{"id":"https://openalex.org/W2019816098","doi":"https://doi.org/10.1090/s0025-5718-1978-0491431-9","title":"Monte Carlo Methods for Index Computation (mod p)","display_name":"Monte Carlo Methods for Index Computation (mod p)","publication_year":1978,"publication_date":"1978-01-01","ids":{"openalex":"https://openalex.org/W2019816098","doi":"https://doi.org/10.1090/s0025-5718-1978-0491431-9","mag":"2019816098"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-1978-0491431-9","doi":"https://doi.org/10.1090/s0025-5718-1978-0491431-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-1978-0491431-9","pdf_url":"https://www.ams.org/mcom/1978-32-143/S0025-5718-1978-0491431-9/S0025-5718-1978-0491431-9.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,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1","vabb-shw"],"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"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1978-32-143/S0025-5718-1978-0491431-9/S0025-5718-1978-0491431-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053916023","display_name":"John M. Pollard","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J. M. Pollard","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5053916023"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7528,"has_fulltext":true,"cited_by_count":950,"citation_normalized_percentile":{"value":0.8984375,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"32","issue":"143","first_page":"918","last_page":"918"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9901999831199646,"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"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9901999831199646,"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"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.003800000064074993,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T13806","display_name":"Mathematical and Computational Methods","score":0.0017000000225380063,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discrete-logarithm-problem","display_name":"discrete logarithm problem","score":0.7879999876022339},{"id":"https://openalex.org/keywords/index-computation","display_name":"index computation","score":0.7670000195503235},{"id":"https://openalex.org/keywords/primitive-roots","display_name":"primitive roots","score":0.7689999938011169},{"id":"https://openalex.org/keywords/prime-modulus","display_name":"prime modulus","score":0.5920000076293945},{"id":"https://openalex.org/keywords/randomized-algorithms","display_name":"randomized algorithms","score":0.652999997138977},{"id":"https://openalex.org/keywords/integer-factorization","display_name":"integer factorization","score":0.871999979019165},{"id":"https://openalex.org/keywords/monte-carlo-methods","display_name":"Monte Carlo methods","score":0.42800000309944153}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6386398673057556},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.42743033170700073},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39958444237709045}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-1978-0491431-9","doi":"https://doi.org/10.1090/s0025-5718-1978-0491431-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-1978-0491431-9","pdf_url":"https://www.ams.org/mcom/1978-32-143/S0025-5718-1978-0491431-9/S0025-5718-1978-0491431-9.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,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1","vabb-shw"],"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":"doi:10.2307/2006496","doi":"https://doi.org/10.2307/2006496","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2006496","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,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1","vabb-shw"],"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/s0025-5718-1978-0491431-9","doi":"https://doi.org/10.1090/s0025-5718-1978-0491431-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-1978-0491431-9","pdf_url":"https://www.ams.org/mcom/1978-32-143/S0025-5718-1978-0491431-9/S0025-5718-1978-0491431-9.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,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1","vabb-shw"],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2019816098.pdf","grobid_xml":"https://content.openalex.org/works/W2019816098.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1600795850","https://openalex.org/W1970252670","https://openalex.org/W1970822433","https://openalex.org/W1981663184","https://openalex.org/W1988524997","https://openalex.org/W2039338757","https://openalex.org/W2071593615","https://openalex.org/W2084121711","https://openalex.org/W2088579593","https://openalex.org/W2145964906","https://openalex.org/W2156186849","https://openalex.org/W2752853835","https://openalex.org/W3157578321","https://openalex.org/W3198160809","https://openalex.org/W4232859834"],"related_works":["https://openalex.org/W7154171003","https://openalex.org/W4231105226","https://openalex.org/W6903728742","https://openalex.org/W2189328230","https://openalex.org/W6941490406","https://openalex.org/W7095461833","https://openalex.org/W2395799309","https://openalex.org/W2082284119","https://openalex.org/W30528624","https://openalex.org/W2402076812"],"abstract_inverted_index":{"We":[0],"describe":[1],"some":[2],"novel":[3],"methods":[4],"to":[5,13,63],"compute":[6],"the":[7,26,59,103],"index":[8,60],"of":[9,18,28,53,83,93,100,105],"any":[10],"integer":[11],"relative":[12],"a":[14,19,51,66],"given":[15],"primitive":[16],"root":[17],"prime":[20],"p.":[21],"Our":[22,43],"first":[23],"method":[24,52],"avoids":[25],"use":[27],"stored":[29],"tables":[30],"and":[31],"apparently":[32],"requires":[33,70],"O":[34,71],"(":[35,72],"p":[36],"1":[37,74],"/":[38,75],"2":[39,76],")":[40,77],"O(p^{1/2})":[41],"operations.":[42],"second":[44],"algorithm,":[45],"which":[46],"may":[47],"be":[48],"regarded":[49],"as":[50],"catching":[54],"kangaroos,":[55],"is":[56,61],"applicable":[57],"when":[58],"known":[62],"lie":[64],"in":[65],"certain":[67],"interval;":[68],"it":[69],"w":[73,85],"O(w^{1/2})":[78],"operations":[79],"for":[80],"an":[81],"interval":[82],"width":[84],",":[86],"but":[87],"does":[88],"not":[89],"have":[90],"complete":[91],"certainty":[92],"success.":[94],"It":[95],"has":[96],"several":[97],"possible":[98],"areas":[99],"application,":[101],"including":[102],"factorization":[104],"integers.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":14},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":18},{"year":2022,"cited_by_count":21},{"year":2021,"cited_by_count":39},{"year":2020,"cited_by_count":39},{"year":2019,"cited_by_count":33},{"year":2018,"cited_by_count":42},{"year":2017,"cited_by_count":34},{"year":2016,"cited_by_count":40},{"year":2015,"cited_by_count":34},{"year":2014,"cited_by_count":51},{"year":2013,"cited_by_count":37},{"year":2012,"cited_by_count":57}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2016-06-24T00:00:00"}