{"id":"https://openalex.org/W2073799044","doi":"https://doi.org/10.1090/s0025-5718-01-01343-6","title":"The parallelized Pollard kangaroo method in real quadratic function fields","display_name":"The parallelized Pollard kangaroo method in real quadratic function fields","publication_year":2001,"publication_date":"2001-10-04","ids":{"openalex":"https://openalex.org/W2073799044","doi":"https://doi.org/10.1090/s0025-5718-01-01343-6","mag":"2073799044"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-01-01343-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01343-6","pdf_url":"https://www.ams.org/mcom/2002-71-238/S0025-5718-01-01343-6/S0025-5718-01-01343-6.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/2002-71-238/S0025-5718-01-01343-6/S0025-5718-01-01343-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037077185","display_name":"Andreas Stein","orcid":"https://orcid.org/0000-0003-3829-1467"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Andreas Stein","raw_affiliation_strings":["University of Illinois at Urbana-Champaign, Department of Mathematics, 1409 West Green Street, Urbana, Illinois 61801"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign, Department of Mathematics, 1409 West Green Street, Urbana, Illinois 61801","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003024529","display_name":"Edlyn Teske","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Edlyn Teske","raw_affiliation_strings":["University of Waterloo, Department of Combinatorics and Optimization, Waterloo, Ontario, Canada N2L 3G1"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Department of Combinatorics and Optimization, Waterloo, Ontario, Canada N2L 3G1","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037077185"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":1.4461,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.80284473,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"71","issue":"238","first_page":"793","last_page":"814"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9932000041007996,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9804999828338623,"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/mathematics","display_name":"Mathematics","score":0.703993022441864},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6497811079025269},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.6033764481544495},{"id":"https://openalex.org/keywords/divisor","display_name":"Divisor (algebraic geometry)","score":0.5973970890045166},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5641261339187622},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5205953121185303},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.49241578578948975},{"id":"https://openalex.org/keywords/function-field","display_name":"Function field","score":0.4688255488872528},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.46594297885894775},{"id":"https://openalex.org/keywords/genus","display_name":"Genus","score":0.4448546767234802},{"id":"https://openalex.org/keywords/hyperelliptic-curve-cryptography","display_name":"Hyperelliptic curve cryptography","score":0.4353146553039551},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4125165343284607},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3772027790546417},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3630576431751251},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35794728994369507},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27186277508735657},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2496476173400879},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24703183770179749},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18706899881362915},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0936417281627655},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0737631618976593}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.703993022441864},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6497811079025269},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.6033764481544495},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.5973970890045166},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5641261339187622},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5205953121185303},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.49241578578948975},{"id":"https://openalex.org/C2778795570","wikidata":"https://www.wikidata.org/wiki/Q5508772","display_name":"Function field","level":3,"score":0.4688255488872528},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.46594297885894775},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.4448546767234802},{"id":"https://openalex.org/C166780011","wikidata":"https://www.wikidata.org/wiki/Q3005926","display_name":"Hyperelliptic curve cryptography","level":5,"score":0.4353146553039551},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4125165343284607},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3772027790546417},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3630576431751251},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35794728994369507},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27186277508735657},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2496476173400879},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24703183770179749},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18706899881362915},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0936417281627655},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0737631618976593},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-01-01343-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01343-6","pdf_url":"https://www.ams.org/mcom/2002-71-238/S0025-5718-01-01343-6/S0025-5718-01-01343-6.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:CiteSeerX.psu:10.1.1.43.1336","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.1336","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cacr.math.uwaterloo.ca/techreports/2000/corr2000-35.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-01-01343-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01343-6","pdf_url":"https://www.ams.org/mcom/2002-71-238/S0025-5718-01-01343-6/S0025-5718-01-01343-6.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":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.6100000143051147}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2073799044.pdf","grobid_xml":"https://content.openalex.org/works/W2073799044.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1480802403","https://openalex.org/W1519023517","https://openalex.org/W1557415002","https://openalex.org/W1592804047","https://openalex.org/W1927552788","https://openalex.org/W1966714372","https://openalex.org/W1969338239","https://openalex.org/W1985265065","https://openalex.org/W2008272678","https://openalex.org/W2013383029","https://openalex.org/W2019816098","https://openalex.org/W2026145071","https://openalex.org/W2077958919","https://openalex.org/W2085388238","https://openalex.org/W2129086974","https://openalex.org/W2478014714","https://openalex.org/W3157578321","https://openalex.org/W4237505298","https://openalex.org/W4246140522"],"related_works":["https://openalex.org/W2953090529","https://openalex.org/W4292351556","https://openalex.org/W4387560998","https://openalex.org/W2009378037","https://openalex.org/W1974467211","https://openalex.org/W3174262880","https://openalex.org/W2963565827","https://openalex.org/W4301285278","https://openalex.org/W2580644653","https://openalex.org/W2169941043"],"abstract_inverted_index":{"We":[0,32],"show":[1,19,34],"how":[2,20,35],"to":[3,21,26,36],"use":[4],"the":[5,23,27,39,45,48,55,61],"parallelized":[6],"kangaroo":[7,24],"method":[8,25],"for":[9,74],"computing":[10],"invariants":[11],"in":[12,29,60],"real":[13,62],"quadratic":[14,63],"function":[15,68,81],"fields.":[16,31],"Specifically,":[17],"we":[18,71],"apply":[22],"infrastructure":[28],"these":[30],"also":[33],"speed":[37],"up":[38],"computation":[40],"by":[41,53],"using":[42,54],"heuristics":[43],"on":[44],"distribution":[46],"of":[47,65,79,83],"divisor":[49],"class":[50,77],"number,":[51],"and":[52,76],"relatively":[56],"inexpensive":[57],"baby":[58],"steps":[59],"model":[64],"a":[66],"hyperelliptic":[67,80],"field.":[69],"Furthermore,":[70],"provide":[72],"examples":[73],"regulators":[75],"numbers":[78],"fields":[82],"genus":[84],"<inline-formula":[85],"content-type=\"math/mathml\">":[86],"<mml:math":[87],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[88],"alttext=\"3\">":[89],"<mml:semantics>":[90],"<mml:mn>3</mml:mn>":[91],"<mml:annotation":[92],"encoding=\"application/x-tex\">3</mml:annotation>":[93],"</mml:semantics>":[94],"</mml:math>":[95],"</inline-formula>":[96],"that":[97],"are":[98],"larger":[99],"than":[100],"those":[101],"ever":[102],"reported":[103],"before.":[104]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}