{"id":"https://openalex.org/W1682312847","doi":"https://doi.org/10.1109/tc.1976.1674632","title":"Autocorrelation Peaks in Congruential Pseudorandom Number Generators","display_name":"Autocorrelation Peaks in Congruential Pseudorandom Number Generators","publication_year":1976,"publication_date":"1976-05-01","ids":{"openalex":"https://openalex.org/W1682312847","doi":"https://doi.org/10.1109/tc.1976.1674632","mag":"1682312847"},"language":"en","primary_location":{"id":"doi:10.1109/tc.1976.1674632","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1976.1674632","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"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 Computers","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/A5030467227","display_name":"Neuman","orcid":null},"institutions":[{"id":"https://openalex.org/I1280536761","display_name":"Ames Research Center","ror":"https://ror.org/02acart68","country_code":"US","type":"facility","lineage":["https://openalex.org/I1280536761","https://openalex.org/I4210124779"]},{"id":"https://openalex.org/I4210124779","display_name":"National Aeronautics and Space Administration","ror":"https://ror.org/027ka1x80","country_code":"US","type":"government","lineage":["https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Neuman","raw_affiliation_strings":["Ames Research Center, National Aeronautics and Space Administration","Ames Research Center, NASA, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ames Research Center, National Aeronautics and Space Administration","institution_ids":["https://openalex.org/I1280536761","https://openalex.org/I4210124779"]},{"raw_affiliation_string":"Ames Research Center, NASA, CA, USA","institution_ids":["https://openalex.org/I1280536761"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5097030591","display_name":"Merrick","orcid":null},"institutions":[{"id":"https://openalex.org/I1280536761","display_name":"Ames Research Center","ror":"https://ror.org/02acart68","country_code":"US","type":"facility","lineage":["https://openalex.org/I1280536761","https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Merrick","raw_affiliation_strings":["Ames Research Center, NASA, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ames Research Center, NASA, CA, USA","institution_ids":["https://openalex.org/I1280536761"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7227,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.82985554,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"C-25","issue":"5","first_page":"457","last_page":"460"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9929999709129333,"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":0.9929999709129333,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9812999963760376,"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/pseudorandom-number-generator","display_name":"Pseudorandom number generator","score":0.8965190649032593},{"id":"https://openalex.org/keywords/autocorrelation","display_name":"Autocorrelation","score":0.7437231540679932},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7172051668167114},{"id":"https://openalex.org/keywords/random-number-generation","display_name":"Random number generation","score":0.6675460934638977},{"id":"https://openalex.org/keywords/pseudorandom-generator-theorem","display_name":"Pseudorandom generator theorem","score":0.5978970527648926},{"id":"https://openalex.org/keywords/linear-congruential-generator","display_name":"Linear congruential generator","score":0.5445180535316467},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5400330424308777},{"id":"https://openalex.org/keywords/pseudorandom-generator","display_name":"Pseudorandom generator","score":0.5165532827377319},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49213308095932007},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.47829514741897583},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.47594308853149414},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.46972620487213135},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.4686533808708191},{"id":"https://openalex.org/keywords/pseudorandomness","display_name":"Pseudorandomness","score":0.46234479546546936},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4452272951602936},{"id":"https://openalex.org/keywords/shift-register","display_name":"Shift register","score":0.44300591945648193},{"id":"https://openalex.org/keywords/coprime-integers","display_name":"Coprime integers","score":0.43768996000289917},{"id":"https://openalex.org/keywords/number-theory","display_name":"Number theory","score":0.4369277358055115},{"id":"https://openalex.org/keywords/arithmetic-function","display_name":"Arithmetic function","score":0.426352858543396},{"id":"https://openalex.org/keywords/prime-number","display_name":"Prime number","score":0.4119330644607544},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35257482528686523},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3367360532283783},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2020626664161682},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11588814854621887},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.08396795392036438}],"concepts":[{"id":"https://openalex.org/C140642157","wikidata":"https://www.wikidata.org/wiki/Q1623338","display_name":"Pseudorandom number generator","level":2,"score":0.8965190649032593},{"id":"https://openalex.org/C5297727","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation","level":2,"score":0.7437231540679932},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7172051668167114},{"id":"https://openalex.org/C201866948","wikidata":"https://www.wikidata.org/wiki/Q228206","display_name":"Random number generation","level":2,"score":0.6675460934638977},{"id":"https://openalex.org/C180233235","wikidata":"https://www.wikidata.org/wiki/Q7255475","display_name":"Pseudorandom generator theorem","level":4,"score":0.5978970527648926},{"id":"https://openalex.org/C141890704","wikidata":"https://www.wikidata.org/wiki/Q1190228","display_name":"Linear congruential generator","level":3,"score":0.5445180535316467},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5400330424308777},{"id":"https://openalex.org/C92913381","wikidata":"https://www.wikidata.org/wiki/Q7255474","display_name":"Pseudorandom generator","level":3,"score":0.5165532827377319},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49213308095932007},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.47829514741897583},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.47594308853149414},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.46972620487213135},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.4686533808708191},{"id":"https://openalex.org/C19086982","wikidata":"https://www.wikidata.org/wiki/Q2115856","display_name":"Pseudorandomness","level":3,"score":0.46234479546546936},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4452272951602936},{"id":"https://openalex.org/C49654631","wikidata":"https://www.wikidata.org/wiki/Q746165","display_name":"Shift register","level":3,"score":0.44300591945648193},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.43768996000289917},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.4369277358055115},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.426352858543396},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.4119330644607544},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35257482528686523},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3367360532283783},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2020626664161682},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11588814854621887},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.08396795392036438},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.1976.1674632","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1976.1674632","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"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 Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W834762177","https://openalex.org/W1022390629","https://openalex.org/W1964657429","https://openalex.org/W1969193576","https://openalex.org/W1994881454","https://openalex.org/W2004046270","https://openalex.org/W2014208555","https://openalex.org/W2023171532","https://openalex.org/W2045754196","https://openalex.org/W2065632557","https://openalex.org/W2752853835","https://openalex.org/W2752908210","https://openalex.org/W2801179766"],"related_works":["https://openalex.org/W44435986","https://openalex.org/W2054944103","https://openalex.org/W1994207320","https://openalex.org/W2966058278","https://openalex.org/W2161451071","https://openalex.org/W2033896979","https://openalex.org/W1972193539","https://openalex.org/W2050598895","https://openalex.org/W1516055552","https://openalex.org/W147864474"],"abstract_inverted_index":{"One":[0],"of":[1,5,14,35,44,60,69,75,78,104,137],"the":[2,12,41,51,66,71,79,87,91,98,105],"desirable":[3],"properties":[4],"a":[6,135],"pseudorandom":[7],"number":[8,126],"generator":[9],"is":[10,53,111],"that":[11,32,116],"sequence":[13],"numbers":[15,47],"it":[16,110],"generates":[17],"should":[18],"have":[19],"very":[20],"low":[21],"autocorrelation":[22],"for":[23,27,101,133],"all":[24,102],"shifts":[25,134],"except":[26],"zero":[28],"shift":[29],"and":[30,82,122,128],"those":[31],"are":[33],"multiples":[34],"its":[36],"cycle":[37,84,139],"length.":[38,85],"Due":[39],"to":[40],"simple":[42,67],"methods":[43],"constructing":[45],"random":[46,125],"via":[48],"modulo":[49],"arithmetic,":[50],"ideal":[52],"often":[54],"not":[55],"quite":[56],"fulfilled.":[57],"The":[58],"results":[59],"this":[61,114],"paper":[62,115],"were":[63,89,94],"obtained":[64],"by":[65],"method":[68],"examining":[70],"complete":[72],"correlation":[73,118],"structure":[74],"several":[76],"generators":[77,103,127,132],"same":[80,106],"type":[81],"small":[83],"Once":[86],"regularities":[88],"discovered,":[90],"mathematical":[92],"relationships":[93],"derived":[95],"which":[96],"describe":[97],"regular":[99],"behavior":[100],"class.":[107],"As":[108],"examples,":[109],"shown":[112],"in":[113,120],"high":[117],"exists":[119],"mixed":[121],"multiplicative":[123],"congruential":[124],"prime":[129],"moduli":[130],"Lehmer":[131],"fraction":[136],"their":[138],"lengths.":[140]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
