{"id":"https://openalex.org/W2971922132","doi":"https://doi.org/10.1093/comjnl/bxz057","title":"On Equivalence of Cascade Connections of Two Nonlinear Feedback Shift Registers","display_name":"On Equivalence of Cascade Connections of Two Nonlinear Feedback Shift Registers","publication_year":2019,"publication_date":"2019-05-14","ids":{"openalex":"https://openalex.org/W2971922132","doi":"https://doi.org/10.1093/comjnl/bxz057","mag":"2971922132"},"language":"en","primary_location":{"id":"doi:10.1093/comjnl/bxz057","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comjnl/bxz057","pdf_url":null,"source":{"id":"https://openalex.org/S44643521","display_name":"The Computer Journal","issn_l":"0010-4620","issn":["0010-4620","1460-2067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Computer Journal","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/A5100704772","display_name":"Jianghua Zhong","orcid":"https://orcid.org/0000-0001-5576-6319"},"institutions":[{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jianghua Zhong","raw_affiliation_strings":["State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China","institution_ids":["https://openalex.org/I4210156404","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008820992","display_name":"Dongdai Lin","orcid":"https://orcid.org/0000-0002-3951-7889"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dongdai Lin","raw_affiliation_strings":["State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China","institution_ids":["https://openalex.org/I4210156404","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100704772"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210156404"],"apc_list":{"value":2635,"currency":"GBP","value_usd":3232},"apc_paid":null,"fwci":0.7001,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.78110719,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":97},"biblio":{"volume":"62","issue":"12","first_page":"1793","last_page":"1804"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cascade","display_name":"Cascade","score":0.9405301213264465},{"id":"https://openalex.org/keywords/stream-cipher","display_name":"Stream cipher","score":0.8253682255744934},{"id":"https://openalex.org/keywords/linear-feedback-shift-register","display_name":"Linear feedback shift register","score":0.6948731541633606},{"id":"https://openalex.org/keywords/shift-register","display_name":"Shift register","score":0.6063752770423889},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.6011335849761963},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.533804714679718},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4964173436164856},{"id":"https://openalex.org/keywords/block-cipher","display_name":"Block cipher","score":0.46838289499282837},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4475305676460266},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43577420711517334},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.41295573115348816},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.38007381558418274},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2638068199157715},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.23842117190361023},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2055804431438446},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.08684563636779785},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06298321485519409}],"concepts":[{"id":"https://openalex.org/C34146451","wikidata":"https://www.wikidata.org/wiki/Q5048094","display_name":"Cascade","level":2,"score":0.9405301213264465},{"id":"https://openalex.org/C92950451","wikidata":"https://www.wikidata.org/wiki/Q864718","display_name":"Stream cipher","level":3,"score":0.8253682255744934},{"id":"https://openalex.org/C159862308","wikidata":"https://www.wikidata.org/wiki/Q681101","display_name":"Linear feedback shift register","level":4,"score":0.6948731541633606},{"id":"https://openalex.org/C49654631","wikidata":"https://www.wikidata.org/wiki/Q746165","display_name":"Shift register","level":3,"score":0.6063752770423889},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.6011335849761963},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.533804714679718},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4964173436164856},{"id":"https://openalex.org/C106544461","wikidata":"https://www.wikidata.org/wiki/Q543151","display_name":"Block cipher","level":3,"score":0.46838289499282837},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4475305676460266},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43577420711517334},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.41295573115348816},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.38007381558418274},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2638068199157715},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.23842117190361023},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2055804431438446},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.08684563636779785},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06298321485519409},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C165005293","wikidata":"https://www.wikidata.org/wiki/Q1074500","display_name":"Chip","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/comjnl/bxz057","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comjnl/bxz057","pdf_url":null,"source":{"id":"https://openalex.org/S44643521","display_name":"The Computer Journal","issn_l":"0010-4620","issn":["0010-4620","1460-2067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Computer Journal","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2941796924","display_name":null,"funder_award_id":"61772029","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4117432206","display_name":null,"funder_award_id":"61702124","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5361398898","display_name":null,"funder_award_id":"61872359","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W567151721","https://openalex.org/W1488435683","https://openalex.org/W1827311732","https://openalex.org/W1970441315","https://openalex.org/W1971224531","https://openalex.org/W1979548008","https://openalex.org/W1985351346","https://openalex.org/W2014737124","https://openalex.org/W2041749201","https://openalex.org/W2065417430","https://openalex.org/W2068492922","https://openalex.org/W2068773548","https://openalex.org/W2095701698","https://openalex.org/W2113688179","https://openalex.org/W2120629199","https://openalex.org/W2141060521","https://openalex.org/W2160533336","https://openalex.org/W2260467064","https://openalex.org/W2276318674","https://openalex.org/W2340667721","https://openalex.org/W2402108048","https://openalex.org/W2486512961","https://openalex.org/W2530614786","https://openalex.org/W2572117397","https://openalex.org/W2605279000","https://openalex.org/W2619974965","https://openalex.org/W2757432818","https://openalex.org/W2809398638","https://openalex.org/W2964305055","https://openalex.org/W3080149132","https://openalex.org/W4213193213","https://openalex.org/W4245793730","https://openalex.org/W4256468542","https://openalex.org/W6645314414","https://openalex.org/W6667628523","https://openalex.org/W6713245938","https://openalex.org/W6736505873"],"related_works":["https://openalex.org/W3157572643","https://openalex.org/W2469870931","https://openalex.org/W3028798907","https://openalex.org/W1504687861","https://openalex.org/W2067080229","https://openalex.org/W1979198062","https://openalex.org/W185758473","https://openalex.org/W2364182266","https://openalex.org/W4205746750","https://openalex.org/W2506471491"],"abstract_inverted_index":{"Abstract":[0],"Grain":[1,36,72,186],"is":[2,65,138],"a":[3,13,97],"hardware-oriented":[4],"finalist":[5],"in":[6,34],"the":[7,30,35,68,71,115,120,154,165,180,184,193],"eSTREAM":[8],"Stream":[9],"Cipher":[10],"Project.":[11],"As":[12,174],"particular":[14],"Galois":[15,106],"nonlinear":[16],"feedback":[17,84,155,166],"shift":[18],"register":[19],"(NFSR),":[20],"cascade":[21,60,88,98,127,143,206],"connection":[22,99,128,144],"of":[23,38,51,58,62,70,74,83,90,100,129,145,157,168,177,188,198],"two":[24,63,91,101,204],"NFSRs":[25,42,64,102],"has":[26],"been":[27],"used":[28,192],"as":[29],"main":[31],"building":[32],"block":[33],"family":[37,73,187],"stream":[39,75,189],"ciphers.":[40,76],"Two":[41],"are":[43,54,161,172],"said":[44],"to":[45,67],"be":[46],"equivalent":[47,59,87,105,142,205],"if":[48,112],"their":[49,202,209],"sets":[50],"output":[52],"sequences":[53],"equal.":[55],"Finding":[56],"properties":[57,82],"connections":[61,89],"useful":[66],"design":[69,211],"This":[77],"paper":[78,121,181],"first":[79],"gives":[80],"some":[81],"functions":[85,156,167],"between":[86,201],"NFSRs.":[92],"It":[93],"then":[94],"shows":[95,182],"that":[96,123,183],"and":[103,159,164,170],"its":[104],"NFSR":[107],"have":[108,114,191],"isomorphic":[109],"state":[110],"diagrams":[111],"they":[113],"same":[116],"stage":[117],"number.":[118],"Finally,":[119],"reveals":[122],"for":[124],"any":[125],"given":[126],"an":[130,134,146,150,175],"$m$-stage":[131,147],"NFSR1":[132,158],"into":[133,149],"$n$-stage":[135,151],"NFSR2,":[136],"there":[137],"only":[139],"another":[140],"one":[141],"NFSR3":[148,160],"NFSR4;":[152],"moreover,":[153],"dual":[162],"complementary,":[163],"NFSR2":[169],"NFSR4":[171],"complementary.":[173],"application":[176],"this":[178],"property,":[179],"existing":[185],"ciphers":[190],"ones":[194],"with":[195],"lower":[196],"cost":[197],"hardware":[199],"implementations":[200],"own":[203],"connections,":[207],"confirming":[208],"good":[210],"criteria.":[212]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}