{"id":"https://openalex.org/W3151245374","doi":"https://doi.org/10.1109/date.2008.4484856","title":"On Analysis and Synthesis of (n,k)-Non-Linear Feedback Shift Registers","display_name":"On Analysis and Synthesis of (n,k)-Non-Linear Feedback Shift Registers","publication_year":2008,"publication_date":"2008-03-01","ids":{"openalex":"https://openalex.org/W3151245374","doi":"https://doi.org/10.1109/date.2008.4484856","mag":"3151245374"},"language":"en","primary_location":{"id":"doi:10.1109/date.2008.4484856","is_oa":false,"landing_page_url":"https://doi.org/10.1109/date.2008.4484856","pdf_url":null,"source":{"id":"https://openalex.org/S4363607582","display_name":"2008 Design, Automation and Test in Europe","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 Design, Automation and Test in Europe","raw_type":"proceedings-article"},"type":"conference-paper","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/A5011438358","display_name":"Elena Dubrova","orcid":"https://orcid.org/0000-0001-7382-9408"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Elena Dubrova","raw_affiliation_strings":["Royal Institute of Technology, Kista, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Royal Institute of Technology, Kista, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058899830","display_name":"Maxim Teslenko","orcid":null},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Maxim Teslenko","raw_affiliation_strings":["Royal Institute of Technology, Kista, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Royal Institute of Technology, Kista, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003371230","display_name":"Hannu Tenhunen","orcid":"https://orcid.org/0000-0003-1959-6513"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Hannu Tenhunen","raw_affiliation_strings":["Royal Institute of Technology, Kista, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Royal Institute of Technology, Kista, Sweden","institution_ids":["https://openalex.org/I86987016"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I86987016"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1286","last_page":"1291"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9948999881744385,"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":0.9948999881744385,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9872999787330627,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10904","display_name":"Embedded Systems Design Techniques","score":0.9804999828338623,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/shift-register","display_name":"Shift register","score":0.5807496309280396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5359421968460083},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3267212510108948},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22807002067565918},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.15954384207725525}],"concepts":[{"id":"https://openalex.org/C49654631","wikidata":"https://www.wikidata.org/wiki/Q746165","display_name":"Shift register","level":3,"score":0.5807496309280396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5359421968460083},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3267212510108948},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22807002067565918},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.15954384207725525},{"id":"https://openalex.org/C165005293","wikidata":"https://www.wikidata.org/wiki/Q1074500","display_name":"Chip","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/date.2008.4484856","is_oa":false,"landing_page_url":"https://doi.org/10.1109/date.2008.4484856","pdf_url":null,"source":{"id":"https://openalex.org/S4363607582","display_name":"2008 Design, Automation and Test in Europe","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 Design, Automation and Test in Europe","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.605.8382","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.605.8382","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.date-conference.com/archive/conference/proceedings/PAPERS/2008/DATE08/PDFFILES/10.4_3.PDF","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W29630963","https://openalex.org/W197055099","https://openalex.org/W1531434127","https://openalex.org/W1572199847","https://openalex.org/W1585247305","https://openalex.org/W1590556184","https://openalex.org/W1602113401","https://openalex.org/W1755066991","https://openalex.org/W1814068099","https://openalex.org/W1974292899","https://openalex.org/W1979198062","https://openalex.org/W1980699137","https://openalex.org/W2002667370","https://openalex.org/W2031260081","https://openalex.org/W2041749201","https://openalex.org/W2043565230","https://openalex.org/W2061438988","https://openalex.org/W2070645901","https://openalex.org/W2071705091","https://openalex.org/W2076397729","https://openalex.org/W2080267935","https://openalex.org/W2099120582","https://openalex.org/W2107285942","https://openalex.org/W2146438343","https://openalex.org/W2152060707","https://openalex.org/W2407796027","https://openalex.org/W2520093650","https://openalex.org/W4230586716","https://openalex.org/W4285754033","https://openalex.org/W4394925238","https://openalex.org/W6601228211","https://openalex.org/W6635223447","https://openalex.org/W6636107910","https://openalex.org/W6637613954","https://openalex.org/W6638466892","https://openalex.org/W6713930467"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W1979635423","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W4250137176","https://openalex.org/W2494420798"],"abstract_inverted_index":{"Non-linear":[0],"feedback":[1,46],"shift":[2],"registers":[3],"(NLFSRs)":[4],"have":[5],"been":[6],"proposed":[7],"as":[8],"an":[9,43,169,191,212],"alternative":[10,118],"to":[11,68,86,175,205],"Linear":[12],"Feedback":[13],"Shift":[14],"Registers":[15],"(LFSRs)":[16],"for":[17,21,73,103,214,229],"generating":[18,141],"pseudo-random":[19],"sequences":[20,143],"stream":[22,104],"ciphers.":[23],"In":[24,42],"this":[25,75,207,240],"paper,":[26],"we":[27,134,159,186],"introduce":[28],"(n,k)-NLFSRs":[29,113,223],"which":[30,148,224],"can":[31,47,61],"be":[32,48,62,115,150],"considered":[33],"a":[34,116,126],"generalization":[35],"of":[36,40,52,66,98,128,130,140,156,164,168,178,182,190,218,220,222,233],"the":[37,45,53,57,96,108,120,153,162,165,176,179,188,216,231,236],"Galois":[38,81],"type":[39,76,155],"LFSR.":[41],"(n,fc)-NLFSR,":[44],"taken":[49],"from":[50,194],"any":[51,63],"n":[54],"bits,":[55],"and":[56,202,235],"next":[58,89],"state":[59,90],"functions":[60],"Boolean":[64],"function":[65,91],"up":[67],"k":[69],"variables.":[70],"Our":[71],"motivation":[72],"considering":[74],"NLFSRs":[77,197],"is":[78,111,171],"that":[79,136,161],"their":[80],"configuration":[82],"makes":[83],"it":[84],"possible":[85],"compute":[87,187],"each":[88],"in":[92],"parallel,":[93],"thus":[94],"increasing":[95],"speed":[97,110],"output":[99,142,166],"sequence":[100,167],"generation.":[101],"Thus,":[102],"cipher":[105],"application":[106],"where":[107],"encryption":[109],"important,":[112],"may":[114],"better":[117],"than":[119],"traditional":[121],"Fibonacci":[122,154],"ones.":[123],"We":[124,209],"derive":[125],"number":[127],"properties":[129,147],"(n,k)-":[131],"NLFSRs.":[132,157],"First,":[133],"demonstrate":[135],"they":[137],"are":[138,200],"capable":[139],"with":[144],"good":[145],"statistical":[146],"cannot":[149],"generated":[151],"by":[152],"Second,":[158],"show":[160,203],"period":[163,189],"(n,k)-NLFSR":[170,192],"not":[172],"necessarily":[173],"equal":[174],"length":[177,217],"largest":[180],"cycle":[181],"its":[183],"states.":[184],"Third,":[185],"constructed":[193],"several":[195],"parallel":[196],"whose":[198],"outputs":[199],"XOR-ed":[201],"how":[204],"maximize":[206],"period.":[208],"also":[210],"present":[211],"algorithm":[213],"estimating":[215],"cycles":[219],"states":[221,234],"uses":[225],"binary":[226],"decision":[227],"diagrams":[228],"representing":[230],"set":[232],"transition":[237],"relation":[238],"on":[239],"set.":[241]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}