{"id":"https://openalex.org/W2164284862","doi":"https://doi.org/10.1137/0213053","title":"How to Generate Cryptographically Strong Sequences of Pseudorandom Bits","display_name":"How to Generate Cryptographically Strong Sequences of Pseudorandom Bits","publication_year":1984,"publication_date":"1984-11-01","ids":{"openalex":"https://openalex.org/W2164284862","doi":"https://doi.org/10.1137/0213053","mag":"2164284862"},"language":"en","primary_location":{"id":"doi:10.1137/0213053","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0213053","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5102766796","display_name":"Manuel Blum","orcid":"https://orcid.org/0000-0002-0982-4845"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Manuel Blum","raw_affiliation_strings":["University of California\u2013Berkeley"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California\u2013Berkeley","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030198184","display_name":"Silvio Micali","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Silvio Micali","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, Ma#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, Ma#TAB#","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102766796"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":25.1818,"has_fulltext":false,"cited_by_count":1331,"citation_normalized_percentile":{"value":0.99733066,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"13","issue":"4","first_page":"850","last_page":"864"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9991999864578247,"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":0.9991999864578247,"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/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discrete-logarithm","display_name":"Discrete logarithm","score":0.717739462852478},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6775869131088257},{"id":"https://openalex.org/keywords/pseudorandom-number-generator","display_name":"Pseudorandom number generator","score":0.6490192413330078},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5780465006828308},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5761314630508423},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5691626667976379},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5241366028785706},{"id":"https://openalex.org/keywords/random-number-generation","display_name":"Random number generation","score":0.5147888660430908},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5128600597381592},{"id":"https://openalex.org/keywords/pseudorandom-generator","display_name":"Pseudorandom generator","score":0.5125324726104736},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4834917187690735},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.46757227182388306},{"id":"https://openalex.org/keywords/pseudorandomness","display_name":"Pseudorandomness","score":0.46046754717826843},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4549413025379181},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.44534578919410706},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.44375061988830566},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.4161486327648163},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3758375644683838},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.13727587461471558},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.08412915468215942}],"concepts":[{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.717739462852478},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6775869131088257},{"id":"https://openalex.org/C140642157","wikidata":"https://www.wikidata.org/wiki/Q1623338","display_name":"Pseudorandom number generator","level":2,"score":0.6490192413330078},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5780465006828308},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5761314630508423},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5691626667976379},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5241366028785706},{"id":"https://openalex.org/C201866948","wikidata":"https://www.wikidata.org/wiki/Q228206","display_name":"Random number generation","level":2,"score":0.5147888660430908},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5128600597381592},{"id":"https://openalex.org/C92913381","wikidata":"https://www.wikidata.org/wiki/Q7255474","display_name":"Pseudorandom generator","level":3,"score":0.5125324726104736},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4834917187690735},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.46757227182388306},{"id":"https://openalex.org/C19086982","wikidata":"https://www.wikidata.org/wiki/Q2115856","display_name":"Pseudorandomness","level":3,"score":0.46046754717826843},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4549413025379181},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44534578919410706},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.44375061988830566},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.4161486327648163},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3758375644683838},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.13727587461471558},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.08412915468215942},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0213053","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0213053","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1480319329","https://openalex.org/W1519919954","https://openalex.org/W1964053266","https://openalex.org/W1973452640","https://openalex.org/W1981455414","https://openalex.org/W2012857639","https://openalex.org/W2013455832","https://openalex.org/W2027466944","https://openalex.org/W2075488055","https://openalex.org/W2118755837","https://openalex.org/W2128531813","https://openalex.org/W2138109426","https://openalex.org/W2169377825","https://openalex.org/W2329849663","https://openalex.org/W2401610261","https://openalex.org/W3150645827","https://openalex.org/W4210300416","https://openalex.org/W4232836212"],"related_works":["https://openalex.org/W4241950541","https://openalex.org/W2077146536","https://openalex.org/W44435986","https://openalex.org/W2161451071","https://openalex.org/W2062045810","https://openalex.org/W2988803943","https://openalex.org/W1503711153","https://openalex.org/W3111658143","https://openalex.org/W2025294130","https://openalex.org/W2772380824"],"abstract_inverted_index":{"We":[0,43],"give":[1,44],"a":[2,19,30,36,52,114],"set":[3],"of":[4,39,47],"conditions":[5],"that":[6,28],"allow":[7],"one":[8],"to":[9,75],"generate":[10],"50\u201350":[11,70],"unpredictable":[12,40],"bits.Based":[13],"on":[14],"those":[15],"conditions,":[16],"we":[17],"present":[18],"general":[20],"algorithmic":[21],"scheme":[22,49],"for":[23,56,61,80],"constructing":[24],"polynomial-time":[25,102],"deterministic":[26],"algorithms":[27],"stretch":[29],"short":[31],"secret":[32],"random":[33],"input":[34],"into":[35],"long":[37],"sequence":[38],"pseudo-random":[41,53],"bits.":[42],"an":[45,76],"implementation":[46],"our":[48],"and":[50],"exhibit":[51],"bit":[54,66,109],"generator":[55],"which":[57],"any":[58],"efficient":[59],"strategy":[60],"predicting":[62],"the":[63,82,89,106],"next":[64,107],"output":[65,108],"with":[67],"better":[68,110],"than":[69,111],"chance":[71],"is":[72],"easily":[73],"transformable":[74],"\u201cequally":[77],"efficient\u201d":[78],"algorithm":[79,103],"solving":[81],"discrete":[83,90],"logarithm":[84,91],"problem.":[85],"In":[86],"particular:":[87],"if":[88,116,120],"problem":[92],"cannot":[93],"be":[94],"solved":[95],"in":[96],"probabilistic":[97,101],"polynomial":[98],"time,":[99],"no":[100],"can":[104],"guess":[105,118,122],"by":[112],"flipping":[113],"coin:":[115],"\u201chead\u201d":[117],"\u201c0\u201d,":[119],"\u201ctail\u201d":[121],"\u201c1\u201d":[123]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":15},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":30},{"year":2022,"cited_by_count":32},{"year":2021,"cited_by_count":34},{"year":2020,"cited_by_count":23},{"year":2019,"cited_by_count":18},{"year":2018,"cited_by_count":22},{"year":2017,"cited_by_count":32},{"year":2016,"cited_by_count":24},{"year":2015,"cited_by_count":37},{"year":2014,"cited_by_count":43},{"year":2013,"cited_by_count":41},{"year":2012,"cited_by_count":43}],"updated_date":"2026-05-20T08:49:12.498775","created_date":"2025-10-10T00:00:00"}