{"id":"https://openalex.org/W2883452956","doi":"https://doi.org/10.1109/tit.2018.2858769","title":"A New Method for Finding Affine Sub-Families of NFSR Sequences","display_name":"A New Method for Finding Affine Sub-Families of NFSR Sequences","publication_year":2018,"publication_date":"2018-07-23","ids":{"openalex":"https://openalex.org/W2883452956","doi":"https://doi.org/10.1109/tit.2018.2858769","mag":"2883452956"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2018.2858769","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2858769","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","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/A5100778292","display_name":"Jiamin Zhang","orcid":"https://orcid.org/0000-0001-5691-5777"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jia-Min Zhang","raw_affiliation_strings":["National Digital Switching System Engineering and Technological Research Center, Zhengzhou, China"],"raw_orcid":"https://orcid.org/0000-0001-5691-5777","affiliations":[{"raw_affiliation_string":"National Digital Switching System Engineering and Technological Research Center, Zhengzhou, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100419125","display_name":"Tian Tian","orcid":"https://orcid.org/0000-0002-6044-9083"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tian Tian","raw_affiliation_strings":["National Digital Switching System Engineering and Technological Research Center, Zhengzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-6044-9083","affiliations":[{"raw_affiliation_string":"National Digital Switching System Engineering and Technological Research Center, Zhengzhou, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101738495","display_name":"Wen\u2010Feng Qi","orcid":"https://orcid.org/0000-0002-3031-4719"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wen-Feng Qi","raw_affiliation_strings":["National Digital Switching System Engineering and Technological Research Center, Zhengzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-3031-4719","affiliations":[{"raw_affiliation_string":"National Digital Switching System Engineering and Technological Research Center, Zhengzhou, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010491864","display_name":"Qun-Xiong Zheng","orcid":"https://orcid.org/0000-0002-6929-1999"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qun-Xiong Zheng","raw_affiliation_strings":["National Digital Switching System Engineering and Technological Research Center, Zhengzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-6929-1999","affiliations":[{"raw_affiliation_string":"National Digital Switching System Engineering and Technological Research Center, Zhengzhou, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1827,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.84347612,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"65","issue":"2","first_page":"1249","last_page":"1257"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9973999857902527,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9933000206947327,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5239399075508118},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38134825229644775},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37713757157325745},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34345805644989014},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33994829654693604},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2583521604537964},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11112990975379944}],"concepts":[{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5239399075508118},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38134825229644775},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37713757157325745},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34345805644989014},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33994829654693604},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2583521604537964},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11112990975379944}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2018.2858769","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2858769","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4137032510","display_name":null,"funder_award_id":"61521003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6704336960","display_name":null,"funder_award_id":"61672533","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G903352529","display_name":null,"funder_award_id":"61402524","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W137846029","https://openalex.org/W1480210121","https://openalex.org/W1573222895","https://openalex.org/W1594652978","https://openalex.org/W1601321736","https://openalex.org/W1827311732","https://openalex.org/W1974298486","https://openalex.org/W1998466624","https://openalex.org/W2001723182","https://openalex.org/W2019882072","https://openalex.org/W2023130409","https://openalex.org/W2041749201","https://openalex.org/W2068323665","https://openalex.org/W2073504630","https://openalex.org/W2090600233","https://openalex.org/W2146453677","https://openalex.org/W2170368342","https://openalex.org/W2263835564","https://openalex.org/W2624893993","https://openalex.org/W2732251371","https://openalex.org/W4234875403"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W4391913857"],"abstract_inverted_index":{"In":[0],"this":[1,241,312],"paper,":[2,313],"a":[3,14,74,84,128,138,194,223,243,264,269,305],"new":[4,265,309],"and":[5,93,167,275],"efficient":[6],"method":[7,266,310],"for":[8,317],"solving":[9],"affine":[10,33,287],"sub-families":[11,248,288],"included":[12],"in":[13,104,176,295,311],"family":[15],"of":[16,77,101,109,125,130,141,170,173,189,196,226,246,289],"nonlinear":[17],"feedback":[18,132],"shift":[19,133],"register":[20,134,293],"(NFSR)":[21],"sequences":[22,135,229],"is":[23,28,35,83,119,127,183,193,222,315],"proposed.":[24],"The":[25],"linear":[26,123,131,187,227,247,270],"case":[27,34],"focused":[29],"on":[30,240],"since":[31,231],"the":[32,99,105,114,142,212,281,290,308],"an":[36,78],"analogy.":[37],"Let":[38,87],"f(x":[39],"<sub":[40,44,48,54,58,62,66,70,95,145,149,159,164,178,200,204,216,257],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[41,45,49,55,59,63,67,71,96,146,150,154,160,165,179,201,205,209,217,258],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">0</sub>":[42,56],",x":[43],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[46,60,64],",...,x":[47,65],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sub>":[50,72],")":[51,192],"=":[52,89,237],"x":[53,152,207],"\u2295f":[57],"(x":[61],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n-1</sub>":[68],")\u2295x":[69],"be":[73,98,250,299],"characteristic":[75,139],"function":[76],"n-stage":[79],"NFSR,":[80],"where":[81,157],"n":[82],"positive":[85],"integer.":[86],"deg(f)":[88],"d":[90,236],">":[91],"1":[92],"f":[94,110,177,191],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">[d]</sub>":[97,180],"summation":[100],"all":[102,171,286],"terms":[103],"algebraic":[106],"normal":[107],"form":[108,143],"whose":[111,272],"degrees":[112],"attain":[113],"maximum":[115],"d.":[116],"First,":[117],"it":[118,232],"proved":[120],"that":[121],"every":[122,186],"sub-family":[124,129,188,271],"G(f)":[126],"generated":[136],"by":[137,252,304],"polynomial":[140,198,253],"\u03a3":[144,199],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">i\u2208S</sub>":[147,202],"c":[148,158,203],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">i</sub>":[151,161,206],"<sup":[153,208],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">i</sup>":[155,210],",":[156],"\u2208":[162],"F":[163,215,256],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[166,218,259],"S":[168],"consists":[169],"subscripts":[172],"variables":[174],"appearing":[175],".":[181,219,260],"That":[182],"to":[184,267],"say,":[185],"G(":[190],"factor":[195],"some":[197],"over":[211,255],"finite":[213],"field":[214],"This":[220],"result":[221],"well":[224],"generalization":[225],"recurring":[228],"theory":[230],"also":[233],"holds":[234],"if":[235],"1.":[238],"Based":[239],"result,":[242],"candidate":[244],"set":[245],"could":[249,298],"obtained":[251],"factorizations":[254],"Second,":[261],"we":[262],"propose":[263],"verify":[268],"memory":[273],"requirement":[274],"time":[276],"complexity":[277],"are":[278],"clearer":[279],"than":[280],"previous":[282,318],"method.":[283],"For":[284],"instance,":[285],"160-bit":[291],"main":[292],"used":[294],"Grain":[296],"v1":[297],"determined":[300],"within":[301],"two":[302],"seconds":[303],"PC":[306],"using":[307],"which":[314],"unobtainable":[316],"algorithms.":[319]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}