"listed_in":[],"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":"Optics express","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1364/oe.615359","doi":"https://doi.org/10.1364/oe.615359","is_oa":true,"landing_page_url":"https://doi.org/10.1364/oe.615359","pdf_url":null,"source":{"id":"https://openalex.org/S178776955","display_name":"Optics Express","issn_l":"1094-4087","issn":["1094-4087"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-b","jufo-1","ki-jl-1","medline","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315679","host_organization_name":"Optica Publishing Group","host_organization_lineage":["https://openalex.org/P4310315679"],"host_organization_lineage_names":["Optica Publishing Group"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optics Express","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.5378999710083008}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W2582619980","https://openalex.org/W3096173566","https://openalex.org/W3120522579","https://openalex.org/W3209087856","https://openalex.org/W4210331759","https://openalex.org/W4220689519","https://openalex.org/W4293824953","https://openalex.org/W4294690638","https://openalex.org/W4296523907","https://openalex.org/W4322764085","https://openalex.org/W4323038202","https://openalex.org/W4327947324","https://openalex.org/W4363677144","https://openalex.org/W4367041870","https://openalex.org/W4380930454","https://openalex.org/W4385277689","https://openalex.org/W4387092581","https://openalex.org/W4388740270","https://openalex.org/W4390659164","https://openalex.org/W4396509089","https://openalex.org/W4396858259","https://openalex.org/W4398768008","https://openalex.org/W4399391065","https://openalex.org/W4400467966","https://openalex.org/W4405506969","https://openalex.org/W4409723631","https://openalex.org/W4411586388"],"related_works":["https://openalex.org/W4396858259","https://openalex.org/W3165526662","https://openalex.org/W4313417902","https://openalex.org/W2915225815","https://openalex.org/W4398768008","https://openalex.org/W4404126514","https://openalex.org/W3083430050","https://openalex.org/W4406265815","https://openalex.org/W3135447086","https://openalex.org/W7143488877"],"abstract_inverted_index":{"Radio":[0],"over":[1,151],"fiber":[2,157],"(RoF)":[3],"links":[4],"support":[5],"high-capacity":[6],"transmission":[7,134,251],"for":[8,53],"next":[9],"generation":[10,65],"mobile":[11],"fronthaul":[12],"but":[13],"remain":[14],"vulnerable":[15],"to":[16,70,105,118,201,238],"security":[17,32,248],"threats.":[18],"For":[19],"RoF":[20],"systems":[21],"operating":[22],"at":[23,148,214],"high":[24],"data":[25],"rates,":[26],"physical-layer":[27,247],"encryption":[28,51],"should":[29],"provide":[30],"enhanced":[31,246],"without":[33],"imposing":[34],"substantial":[35],"processing":[36],"overhead":[37],"on":[38],"the":[39,76,90,106,191,202,215,228,240],"signal":[40,147],"path.":[41],"This":[42,87],"paper":[43],"proposes":[44],"and":[45,78,128,188,211,236],"experimentally":[46,159],"validates":[47],"a":[48,67,124,129,136,232],"hierarchical":[49],"chaotic":[50,62,85],"scheme":[52],"delta":[54],"sigma":[55],"modulation":[56,142,164],"(DSM)":[57],"systems.":[58],"The":[59,174],"proposed":[60,117],"rule-constructed":[61],"sequence":[63,69],"(RCCS)":[64],"uses":[66],"logistic":[68],"dynamically":[71],"select":[72],"state":[73],"variables":[74],"from":[75],"Lorenz":[77],"Halvorsen":[79],"systems,":[80],"thereby":[81],"generating":[82],"three":[83,102],"composite":[84],"outputs.":[86],"design":[88],"expands":[89],"effective":[91,178],"key":[92,97,179],"space":[93,180],"through":[94],"multiple":[95],"secret":[96],"parameters":[98],"while":[99],"applying":[100],"only":[101],"perturbation":[103],"sequences":[104],"transmitted":[107,241],"signal.":[108],"A":[109],"Chaotic":[110],"Sorting":[111],"Stride":[112],"Permutation":[113],"(CSSP)":[114],"algorithm":[115],"is":[116,158],"enhance":[119],"permutation":[120],"variability":[121],"by":[122],"introducing":[123],"dynamic":[125],"starting":[126],"position":[127],"cyclic":[130],"access":[131],"stride.":[132],"Secure":[133],"of":[135,154,181,208],"3":[137],"GHz":[138],"65536-ary":[139],"quadrature":[140],"amplitude":[141],"(65536-QAM)":[143],"discrete":[144],"multitone":[145],"(DMT)":[146],"42.2":[149],"Gb/s":[150],"2":[152,223],"km":[153,224],"standard":[155],"single-mode":[156],"demonstrated":[160],"using":[161],"an":[162,177],"intensity":[163],"direct":[165],"detection":[166],"system":[167],"with":[168,205,249],"two":[169],"cascaded":[170],"fourth-order":[171],"1-bit":[172],"DSMs.":[173],"RCCS":[175],"provides":[176],"approximately":[182,209],"10":[183],"208":[184],".":[185],"At":[186],"50":[187],"60":[189],"Gbaud,":[190],"authorized":[192],"receiver":[193,206,230],"shows":[194],"bit":[195],"error":[196],"rata":[197],"(BER)":[198],"performance":[199],"comparable":[200],"unencrypted":[203],"system,":[204],"sensitivities":[207],"\u22125.0":[210],"\u22124.6":[212],"dBm":[213],"7%":[216],"hard-decision":[217],"forward-error":[218],"correction":[219],"(HD-FEC)":[220],"threshold":[221],"after":[222],"transmission.":[225],"In":[226],"contrast,":[227],"unauthorized":[229],"maintains":[231],"BER":[233],"near":[234],"0.5":[235],"fails":[237],"recover":[239],"information.":[242],"These":[243],"results":[244],"demonstrate":[245],"negligible":[250],"penalty.":[252]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-09T00:00:00"}
