{"id":"https://openalex.org/W1978880981","doi":"https://doi.org/10.1090/s0025-5718-2013-02780-9","title":"Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators","display_name":"Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators","publication_year":2013,"publication_date":"2013-09-30","ids":{"openalex":"https://openalex.org/W1978880981","doi":"https://doi.org/10.1090/s0025-5718-2013-02780-9","mag":"1978880981"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2013-02780-9","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2013-02780-9","pdf_url":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063691894","display_name":"Domingo G\u00f3mez\u2010P\u00e9rez","orcid":"https://orcid.org/0000-0002-5780-2165"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Domingo G\u00f3mez-P\u00e9rez","raw_affiliation_strings":["Department of Mathematics, University of Cantabria, Santander 39005, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Cantabria, Santander 39005, Spain","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008253632","display_name":"Alina Ostafe","orcid":"https://orcid.org/0000-0001-7398-0589"},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Alina Ostafe","raw_affiliation_strings":["Department of Computing, Macquarie University, Sydney NSW 2109, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing, Macquarie University, Sydney NSW 2109, Australia","institution_ids":["https://openalex.org/I99043593"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030033231","display_name":"Igor E. Shparlinski","orcid":"https://orcid.org/0000-0002-5246-9391"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]},{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Igor Shparlinski","raw_affiliation_strings":["Department of Computing, Macquarie University, Sydney NSW 2109, Australia","Department of Pure Mathematics, University of New South Wales, Sydney, \\indent NSW 2052, Australia","Department of Pure Mathematics, University of New South Wales, Sydney, \\\\indent NSW 2052, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing, Macquarie University, Sydney NSW 2109, Australia","institution_ids":["https://openalex.org/I99043593"]},{"raw_affiliation_string":"Department of Pure Mathematics, University of New South Wales, Sydney, \\indent NSW 2052, Australia","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"Department of Pure Mathematics, University of New South Wales, Sydney, \\\\indent NSW 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2868,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.7518407,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"83","issue":"287","first_page":"1535","last_page":"1550"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9962000250816345,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9921000003814697,"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/automorphism","display_name":"Automorphism","score":0.8407677412033081},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8298324346542358},{"id":"https://openalex.org/keywords/pseudorandom-number-generator","display_name":"Pseudorandom number generator","score":0.7999169826507568},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.7724331021308899},{"id":"https://openalex.org/keywords/pseudorandomness","display_name":"Pseudorandomness","score":0.5615864992141724},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5025312900543213},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4690970182418823},{"id":"https://openalex.org/keywords/pseudorandom-generator-theorem","display_name":"Pseudorandom generator theorem","score":0.4632358253002167},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40733569860458374},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38228198885917664},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13816729187965393},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10660618543624878}],"concepts":[{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.8407677412033081},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8298324346542358},{"id":"https://openalex.org/C140642157","wikidata":"https://www.wikidata.org/wiki/Q1623338","display_name":"Pseudorandom number generator","level":2,"score":0.7999169826507568},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.7724331021308899},{"id":"https://openalex.org/C19086982","wikidata":"https://www.wikidata.org/wiki/Q2115856","display_name":"Pseudorandomness","level":3,"score":0.5615864992141724},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5025312900543213},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4690970182418823},{"id":"https://openalex.org/C180233235","wikidata":"https://www.wikidata.org/wiki/Q7255475","display_name":"Pseudorandom generator theorem","level":4,"score":0.4632358253002167},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40733569860458374},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38228198885917664},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13816729187965393},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10660618543624878},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-2013-02780-9","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2013-02780-9","pdf_url":null,"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"},{"id":"pmh:oai:dnet:ucreareposit::068c11856d1d5080455381f44069c8ed","is_oa":false,"landing_page_url":"http://hdl.handle.net/10902/7949","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Mathematics of Computation Volume 83, Issue 287, May 2014, Pages 1535-1550","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W645185567","https://openalex.org/W1537173196","https://openalex.org/W1593383640","https://openalex.org/W1977292688","https://openalex.org/W2013111830","https://openalex.org/W2017331848","https://openalex.org/W2027150476","https://openalex.org/W2037462567","https://openalex.org/W2043419861","https://openalex.org/W2045672930","https://openalex.org/W2064122575","https://openalex.org/W2070084604","https://openalex.org/W2077958720","https://openalex.org/W2131015627","https://openalex.org/W2138552072","https://openalex.org/W2140262981","https://openalex.org/W2150898678","https://openalex.org/W2171816248","https://openalex.org/W2972427581","https://openalex.org/W3037659403","https://openalex.org/W3099946464","https://openalex.org/W3100426004","https://openalex.org/W4212933304","https://openalex.org/W4231089552","https://openalex.org/W4233144126","https://openalex.org/W4239691897","https://openalex.org/W4297952518","https://openalex.org/W4300580367"],"related_works":["https://openalex.org/W4241950541","https://openalex.org/W1994207320","https://openalex.org/W2143898630","https://openalex.org/W44435986","https://openalex.org/W2161451071","https://openalex.org/W2050598895","https://openalex.org/W1968784238","https://openalex.org/W1972193539","https://openalex.org/W1979902210","https://openalex.org/W3170259722"],"abstract_inverted_index":{"We":[0,29],"present":[1],"several":[2,32],"general":[3,41],"results":[4],"that":[5,35],"show":[6],"how":[7],"algebraic":[8],"dynamical":[9],"systems":[10],"with":[11],"a":[12],"slow":[13],"degree":[14],"growth":[15],"and":[16],"also":[17],"rational":[18],"automorphisms":[19],"can":[20],"be":[21],"used":[22],"to":[23],"construct":[24],"stronger":[25],"pseudorandom":[26],"number":[27],"generators.":[28],"then":[30],"give":[31],"concrete":[33],"constructions":[34],"illustrate":[36],"the":[37],"applicability":[38],"of":[39],"these":[40],"results.":[42]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}