{"id":"https://openalex.org/W3126257419","doi":"https://doi.org/10.1145/3503536","title":"Kummer versus Montgomery Face-off over Prime Order Fields","display_name":"Kummer versus Montgomery Face-off over Prime Order Fields","publication_year":2022,"publication_date":"2022-02-11","ids":{"openalex":"https://openalex.org/W3126257419","doi":"https://doi.org/10.1145/3503536","mag":"3126257419"},"language":"en","primary_location":{"id":"doi:10.1145/3503536","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3503536","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038622157","display_name":"Kaushik Nath","orcid":"https://orcid.org/0000-0002-8159-4589"},"institutions":[{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Kaushik Nath","raw_affiliation_strings":["Indian Statistical Institute, Kolkata, West Bengal, India"],"raw_orcid":"https://orcid.org/0000-0002-8159-4589","affiliations":[{"raw_affiliation_string":"Indian Statistical Institute, Kolkata, West Bengal, India","institution_ids":["https://openalex.org/I6498739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036784831","display_name":"Palash Sarkar","orcid":"https://orcid.org/0000-0002-5346-2650"},"institutions":[{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Palash Sarkar","raw_affiliation_strings":["Indian Statistical Institute, Kolkata, West Bengal, India"],"raw_orcid":"https://orcid.org/0000-0002-5346-2650","affiliations":[{"raw_affiliation_string":"Indian Statistical Institute, Kolkata, West Bengal, India","institution_ids":["https://openalex.org/I6498739"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I6498739"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.001923,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"48","issue":"2","first_page":"1","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9896000027656555,"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":0.9896000027656555,"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":0.9675999879837036,"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"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9420999884605408,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.7027267217636108},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6047543287277222},{"id":"https://openalex.org/keywords/face","display_name":"Face (sociological concept)","score":0.5940709114074707},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46938011050224304},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4135648012161255},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40493112802505493},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2753763198852539},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.1267162561416626},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.052331507205963135},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.045510828495025635},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.0408555269241333}],"concepts":[{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.7027267217636108},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6047543287277222},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.5940709114074707},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46938011050224304},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4135648012161255},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40493112802505493},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2753763198852539},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.1267162561416626},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.052331507205963135},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.045510828495025635},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0408555269241333}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3503536","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3503536","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},{"id":"mag:3126257419","is_oa":false,"landing_page_url":"https://eprint.iacr.org/2021/019.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2764847869","display_name":"IACR Cryptology ePrint Archive","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4322614454"],"host_organization_lineage_names":["Cryptology ePrint Archive"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IACR Cryptology ePrint Archive","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1910751411","https://openalex.org/W1971605365","https://openalex.org/W2003736153","https://openalex.org/W2008876968","https://openalex.org/W2021358506","https://openalex.org/W2036378739","https://openalex.org/W2037107113","https://openalex.org/W2062454016","https://openalex.org/W2083550283","https://openalex.org/W2134258244","https://openalex.org/W2156186849","https://openalex.org/W2402976487","https://openalex.org/W2594174595","https://openalex.org/W2612824548","https://openalex.org/W2779269605","https://openalex.org/W2794919770","https://openalex.org/W2913570393","https://openalex.org/W2950388795","https://openalex.org/W2966682887","https://openalex.org/W3018417022","https://openalex.org/W3093596850","https://openalex.org/W3155622575","https://openalex.org/W4243791792","https://openalex.org/W6696286977","https://openalex.org/W6713761476","https://openalex.org/W6770866196","https://openalex.org/W6776851340","https://openalex.org/W6777197233","https://openalex.org/W6782571401"],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"makes":[2],"a":[3],"comprehensive":[4],"comparison":[5],"of":[6,9,12,31,40,65],"the":[7,23,84],"efficiencies":[8],"vectorized":[10,57],"implementations":[11,39,59],"Kummer":[13,26,43,75],"lines":[14,27,44,76],"and":[15,36,55],"Montgomery":[16,51,81],"curves":[17,52],"at":[18],"various":[19],"security":[20,73],"levels.":[21],"For":[22],"comparison,":[24],"nine":[25,42],"are":[28,34,53,77],"considered,":[29],"out":[30],"which":[32],"eight":[33],"new,":[35],"new":[37,56],"assembly":[38,58],"all":[41,72],"have":[45,60],"been":[46,61],"made.":[47],"Seven":[48],"previously":[49],"proposed":[50],"considered":[54],"made":[62],"for":[63,71],"three":[64],"them.":[66],"Our":[67],"comparisons":[68],"show":[69],"that":[70],"levels,":[74],"consistently":[78],"faster":[79],"than":[80],"curves,":[82],"though":[83],"speed-up":[85],"gap":[86],"is":[87],"not":[88],"much.":[89]},"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
