{"id":"https://openalex.org/W2252149818","doi":"https://doi.org/10.1145/2792978","title":"Substitution-Permutation Networks, Pseudorandom Functions, and Natural Proofs","display_name":"Substitution-Permutation Networks, Pseudorandom Functions, and Natural Proofs","publication_year":2015,"publication_date":"2015-12-10","ids":{"openalex":"https://openalex.org/W2252149818","doi":"https://doi.org/10.1145/2792978","mag":"2252149818"},"language":"en","primary_location":{"id":"doi:10.1145/2792978","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2792978","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/2792978?download=true","source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/2792978?download=true","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025615562","display_name":"Eric Miles","orcid":null},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Eric Miles","raw_affiliation_strings":["Northeastern University, Los Angeles, CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Northeastern University, Los Angeles, CA","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072846764","display_name":"Emanuele Viola","orcid":"https://orcid.org/0000-0001-6091-1824"},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Emanuele Viola","raw_affiliation_strings":["Northeastern University, Boston, MA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Northeastern University, Boston, MA","institution_ids":["https://openalex.org/I12912129"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025615562"],"corresponding_institution_ids":["https://openalex.org/I12912129"],"apc_list":null,"apc_paid":null,"fwci":1.3355,"has_fulltext":true,"cited_by_count":25,"citation_normalized_percentile":{"value":0.86910707,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"62","issue":"6","first_page":"1","last_page":"29"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9997000098228455,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9997000098228455,"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/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"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/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.9987999796867371,"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/pseudorandom-number-generator","display_name":"Pseudorandom number generator","score":0.6679142713546753},{"id":"https://openalex.org/keywords/pseudorandom-generator","display_name":"Pseudorandom generator","score":0.6606961488723755},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.5831815600395203},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.539998471736908},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5296047925949097},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5248808264732361},{"id":"https://openalex.org/keywords/random-permutation","display_name":"Random permutation","score":0.5224734544754028},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5188887715339661},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.48743703961372375},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.47588005661964417},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.42393261194229126},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3559854030609131},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.277873158454895},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10850554704666138}],"concepts":[{"id":"https://openalex.org/C140642157","wikidata":"https://www.wikidata.org/wiki/Q1623338","display_name":"Pseudorandom number generator","level":2,"score":0.6679142713546753},{"id":"https://openalex.org/C92913381","wikidata":"https://www.wikidata.org/wiki/Q7255474","display_name":"Pseudorandom generator","level":3,"score":0.6606961488723755},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.5831815600395203},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.539998471736908},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5296047925949097},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5248808264732361},{"id":"https://openalex.org/C200985842","wikidata":"https://www.wikidata.org/wiki/Q3375503","display_name":"Random permutation","level":3,"score":0.5224734544754028},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5188887715339661},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.48743703961372375},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.47588005661964417},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.42393261194229126},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3559854030609131},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.277873158454895},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10850554704666138},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2792978","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2792978","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/2792978?download=true","source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1145/2792978","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2792978","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/2792978?download=true","source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4343776779","display_name":null,"funder_award_id":"CCF-0845003","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4716970331","display_name":null,"funder_award_id":"CCF-1319206","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5710847777","display_name":null,"funder_award_id":"1319206","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7695462847","display_name":"CAREER: New Pseudorandom Generators: Unconditional Results and Efficient Constructions (TOC)","funder_award_id":"0845003","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2252149818.pdf","grobid_xml":"https://content.openalex.org/works/W2252149818.grobid-xml"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W29269980","https://openalex.org/W103427359","https://openalex.org/W147005573","https://openalex.org/W190530026","https://openalex.org/W605043455","https://openalex.org/W1490590996","https://openalex.org/W1509697755","https://openalex.org/W1528065150","https://openalex.org/W1548880861","https://openalex.org/W1549737830","https://openalex.org/W1556212265","https://openalex.org/W1562183207","https://openalex.org/W1568642505","https://openalex.org/W1572300106","https://openalex.org/W1580062474","https://openalex.org/W1629301835","https://openalex.org/W1964723977","https://openalex.org/W1969341770","https://openalex.org/W1972464518","https://openalex.org/W1984184793","https://openalex.org/W1984477611","https://openalex.org/W1985614194","https://openalex.org/W1988413780","https://openalex.org/W1993138363","https://openalex.org/W1994423049","https://openalex.org/W1995851745","https://openalex.org/W1997228246","https://openalex.org/W1997643965","https://openalex.org/W2006667137","https://openalex.org/W2015880590","https://openalex.org/W2019807548","https://openalex.org/W2024091095","https://openalex.org/W2027528470","https://openalex.org/W2036650989","https://openalex.org/W2037514418","https://openalex.org/W2058838206","https://openalex.org/W2064939672","https://openalex.org/W2067107502","https://openalex.org/W2077300005","https://openalex.org/W2081259981","https://openalex.org/W2105994318","https://openalex.org/W2106793914","https://openalex.org/W2109322425","https://openalex.org/W2109394932","https://openalex.org/W2117362057","https://openalex.org/W2121048498","https://openalex.org/W2124218043","https://openalex.org/W2125591151","https://openalex.org/W2127815364","https://openalex.org/W2147503428","https://openalex.org/W2159268377","https://openalex.org/W2162860799","https://openalex.org/W2163137752","https://openalex.org/W2171959510","https://openalex.org/W2181873030","https://openalex.org/W2234576048","https://openalex.org/W2340787257","https://openalex.org/W2400552030","https://openalex.org/W2405068754","https://openalex.org/W2912080987","https://openalex.org/W3083295155","https://openalex.org/W3117450064"],"related_works":["https://openalex.org/W4242117757","https://openalex.org/W1576065320","https://openalex.org/W3197588836","https://openalex.org/W2015880590","https://openalex.org/W1513039030","https://openalex.org/W2792338823","https://openalex.org/W2553569605","https://openalex.org/W2077146536","https://openalex.org/W1559931973","https://openalex.org/W2913176662"],"abstract_inverted_index":{"This":[0,19],"article":[1],"takes":[2],"a":[3,101,147,195],"new":[4],"step":[5],"towards":[6],"closing":[7],"the":[8,43,67,111,141,199,250,297,305,308],"gap":[9,20,306],"between":[10,307],"pseudorandom":[11],"functions":[12],"(PRF)":[13],"and":[14,35,171,183,230,284,312,323],"their":[15],"popular,":[16],"bounded-input-length":[17],"counterparts.":[18],"is":[21,95,100,137,143,158,194,212,233,262,272],"both":[22],"quantitative,":[23],"because":[24,37],"these":[25,38],"counterparts":[26,39],"are":[27,64,74,83],"more":[28,75],"efficient":[29,76],"than":[30,77],"PRF":[31,60],"in":[32,42,122,150,205,316],"various":[33],"ways,":[34],"methodological,":[36],"usually":[40],"fit":[41],"substitution-permutation":[44],"network":[45],"paradigm":[46],"(SPN),":[47],"which":[48],"has":[49,174],"not":[50],"been":[51],"used":[52],"to":[53],"construct":[54],"PRF.":[55],"We":[56,113,153,207,267],"give":[57],"several":[58],"candidate":[59],"F":[61,87,116,129,156,187,210,238,270],"i":[62],"that":[63,115,120,155,172,209,231,269,285],"inspired":[65],"by":[66,274],"SPN":[68,97,139,200,251],"paradigm.":[69],"Most":[70],"of":[71,110,163,218,249,276,299],"our":[72,300,302],"candidates":[73,82],"previous":[78],"ones.":[79],"Our":[80],"main":[81],"as":[84,108],"follows.":[85],"\u2014":[86,128,186,237],"1":[88,117,221],":":[89,131,189,240],"{0,1}":[90,93,132,135,190,193,241,244],"n":[91,94,133,136,165,170,179,191,220,242,278,283,294],"\u2192":[92,134,192,243],"an":[96,138,246],"whose":[98],"S-box":[99,142,261],"random":[102],"function":[103],"on":[104,198,291],"b":[105],"bits":[106],"given":[107],"part":[109],"seed.":[112],"prove":[114],"resists":[118],"attacks":[119],"run":[121],"time":[123],"\u2264":[124],"2":[125,130,157,177],"\u03f5b":[126],".":[127],"where":[140,202],"(patched)":[144,264],"field":[145,265],"inversion,":[146],"common":[148],"choice":[149],"practical":[151],"constructions.":[152],"show":[154,208,268],"computable":[159,213,273],"with":[160,214],"boolean":[161],"circuits":[162,217,275],"size":[164,219,277],"\u22c5":[166,279],"log":[167,280],"O":[168,281],"(1)":[169,282],"it":[173,232,286],"exponential":[175],"security":[176,298],"\u03a9(":[178],")":[180],"against":[181],"linear":[182],"differential":[184],"cryptanalysis.":[185],"3":[188,211],"nonstandard":[196],"variant":[197],"paradigm,":[201],"\u201cstates\u201d":[203],"grow":[204],"length.":[206],"TC":[215,320],"0":[216,321],"+":[222],"\u03f5":[223,227],",":[224],"for":[225],"any":[226],"&gt;":[228],"0,":[229],"almost":[234],"3-wise":[235],"independent.":[236],"4":[239,271],"uses":[245],"extreme":[247],"setting":[248],"parameters":[252],"(one":[253],"round,":[254],"one":[255],"S-box,":[256],"no":[257],"diffusion":[258],"matrix).":[259],"The":[260],"again":[263],"inversion.":[266],"fools":[287],"all":[288],"parity":[289],"tests":[290],"\u22642":[292],"0.9":[293],"outputs.":[295],"Assuming":[296],"candidates,":[301],"work":[303],"narrows":[304],"Natural":[309],"Proofs":[310],"barrier":[311],"existing":[313],"lower":[314],"bounds":[315],"three":[317],"models:":[318],"circuits,":[319,322],"Turing":[324],"machines.":[325]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
