{"id":"https://openalex.org/W2242705832","doi":"https://doi.org/10.1137/15m1044333","title":"Universal Security for Randomness Expansion from the Spot-Checking Protocol","display_name":"Universal Security for Randomness Expansion from the Spot-Checking Protocol","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2242705832","doi":"https://doi.org/10.1137/15m1044333","mag":"2242705832"},"language":"en","primary_location":{"id":"doi:10.1137/15m1044333","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1044333","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/A5063535590","display_name":"Carl A. Miller","orcid":"https://orcid.org/0000-0003-1917-1531"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Carl A. Miller","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102846971","display_name":"Yaoyun Shi","orcid":"https://orcid.org/0000-0001-5523-6166"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yaoyun Shi","raw_affiliation_strings":["Electrical Engineering and Computer Science - Computer Science and Engineering"],"affiliations":[{"raw_affiliation_string":"Electrical Engineering and Computer Science - Computer Science and Engineering","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063535590"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.7685,"has_fulltext":false,"cited_by_count":76,"citation_normalized_percentile":{"value":0.97390539,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"46","issue":"4","first_page":"1304","last_page":"1335"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9675999879837036,"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/T13209","display_name":"Cold Fusion and Nuclear Reactions","score":0.9214000105857849,"subfield":{"id":"https://openalex.org/subfields/1906","display_name":"Geochemistry and Petrology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.7288612127304077},{"id":"https://openalex.org/keywords/chsh-inequality","display_name":"CHSH inequality","score":0.6789600253105164},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6311485767364502},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.5298497676849365},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5066981911659241},{"id":"https://openalex.org/keywords/bells-theorem","display_name":"Bell's theorem","score":0.4611871838569641},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4540990889072418},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.43562835454940796},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4126276969909668},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.36651068925857544},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3268083333969116},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.2500329911708832},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.17640650272369385},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.1743103265762329},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08844175934791565}],"concepts":[{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.7288612127304077},{"id":"https://openalex.org/C134265032","wikidata":"https://www.wikidata.org/wiki/Q5011347","display_name":"CHSH inequality","level":5,"score":0.6789600253105164},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6311485767364502},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5298497676849365},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5066981911659241},{"id":"https://openalex.org/C128108043","wikidata":"https://www.wikidata.org/wiki/Q388525","display_name":"Bell's theorem","level":4,"score":0.4611871838569641},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4540990889072418},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.43562835454940796},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4126276969909668},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.36651068925857544},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3268083333969116},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.2500329911708832},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.17640650272369385},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.1743103265762329},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08844175934791565},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1044333","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1044333","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":[{"id":"https://openalex.org/G1787099851","display_name":null,"funder_award_id":"1500095","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2393494789","display_name":null,"funder_award_id":"1526928","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7153975081","display_name":null,"funder_award_id":"1216729","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7365502218","display_name":null,"funder_award_id":"1318070","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1508777461","https://openalex.org/W1709784975","https://openalex.org/W1963961606","https://openalex.org/W1986407511","https://openalex.org/W1988732892","https://openalex.org/W1998250432","https://openalex.org/W2006774017","https://openalex.org/W2028815089","https://openalex.org/W2055611553","https://openalex.org/W2058302064","https://openalex.org/W2071339916","https://openalex.org/W2076199628","https://openalex.org/W2082730452","https://openalex.org/W2090418561","https://openalex.org/W2093413746","https://openalex.org/W2093419514","https://openalex.org/W2122166994","https://openalex.org/W2135830616","https://openalex.org/W2144277460","https://openalex.org/W2168792807","https://openalex.org/W2174298480","https://openalex.org/W2337218539","https://openalex.org/W2476679387","https://openalex.org/W2535210057","https://openalex.org/W2762179548","https://openalex.org/W3098060566","https://openalex.org/W3098081881","https://openalex.org/W3103744872"],"related_works":["https://openalex.org/W2553524804","https://openalex.org/W2344277531","https://openalex.org/W2610185052","https://openalex.org/W2031983165","https://openalex.org/W3098290704","https://openalex.org/W961946770","https://openalex.org/W3139385865","https://openalex.org/W2950649891","https://openalex.org/W1985083346","https://openalex.org/W2548857530"],"abstract_inverted_index":{"Colbeck":[0],"[Ph.D.":[1],"thesis,":[2],"2006]":[3],"proposed":[4],"using":[5],"Bell":[6,33,58,117],"inequality":[7,59,155],"violations":[8,60],"to":[9,27,39,64,109],"generate":[10],"certified":[11],"random":[12],"numbers.":[13],"While":[14],"full":[15,66,86],"quantum-security":[16],"proofs":[17],"have":[18],"been":[19],"given,":[20],"it":[21],"remains":[22],"a":[23,92,140],"major":[24],"open":[25],"problem":[26],"identify":[28],"the":[29,48,72,81,121,137,145,152],"broadest":[30],"class":[31,50],"of":[32,51,95,136,156],"inequalities":[34,118],"and":[35,98,105,119,159],"lowest":[36],"performance":[37],"requirements":[38],"achieve":[40,65],"such":[41],"security.":[42,67],"In":[43],"this":[44,108],"paper,":[45],"working":[46],"within":[47],"broad":[49],"spot-checking":[52],"protocols,":[53],"we":[54,106],"prove":[55],"exactly":[56],"which":[57,148],"can":[61],"be":[62],"used":[63,83],"Our":[68],"result":[69],"greatly":[70],"improves":[71],"known":[73,90],"noise":[74,93],"tolerance":[75,94],"for":[76,80,125,144],"secure":[77],"randomness":[78,126],"expansion:":[79],"commonly":[82],"CHSH":[84],"game,":[85],"security":[87,123],"was":[88],"only":[89],"with":[91],"1.5%":[96],"[Miller":[97],"Shi,":[99],"J.":[100],"ACM,":[101],"63":[102],"(2016),":[103],"33],":[104],"improve":[107],"10.3%.":[110],"We":[111],"also":[112],"generalize":[113],"our":[114],"results":[115],"beyond":[116],"give":[120],"first":[122],"proof":[124],"expansion":[127],"based":[128,150],"on":[129,151],"Kochen--Specker":[130],"inequalities.":[131],"The":[132],"central":[133],"technical":[134],"contribution":[135],"paper":[138],"is":[139,149],"new":[141],"uncertainty":[142],"principle":[143],"Schatten":[146],"norm,":[147],"uniform":[153],"convexity":[154],"Ball,":[157],"Carlen,":[158],"Lieb":[160],"[Invent.":[161],"Math.,":[162],"115":[163],"(1994),":[164],"pp.":[165],"463--482].":[166]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}