{"id":"https://openalex.org/W2033024720","doi":"https://doi.org/10.1090/s0025-5718-96-00712-0","title":"The serial test for a nonlinear pseudorandom number generator","display_name":"The serial test for a nonlinear pseudorandom number generator","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2033024720","doi":"https://doi.org/10.1090/s0025-5718-96-00712-0","mag":"2033024720"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-96-00712-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00712-0","pdf_url":"https://www.ams.org/mcom/1996-65-214/S0025-5718-96-00712-0/S0025-5718-96-00712-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1996-65-214/S0025-5718-96-00712-0/S0025-5718-96-00712-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045603336","display_name":"Takashi Kato","orcid":"https://orcid.org/0000-0002-0571-0883"},"institutions":[{"id":"https://openalex.org/I159385669","display_name":"Chiba University","ror":"https://ror.org/01hjzeq58","country_code":"JP","type":"education","lineage":["https://openalex.org/I159385669"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Takashi Kato","raw_affiliation_strings":["Department of Mathematics, Faculty of Education, Chiba University, 1-33 Yayoi-cho, Chiba City, 263 Japan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Education, Chiba University, 1-33 Yayoi-cho, Chiba City, 263 Japan","institution_ids":["https://openalex.org/I159385669"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056605508","display_name":"Li-Ming Wu","orcid":null},"institutions":[{"id":"https://openalex.org/I159385669","display_name":"Chiba University","ror":"https://ror.org/01hjzeq58","country_code":"JP","type":"education","lineage":["https://openalex.org/I159385669"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Li-Ming Wu","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Chiba University, 1-33 Yayoi-cho, Chiba City, 263 Japan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Chiba University, 1-33 Yayoi-cho, Chiba City, 263 Japan","institution_ids":["https://openalex.org/I159385669"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023091838","display_name":"Niro Yanagihara","orcid":null},"institutions":[{"id":"https://openalex.org/I159385669","display_name":"Chiba University","ror":"https://ror.org/01hjzeq58","country_code":"JP","type":"education","lineage":["https://openalex.org/I159385669"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Niro Yanagihara","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Chiba University, 1-33 Yayoi-cho, Chiba City, 263 Japan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Chiba University, 1-33 Yayoi-cho, Chiba City, 263 Japan","institution_ids":["https://openalex.org/I159385669"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045603336"],"corresponding_institution_ids":["https://openalex.org/I159385669"],"apc_list":null,"apc_paid":null,"fwci":0.4984,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.68145544,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"65","issue":"214","first_page":"761","last_page":"769"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5995707511901855},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.333121120929718},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2967730760574341}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5995707511901855},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.333121120929718},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2967730760574341}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-96-00712-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00712-0","pdf_url":"https://www.ams.org/mcom/1996-65-214/S0025-5718-96-00712-0/S0025-5718-96-00712-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-96-00712-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00712-0","pdf_url":"https://www.ams.org/mcom/1996-65-214/S0025-5718-96-00712-0/S0025-5718-96-00712-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2033024720.pdf","grobid_xml":"https://content.openalex.org/works/W2033024720.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W40732046","https://openalex.org/W1981663184","https://openalex.org/W1988036189","https://openalex.org/W1992670706","https://openalex.org/W2040631919","https://openalex.org/W2043419861","https://openalex.org/W2050104580","https://openalex.org/W2057463668","https://openalex.org/W2075488055","https://openalex.org/W2078295382","https://openalex.org/W2111419092","https://openalex.org/W2145044310","https://openalex.org/W2166639781","https://openalex.org/W2752853835","https://openalex.org/W4232960897","https://openalex.org/W4243786541","https://openalex.org/W4244008072","https://openalex.org/W4245312627","https://openalex.org/W4300580367"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2544423928","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2052122378","https://openalex.org/W2989452537","https://openalex.org/W4313731559"],"abstract_inverted_index":{"Let":[0],"<inline-formula":[1,34,101,173,284,364],"content-type=\"math/mathml\">":[2,35,102,174,285,365],"<mml:math":[3,36,103,175,286,366],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[4,37,104,176,287,367],"alttext=\"upper":[5,38,368],"M":[6,42,55,121,205,306,369],"equals":[7,44,299],"2":[8],"Superscript":[9],"w":[10],"Baseline":[11,43,109,115,122,182,189,197,292,298,303],"comma\">":[12,123,307],"<mml:semantics>":[13,60,124,207,308,372],"<mml:mrow>":[14,61,125,208,309],"<mml:mi>M</mml:mi>":[15,66,81,154,262,343],"<mml:mo>=</mml:mo>":[16,69,331],"<mml:msup>":[17],"<mml:mn>2</mml:mn>":[18],"<mml:mrow":[19,64,131,142,152,211,222,232,244,251,315,326,334,339],"class=\"MJX-TeXAtom-ORD\">":[20,65,132,143,153,212,223,233,245,252,316,327,335,340],"<mml:mi>w</mml:mi>":[21],"</mml:mrow>":[22,25,67,90,134,145,155,158,216,235,237,247,259,264,318,329,337,342,345],"</mml:msup>":[23],"<mml:mo>,</mml:mo>":[24,74,76,80,139,157,323,344],"<mml:annotation":[26,91,159,265,346],"encoding=\"application/x-tex\">M":[27],"=":[28,93],"2^{w},</mml:annotation>":[29],"</mml:semantics>":[30,96,165,279,350],"</mml:math>":[31,97,166,280,351],"</inline-formula>":[32,98,167,281,352],"and":[33],"G":[39,118],"Subscript":[40,107,113,119,178,187,195,290,296,301],"upper":[41,54,117,120,204,305],"StartSet":[45],"1":[46,57,181],"comma":[47,49,53,111,294],"3":[48],"period":[50,51,52,362],"minus":[56],"EndSet":[58],"period\">":[59,206],"<mml:msub>":[62,129,140,150,209,224,242,313,324,332],"<mml:mi>G</mml:mi>":[63,151],"</mml:msub>":[68,135,146,156,217,236,248,319,330,338],"<mml:mo":[70,86,126,136,227,310,320],"fence=\"false\"":[71,87,127,137,311,321],"stretchy=\"false\">{</mml:mo>":[72,128,312],"<mml:mn>1</mml:mn>":[73,85,215],"<mml:mn>3</mml:mn>":[75],"<mml:mo>.</mml:mo>":[77,78,79,89,263],"<mml:mo>":[82,147,218],"\u2212":[83],"</mml:mo>":[84,149,220,230],"stretchy=\"false\">}</mml:mo>":[88,138,322],"encoding=\"application/x-tex\">G_{M}":[92],"\\{1,3,...,M-1":[94],"\\}.</mml:annotation>":[95],"A":[99],"sequence":[100,283,355],"alttext=\"left-brace":[105,288],"y":[106,112,185,194,300],"n":[108,114,179,188,196,291,297,302],"right-brace":[110,293],"element-of":[116],"<mml:mi>y</mml:mi>":[130,141,210,226,243,333],"<mml:mi>n</mml:mi>":[133,144,213,234,246,317,328,336],"\u2208":[148],"encoding=\"application/x-tex\">\\{y_{n}":[160],"\\},":[161,348],"y_{n}":[162],"\\in":[163],"G_{M},</mml:annotation>":[164],"is":[168,353],"obtained":[169],"by":[170],"the":[171,360],"formula":[172],"alttext=\"y":[177],"plus":[180,190,192],"identical-to":[183],"a":[184,354],"overbar":[186],"b":[191,271],"c":[193],"normal":[198,200,202],"m":[199],"o":[201],"d":[203],"<mml:mo>+</mml:mo>":[214,238,240],"\u2261":[219],"<mml:mi>a</mml:mi>":[221],"<mml:mover>":[225],"accent=\"false\">":[228],"\u00af":[229],"</mml:mover>":[231],"<mml:mi>b</mml:mi>":[239],"<mml:mi>c</mml:mi>":[241],"<mml:mspace":[249,260],"width=\"thickmathspace\"/>":[250,261],"<mml:mi":[253,255,257],"mathvariant=\"normal\">m</mml:mi>":[254],"mathvariant=\"normal\">o</mml:mi>":[256],"mathvariant=\"normal\">d</mml:mi>":[258],"encoding=\"application/x-tex\">y_{n+1}":[266],"\\equiv":[267],"a{\\overline":[268],"{y}_{n}}":[269],"+":[270,272],"cy_{n}":[273],"\\;":[274,277],"\\mathrm":[275],"{mod}":[276],"M.</mml:annotation>":[278],"The":[282],"x":[289,295],"slash":[304,370],"<mml:mi>x</mml:mi>":[314,325],"<mml:mo>/</mml:mo>":[341],"encoding=\"application/x-tex\">\\{x_{n}":[347],"x_{n}=y_{n}/M,</mml:annotation>":[349],"of":[356,359],"pseudorandom":[357],"numbers":[358],"maximal":[361],"length":[363],"2\">":[371]},"counts_by_year":[],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}