{"id":"https://openalex.org/W2799090284","doi":"https://doi.org/10.1090/mcom/3400","title":"Full orbit sequences in affine spaces via fractional jumps and pseudorandom number generation","display_name":"Full orbit sequences in affine spaces via fractional jumps and pseudorandom number generation","publication_year":2018,"publication_date":"2018-09-19","ids":{"openalex":"https://openalex.org/W2799090284","doi":"https://doi.org/10.1090/mcom/3400","mag":"2799090284"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3400","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3400","pdf_url":"https://www.ams.org/mcom/2019-88-318/S0025-5718-2018-03400-7/S0025-5718-2018-03400-7.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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2019-88-318/S0025-5718-2018-03400-7/S0025-5718-2018-03400-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047033089","display_name":"Federico Amadio Guidi","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Federico Amadio Guidi","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045700576","display_name":"Sofia Lindqvist","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Sofia Lindqvist","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050777736","display_name":"Giacomo Micheli","orcid":"https://orcid.org/0000-0002-5265-5207"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Giacomo Micheli","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":0.6552,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.7607522,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"88","issue":"318","first_page":"2005","last_page":"2025"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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/T11130","display_name":"Coding theory and cryptography","score":1.0,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9994999766349792,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/mathematics","display_name":"Mathematics","score":0.8823211789131165},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.7205551266670227},{"id":"https://openalex.org/keywords/pseudorandom-number-generator","display_name":"Pseudorandom number generator","score":0.7170521020889282},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.6720879077911377},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.5758149027824402},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5667450428009033},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.4646880626678467},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.43896064162254333},{"id":"https://openalex.org/keywords/pseudorandomness","display_name":"Pseudorandomness","score":0.43624627590179443},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.429604172706604},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39852988719940186},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37190890312194824},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1811402440071106}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8823211789131165},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7205551266670227},{"id":"https://openalex.org/C140642157","wikidata":"https://www.wikidata.org/wiki/Q1623338","display_name":"Pseudorandom number generator","level":2,"score":0.7170521020889282},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6720879077911377},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.5758149027824402},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5667450428009033},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.4646880626678467},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.43896064162254333},{"id":"https://openalex.org/C19086982","wikidata":"https://www.wikidata.org/wiki/Q2115856","display_name":"Pseudorandomness","level":3,"score":0.43624627590179443},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.429604172706604},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39852988719940186},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37190890312194824},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1811402440071106},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/mcom/3400","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3400","pdf_url":"https://www.ams.org/mcom/2019-88-318/S0025-5718-2018-03400-7/S0025-5718-2018-03400-7.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"},{"id":"pmh:oai:arXiv.org:1712.05258","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.05258","pdf_url":"https://arxiv.org/pdf/1712.05258","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:03524a20-dcb9-48d0-9489-c0a42ed17b3f","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:03524a20-dcb9-48d0-9489-c0a42ed17b3f","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal article"}],"best_oa_location":{"id":"doi:10.1090/mcom/3400","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3400","pdf_url":"https://www.ams.org/mcom/2019-88-318/S0025-5718-2018-03400-7/S0025-5718-2018-03400-7.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":[{"id":"https://openalex.org/G6015831203","display_name":"Regular Sets of Irreducible Polynomials, Applications of a Local to Global Principle for densities, and Cryptography","funder_award_id":"171248","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W645185567","https://openalex.org/W1537173196","https://openalex.org/W1553513225","https://openalex.org/W1572998330","https://openalex.org/W1583935850","https://openalex.org/W1593383640","https://openalex.org/W1596737217","https://openalex.org/W1660562555","https://openalex.org/W1767246049","https://openalex.org/W1970305556","https://openalex.org/W1978880981","https://openalex.org/W2017322818","https://openalex.org/W2045715929","https://openalex.org/W2062393041","https://openalex.org/W2070084604","https://openalex.org/W2081041650","https://openalex.org/W2083368929","https://openalex.org/W2109911086","https://openalex.org/W2111419092","https://openalex.org/W2124831681","https://openalex.org/W2145044310","https://openalex.org/W2163751669","https://openalex.org/W2285866452","https://openalex.org/W2338939684","https://openalex.org/W2581802073","https://openalex.org/W2582794761","https://openalex.org/W3099946464","https://openalex.org/W4212933304","https://openalex.org/W4232960897","https://openalex.org/W4233144126","https://openalex.org/W4239691897","https://openalex.org/W4245312627","https://openalex.org/W4289126832"],"related_works":["https://openalex.org/W2082419723","https://openalex.org/W3203585077","https://openalex.org/W2176553175","https://openalex.org/W4241950541","https://openalex.org/W2185337847","https://openalex.org/W2143898630","https://openalex.org/W1994207320","https://openalex.org/W3087294829","https://openalex.org/W2343905204","https://openalex.org/W2077146536"],"abstract_inverted_index":{"Let":[0],"<inline-formula":[1,33,52,84],"content-type=\"math/mathml\">":[2,34,53,85],"<mml:math":[3,35,54,86],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[4,36,55,87],"alttext=\"n\">":[5,37],"<mml:semantics>":[6,38,59,91],"<mml:mi>n</mml:mi>":[7,39,61,93],"<mml:annotation":[8,40,65,97],"encoding=\"application/x-tex\">n</mml:annotation>":[9,41],"</mml:semantics>":[10,42,67,99],"</mml:math>":[11,43,68,100],"</inline-formula>":[12,44,69,101],"be":[13],"a":[14,22,48],"positive":[15],"integer.":[16],"In":[17,81],"this":[18],"paper":[19],"we":[20,102,119],"provide":[21],"general":[23],"theory":[24],"to":[25,113],"produce":[26],"full":[27],"orbit":[28],"sequences":[29,106],"in":[30],"the":[31,73,76,105,124,129,133],"affine":[32],"-dimensional":[45],"space":[46],"over":[47],"finite":[49],"field.":[50],"For":[51],"alttext=\"n":[56,88],"equals":[57],"1\">":[58,90],"<mml:mrow>":[60,92],"<mml:mo>=</mml:mo>":[62],"<mml:mn>1</mml:mn>":[63,95],"</mml:mrow>":[64,96],"encoding=\"application/x-tex\">n=1</mml:annotation>":[66],"our":[70,109],"construction":[71,110],"covers":[72],"case":[74],"of":[75],"Inversive":[77],"Congruential":[78],"Generators":[79],"(ICG).":[80],"addition,":[82],"for":[83],"greater-than":[89],"<mml:mo>&gt;</mml:mo>":[94],"encoding=\"application/x-tex\">n&gt;1</mml:annotation>":[98],"show":[103],"that":[104,121],"produced":[107],"using":[108,132],"are":[111],"easier":[112],"compute":[114],"than":[115],"ICG":[116],"sequences.":[117],"Furthermore,":[118],"prove":[120],"they":[122],"have":[123],"same":[125],"discrepancy":[126],"bounds":[127],"as":[128],"ones":[130],"constructed":[131],"ICG.":[134]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2018-05-07T00:00:00"}
