{"id":"https://openalex.org/W2035415571","doi":"https://doi.org/10.1090/s0025-5718-00-01200-x","title":"\u201cChinese &amp; Match\u201d, an alternative to Atkin\u2019s \u201cMatch and Sort\u201d method used in the SEA algorithm","display_name":"\u201cChinese &amp; Match\u201d, an alternative to Atkin\u2019s \u201cMatch and Sort\u201d method used in the SEA algorithm","publication_year":2000,"publication_date":"2000-03-02","ids":{"openalex":"https://openalex.org/W2035415571","doi":"https://doi.org/10.1090/s0025-5718-00-01200-x","mag":"2035415571"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-00-01200-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01200-x","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01200-X/S0025-5718-00-01200-X.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/2001-70-234/S0025-5718-00-01200-X/S0025-5718-00-01200-X.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009219098","display_name":"Antoine Joux","orcid":"https://orcid.org/0000-0003-2682-6508"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Antoine Joux","raw_affiliation_strings":["SCSSI, 18 rue du Dr. Zamenhoff, F-92131 Issy-les-Moulineaux, France"],"affiliations":[{"raw_affiliation_string":"SCSSI, 18 rue du Dr. Zamenhoff, F-92131 Issy-les-Moulineaux, France","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108684067","display_name":"Reynald Lercier","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Reynald Lercier","raw_affiliation_strings":["CELAR, Route de Laill\u00c3\u00a9, F-35998 Rennes Arm\u00c3\u00a9es, France","CELAR, Route de Laill\u00e9, F-35998 Rennes Arm\u00e9es, France"],"affiliations":[{"raw_affiliation_string":"CELAR, Route de Laill\u00c3\u00a9, F-35998 Rennes Arm\u00c3\u00a9es, France","institution_ids":[]},{"raw_affiliation_string":"CELAR, Route de Laill\u00e9, F-35998 Rennes Arm\u00e9es, France","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5009219098"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.6264,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.9517183,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"70","issue":"234","first_page":"827","last_page":"836"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9890000224113464,"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":0.9890000224113464,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9837999939918518,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9593999981880188,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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":0.8707013726234436},{"id":"https://openalex.org/keywords/sort","display_name":"sort","score":0.7336568832397461},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4194122552871704},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.34331637620925903}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8707013726234436},{"id":"https://openalex.org/C88548561","wikidata":"https://www.wikidata.org/wiki/Q347599","display_name":"sort","level":2,"score":0.7336568832397461},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4194122552871704},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.34331637620925903}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-00-01200-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01200-x","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01200-X/S0025-5718-00-01200-X.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:HAL:hal-01102024v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01102024","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation, 2001, 70 (234), pp.827-836. &#x27E8;10.1090/S0025-5718-00-01200-X&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-00-01200-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01200-x","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01200-X/S0025-5718-00-01200-X.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":[{"score":0.8700000047683716,"display_name":"Life below water","id":"https://metadata.un.org/sdg/14"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2035415571.pdf","grobid_xml":"https://content.openalex.org/works/W2035415571.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W178569154","https://openalex.org/W1579382575","https://openalex.org/W1803405874","https://openalex.org/W2035381368","https://openalex.org/W2037816851","https://openalex.org/W2039500763","https://openalex.org/W2067361453","https://openalex.org/W2075252632","https://openalex.org/W2146323046","https://openalex.org/W2996504715","https://openalex.org/W4242424230"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2361805396","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"A":[0],"classical":[1],"way":[2,43],"to":[3,34,44,110,116,153,161,221],"compute":[4],"the":[5,46,100,118,127,138,163,217,224],"number":[6,47,164],"of":[7,9,48,113,126,134,156,165,167],"points":[8,49,166],"elliptic":[10,95,120,169],"curves":[11],"defined":[12,171],"over":[13,172],"finite":[14],"fields":[15],"from":[16],"partial":[17,101],"data":[18],"obtained":[19],"in":[20,123],"SEA":[21,128],"(Schoof":[22],"Elkies":[23],"Atkin)":[24],"algorithm":[25,133,225],"is":[26,38,106,141,216,226],"a":[27,39],"so-called":[28],"\u201cMatch":[29],"and":[30],"Sort\u201d":[31],"method":[32,37,146],"due":[33],"Atkin.":[35],"This":[36,130],"\u201cbaby":[40],"step/giant":[41],"step\u201d":[42],"find":[45],"among":[50],"<inline-formula":[51,66,173],"content-type=\"math/mathml\">":[52,67,174],"<mml:math":[53,68,175],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[54,69,176],"alttext=\"upper":[55,70],"C\">":[56],"<mml:semantics>":[57,78,185],"<mml:mi>C</mml:mi>":[58,84],"<mml:annotation":[59,89,203],"encoding=\"application/x-tex\">C</mml:annotation>":[60],"</mml:semantics>":[61,92,206],"</mml:math>":[62,93,207],"</inline-formula>":[63,94,208],"candidates":[64],"with":[65],"O":[71],"left-parenthesis":[72],"StartRoot":[73],"upper":[74,178],"C":[75],"EndRoot":[76],"right-parenthesis\">":[77],"<mml:mrow>":[79],"<mml:mi>O</mml:mi>":[80],"<mml:mo":[81,86],"stretchy=\"false\">(</mml:mo>":[82],"<mml:msqrt>":[83],"</mml:msqrt>":[85],"stretchy=\"false\">)</mml:mo>":[87],"</mml:mrow>":[88,191,199,201],"encoding=\"application/x-tex\">O(\\sqrt":[90],"{C})</mml:annotation>":[91],"curve":[96,121,170],"additions.":[97],"Observing":[98],"that":[99],"information":[102],"modulo":[103],"Atkin\u2019s":[104,145,157],"primes":[105],"redundant,":[107],"we":[108,213],"propose":[109],"take":[111],"advantage":[112],"this":[114,124,215],"redundancy":[115],"eliminate":[117],"usual":[119],"algebra":[122],"phase":[125],"computation.":[129],"yields":[131],"an":[132,154,168],"similar":[135],"complexity,":[136],"but":[137],"space":[139],"needed":[140],"smaller":[142],"than":[143],"what":[144],"requires.":[147],"In":[148],"practice,":[149],"our":[150],"technique":[151],"amounts":[152],"acceleration":[155],"method,":[158],"allowing":[159],"us":[160],"count":[162],"alttext=\"double-struck":[177],"F":[179],"Subscript":[180],"2":[181],"Sub":[182],"Superscript":[183],"1663\">":[184],"<mml:msub>":[186],"<mml:mrow":[187,192,196],"class=\"MJX-TeXAtom-ORD\">":[188,193,197],"<mml:mi":[189],"mathvariant=\"double-struck\">F</mml:mi>":[190],"<mml:msup>":[194],"<mml:mn>2</mml:mn>":[195],"<mml:mn>1663</mml:mn>":[198],"</mml:msup>":[200],"</mml:msub>":[202],"encoding=\"application/x-tex\">\\mathbb":[204],"{F}_{2^{1663}}</mml:annotation>":[205],".":[209],"As":[210],"far":[211],"as":[212],"know,":[214],"largest":[218],"point-counting":[219],"computation":[220],"date.":[222],"Furthermore,":[223],"easily":[227],"parallelized.":[228]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2016-06-24T00:00:00"}
