{"id":"https://openalex.org/W4283806904","doi":"https://doi.org/10.1145/3476446.3536191","title":"Random Primes without Primality Testing","display_name":"Random Primes without Primality Testing","publication_year":2022,"publication_date":"2022-07-04","ids":{"openalex":"https://openalex.org/W4283806904","doi":"https://doi.org/10.1145/3476446.3536191"},"language":"en","primary_location":{"id":"doi:10.1145/3476446.3536191","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3476446.3536191","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal-lirmm.ccsd.cnrs.fr/lirmm-03784821","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064771365","display_name":"Pascal Giorgi","orcid":"https://orcid.org/0000-0002-0489-5134"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]},{"id":"https://openalex.org/I4210101743","display_name":"Laboratoire d'Informatique, de Robotique et de Micro\u00e9lectronique de Montpellier","ror":"https://ror.org/013yean28","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I151295451","https://openalex.org/I19894307","https://openalex.org/I4210101743","https://openalex.org/I4210159245","https://openalex.org/I4405261681"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pascal Giorgi","raw_affiliation_strings":["LIRMM, Univ. Montpellier, CNRS, Montpellier, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIRMM, Univ. Montpellier, CNRS, Montpellier, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I19894307","https://openalex.org/I4210101743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003590565","display_name":"Bruno Grenet","orcid":"https://orcid.org/0000-0003-2057-5429"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]},{"id":"https://openalex.org/I4210101743","display_name":"Laboratoire d'Informatique, de Robotique et de Micro\u00e9lectronique de Montpellier","ror":"https://ror.org/013yean28","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I151295451","https://openalex.org/I19894307","https://openalex.org/I4210101743","https://openalex.org/I4210159245","https://openalex.org/I4405261681"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bruno Grenet","raw_affiliation_strings":["LIRMM, Univ. Montpellier, CNRS, Montpellier, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIRMM, Univ. Montpellier, CNRS, Montpellier, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I19894307","https://openalex.org/I4210101743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030554891","display_name":"Armelle Perret du Cray","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]},{"id":"https://openalex.org/I4210101743","display_name":"Laboratoire d'Informatique, de Robotique et de Micro\u00e9lectronique de Montpellier","ror":"https://ror.org/013yean28","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I151295451","https://openalex.org/I19894307","https://openalex.org/I4210101743","https://openalex.org/I4210159245","https://openalex.org/I4405261681"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Armelle Perret du Cray","raw_affiliation_strings":["LIRMM, Univ. Montpellier, CNRS, Montpellier, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIRMM, Univ. Montpellier, CNRS, Montpellier, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I19894307","https://openalex.org/I4210101743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029873080","display_name":"Daniel S. Roche","orcid":"https://orcid.org/0000-0003-1408-6872"},"institutions":[{"id":"https://openalex.org/I189158971","display_name":"United States Naval Academy","ror":"https://ror.org/00znex860","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I189158971","https://openalex.org/I3130687028"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel S. Roche","raw_affiliation_strings":["United States Naval Academy, Annapolis, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"United States Naval Academy, Annapolis, MD, USA","institution_ids":["https://openalex.org/I189158971"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05348689,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"207","last_page":"215"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9998999834060669,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9998999834060669,"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":0.9991999864578247,"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"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","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/primality-test","display_name":"Primality test","score":0.9488481283187866},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.757810652256012},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.593106746673584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5738276839256287},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5259609222412109},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5250644087791443},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.482133150100708},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4442231059074402},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.41457316279411316},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.41102084517478943},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33565765619277954},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3111267387866974},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.30145263671875},{"id":"https://openalex.org/keywords/prime-number","display_name":"Prime number","score":0.2693648338317871}],"concepts":[{"id":"https://openalex.org/C191421660","wikidata":"https://www.wikidata.org/wiki/Q829546","display_name":"Primality test","level":3,"score":0.9488481283187866},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.757810652256012},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.593106746673584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5738276839256287},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5259609222412109},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5250644087791443},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.482133150100708},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4442231059074402},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.41457316279411316},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.41102084517478943},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33565765619277954},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3111267387866974},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30145263671875},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.2693648338317871},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3476446.3536191","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3476446.3536191","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:lirmm-03784821v1","is_oa":true,"landing_page_url":"https://hal-lirmm.ccsd.cnrs.fr/lirmm-03784821","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.issac-conference.org/2022/","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:HAL:lirmm-03784821v1","is_oa":true,"landing_page_url":"https://hal-lirmm.ccsd.cnrs.fr/lirmm-03784821","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.issac-conference.org/2022/","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W174479171","https://openalex.org/W1491152510","https://openalex.org/W1550016006","https://openalex.org/W1583935850","https://openalex.org/W1603189944","https://openalex.org/W1943663571","https://openalex.org/W1965254799","https://openalex.org/W1969466615","https://openalex.org/W1972418517","https://openalex.org/W1974321539","https://openalex.org/W1990451653","https://openalex.org/W2001224529","https://openalex.org/W2015324383","https://openalex.org/W2015497178","https://openalex.org/W2025977722","https://openalex.org/W2028186291","https://openalex.org/W2052965490","https://openalex.org/W2065660785","https://openalex.org/W2070279173","https://openalex.org/W2071593615","https://openalex.org/W2072251416","https://openalex.org/W2074053034","https://openalex.org/W2102350230","https://openalex.org/W2113600343","https://openalex.org/W2126318803","https://openalex.org/W2136567612","https://openalex.org/W2143563649","https://openalex.org/W2143788002","https://openalex.org/W2613840146","https://openalex.org/W2796546714","https://openalex.org/W2959557165","https://openalex.org/W3199833776","https://openalex.org/W4205630623","https://openalex.org/W6629297887","https://openalex.org/W6648506750","https://openalex.org/W6737668500","https://openalex.org/W6802203628"],"related_works":["https://openalex.org/W1992663735","https://openalex.org/W1526986912","https://openalex.org/W1546940811","https://openalex.org/W1985217658","https://openalex.org/W2043667326","https://openalex.org/W2068149596","https://openalex.org/W3135351507","https://openalex.org/W4234010763","https://openalex.org/W4313227037","https://openalex.org/W4307416302"],"abstract_inverted_index":{"Numerous":[0],"algorithms":[1],"call":[2],"for":[3,121],"computation":[4,82],"over":[5,127],"the":[6,16,26,54,76,80,95,113],"integers":[7],"modulo":[8,83,123],"a":[9,21,32,40,84,128],"randomly-chosen":[10,41,85],"large":[11],"prime.":[12,86],"In":[13],"some":[14],"cases,":[15],"quasi-cubic":[17],"complexity":[18],"of":[19,35,98],"selecting":[20],"random":[22,124],"prime":[23],"can":[24,48,118],"dominate":[25],"total":[27],"running":[28],"time.":[29,108],"We":[30,109],"propose":[31,47],"new":[33],"variant":[34],"dynamic":[36],"evaluation,":[37],"applied":[38],"to":[39,50,93],"(composite)":[42],"integer.":[43],"The":[44,61],"transformation":[45,116],"we":[46,90],"apply":[49],"any":[51,66],"algorithm":[52,64],"in":[53,101,106],"algebraic":[55],"RAM":[56],"model,":[57],"even":[58],"allowing":[59],"randomization.":[60],"resulting":[62],"transformed":[63],"avoids":[65],"primality":[67],"tests":[68],"and":[69],"will,":[70],"with":[71],"constant":[72],"positive":[73],"probability,":[74],"have":[75],"same":[77,114],"result":[78],"as":[79],"original":[81],"As":[87],"an":[88,102],"application,":[89],"demonstrate":[91],"how":[92,112],"compute":[94],"exact":[96],"number":[97],"nonzero":[99],"terms":[100],"unknown":[103],"integer":[104],"polynomial":[105],"quasi-linear":[107],"also":[110],"show":[111],"algorithmic":[115],"technique":[117],"be":[119],"used":[120],"computing":[122],"irreducible":[125],"polynomials":[126],"finite":[129],"field.":[130]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}