{"id":"https://openalex.org/W2048776886","doi":"https://doi.org/10.1109/tit.2012.2214204","title":"A Scalable Method for Constructing Galois NLFSRs With Period $2^n-1$ Using Cross-Join Pairs","display_name":"A Scalable Method for Constructing Galois NLFSRs With Period $2^n-1$ Using Cross-Join Pairs","publication_year":2012,"publication_date":"2012-08-29","ids":{"openalex":"https://openalex.org/W2048776886","doi":"https://doi.org/10.1109/tit.2012.2214204","mag":"2048776886"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2012.2214204","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2214204","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/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":true,"raw_author_name":"Elena Dubrova","raw_affiliation_strings":["Royal Institute of Technology (KTH), Stockholm, Sweden","R. Inst. of Technol. KTH, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Royal Institute of Technology (KTH), Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"R. Inst. of Technol. KTH, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011438358"],"corresponding_institution_ids":["https://openalex.org/I86987016"],"apc_list":null,"apc_paid":null,"fwci":10.8735,"has_fulltext":false,"cited_by_count":66,"citation_normalized_percentile":{"value":0.98305836,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"59","issue":"1","first_page":"703","last_page":"709"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9990000128746033,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/function","display_name":"Function (biology)","score":0.5595800876617432},{"id":"https://openalex.org/keywords/join","display_name":"Join (topology)","score":0.5194777250289917},{"id":"https://openalex.org/keywords/overhead","display_name":"Overhead (engineering)","score":0.5061563849449158},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4996025562286377},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.4877265393733978},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.4737430512905121},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.45638707280158997},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43025678396224976},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4103611707687378},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3723728060722351},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3395904004573822},{"id":"https://openalex.org/keywords/database","display_name":"Database","score":0.1287682056427002},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.11130693554878235}],"concepts":[{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5595800876617432},{"id":"https://openalex.org/C2776124973","wikidata":"https://www.wikidata.org/wiki/Q3183033","display_name":"Join (topology)","level":2,"score":0.5194777250289917},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.5061563849449158},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4996025562286377},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.4877265393733978},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.4737430512905121},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.45638707280158997},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43025678396224976},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4103611707687378},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3723728060722351},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3395904004573822},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.1287682056427002},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.11130693554878235},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2012.2214204","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2214204","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":[],"funders":[{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W197055099","https://openalex.org/W1480210121","https://openalex.org/W1482661747","https://openalex.org/W1519692838","https://openalex.org/W1549665762","https://openalex.org/W1551875162","https://openalex.org/W1569612250","https://openalex.org/W1601090496","https://openalex.org/W1827311732","https://openalex.org/W1880399293","https://openalex.org/W1976395511","https://openalex.org/W2007453203","https://openalex.org/W2009427224","https://openalex.org/W2021003109","https://openalex.org/W2024334686","https://openalex.org/W2035511639","https://openalex.org/W2045874481","https://openalex.org/W2076568250","https://openalex.org/W2128522106","https://openalex.org/W2128920661","https://openalex.org/W2136205168","https://openalex.org/W2141060521","https://openalex.org/W2146438343","https://openalex.org/W2150276672","https://openalex.org/W2592570088","https://openalex.org/W2793140974","https://openalex.org/W2913925549","https://openalex.org/W4234875403","https://openalex.org/W4245551703","https://openalex.org/W4298109338","https://openalex.org/W4394925238","https://openalex.org/W6749795817"],"related_works":["https://openalex.org/W3214148052","https://openalex.org/W2151692181","https://openalex.org/W794462722","https://openalex.org/W2029625042","https://openalex.org/W4248476017","https://openalex.org/W2807741550","https://openalex.org/W2970426051","https://openalex.org/W1525319740","https://openalex.org/W4247864646","https://openalex.org/W1484210779"],"abstract_inverted_index":{"A":[0],"method":[1,96],"for":[2,50,62,121],"constructing":[3],"<i":[4,13,18,123],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[5,14,19,124],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</i>":[6,15,20,125],"-stage":[7,21],"Galois":[8],"NLFSRs":[9],"with":[10],"period":[11],"2":[12],"-1":[16],"from":[17],"maximum":[22],"length":[23],"LFSRs":[24],"is":[25,28,71,119],"presented.":[26],"Nonlinearity":[27],"introduced":[29],"into":[30],"state":[31,65,74],"cycles":[32,75],"by":[33,79],"adding":[34,80],"a":[35,59,81,88,105],"nonlinear":[36],"Boolean":[37],"function":[38,53,86],"to":[39,55,87,110],"the":[40,44,63,84,92,111],"feedback":[41],"polynomial":[42],"of":[43,48,69,83,91],"LFSR.":[45],"Each":[46],"assignment":[47],"variables":[49],"which":[51],"this":[52],"evaluates":[54],"1":[56],"acts":[57],"as":[58],"crossing":[60],"point":[61],"LFSR":[64],"cycle.":[66],"The":[67,94],"effect":[68],"nonlinearity":[70],"cancelled":[72],"and":[73,102],"are":[76],"joined":[77],"back":[78],"copy":[82],"same":[85],"later":[89],"stage":[90],"register.":[93],"presented":[95],"requires":[97],"no":[98],"extra":[99],"time":[100],"steps":[101],"it":[103],"has":[104],"smaller":[106],"area":[107],"overhead":[108],"compared":[109],"previous":[112],"approaches":[113],"based":[114],"on":[115],"cross-join":[116],"pairs.":[117],"It":[118],"feasible":[120],"large":[122],".":[126]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
