{"id":"https://openalex.org/W2114535050","doi":"https://doi.org/10.1515/jmc.2010.007","title":"On the asymptotic effectiveness of Weil descent attacks","display_name":"On the asymptotic effectiveness of Weil descent attacks","publication_year":2010,"publication_date":"2010-08-23","ids":{"openalex":"https://openalex.org/W2114535050","doi":"https://doi.org/10.1515/jmc.2010.007","mag":"2114535050"},"language":"en","primary_location":{"id":"doi:10.1515/jmc.2010.007","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc.2010.007","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc.2010.007/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.degruyter.com/document/doi/10.1515/jmc.2010.007/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087800081","display_name":"Koray Karabina","orcid":"https://orcid.org/0000-0001-9538-8877"},"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":true,"raw_author_name":"Koray Karabina","raw_affiliation_strings":["Department of Combinatorics & Optimization, University of Waterloo, Canada. E-mail:","Department of Combinatorics & Optimization, University of Waterloo, Canada. E-mail: [email\u00a0protected]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Combinatorics & Optimization, University of Waterloo, Canada. E-mail:","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Combinatorics & Optimization, University of Waterloo, Canada. E-mail: [email\u00a0protected]","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019674369","display_name":"Alfred Menezes","orcid":"https://orcid.org/0000-0003-3951-4298"},"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":true,"raw_author_name":"Alfred Menezes","raw_affiliation_strings":["Department of Combinatorics & Optimization, University of Waterloo, Canada. E-mail:","Department of Combinatorics & Optimization, University of Waterloo, Canada. E-mail: [email\u00a0protected]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Combinatorics & Optimization, University of Waterloo, Canada. E-mail:","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Combinatorics & Optimization, University of Waterloo, Canada. E-mail: [email\u00a0protected]","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065324760","display_name":"Carl Pomerance","orcid":"https://orcid.org/0000-0002-0960-1692"},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]},{"id":"https://openalex.org/I4210166639","display_name":"Dartmouth Hospital","ror":"https://ror.org/02j3qj605","country_code":"GB","type":"healthcare","lineage":["https://openalex.org/I4210166639"]}],"countries":["GB","US"],"is_corresponding":true,"raw_author_name":"Carl Pomerance","raw_affiliation_strings":["Mathematics Department, Dartmouth College, USA. E-mail:","Mathematics Department, Dartmouth College, USA. E-mail: [email\u00a0protected]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Dartmouth College, USA. E-mail:","institution_ids":["https://openalex.org/I107672454","https://openalex.org/I4210166639"]},{"raw_affiliation_string":"Mathematics Department, Dartmouth College, USA. E-mail: [email\u00a0protected]","institution_ids":["https://openalex.org/I107672454"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030033231","display_name":"Igor E. Shparlinski","orcid":"https://orcid.org/0000-0002-5246-9391"},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Igor E. Shparlinski","raw_affiliation_strings":["Department of Computing, Macquarie University, Australia. E-mail:","Department of Computing, Macquarie University, Australia. E-mail: [email\u00a0protected]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing, Macquarie University, Australia. E-mail:","institution_ids":["https://openalex.org/I99043593"]},{"raw_affiliation_string":"Department of Computing, Macquarie University, Australia. E-mail: [email\u00a0protected]","institution_ids":["https://openalex.org/I99043593"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5019674369","https://openalex.org/A5030033231","https://openalex.org/A5065324760","https://openalex.org/A5087800081"],"corresponding_institution_ids":["https://openalex.org/I107672454","https://openalex.org/I151746483","https://openalex.org/I4210166639","https://openalex.org/I99043593"],"apc_list":{"value":1050,"currency":"EUR","value_usd":1187},"apc_paid":{"value":1050,"currency":"EUR","value_usd":1187},"fwci":1.1271,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.88685304,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"4","issue":"2","first_page":"175","last_page":"191"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9995999932289124,"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":0.9995999932289124,"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/T11130","display_name":"Coding theory and cryptography","score":0.9952999949455261,"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/T10237","display_name":"Cryptography and Data Security","score":0.9775000214576721,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.8667259812355042},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.8159891366958618},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.707764208316803},{"id":"https://openalex.org/keywords/discrete-logarithm","display_name":"Discrete logarithm","score":0.6550897359848022},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6348847150802612},{"id":"https://openalex.org/keywords/genus","display_name":"Genus","score":0.5407140254974365},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4793449342250824},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4036717712879181},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35956376791000366},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35478317737579346},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32767796516418457},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19265681505203247},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17687729001045227},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.11470559239387512},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08411270380020142},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.06881940364837646},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.06220617890357971}],"concepts":[{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.8667259812355042},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.8159891366958618},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.707764208316803},{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.6550897359848022},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6348847150802612},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.5407140254974365},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4793449342250824},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4036717712879181},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35956376791000366},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35478317737579346},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32767796516418457},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19265681505203247},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17687729001045227},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.11470559239387512},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08411270380020142},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.06881940364837646},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.06220617890357971},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/jmc.2010.007","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc.2010.007","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc.2010.007/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:f725ea9803fa4d25aea41f73dc139c19","is_oa":true,"landing_page_url":"https://doaj.org/article/f725ea9803fa4d25aea41f73dc139c19","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Mathematical Cryptology, Vol 4, Iss 2, Pp 175-191 (2010)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/jmc.2010.007","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc.2010.007","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc.2010.007/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.46000000834465027,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G3716107378","display_name":"Topics in combinatorial and algorithmic number theory","funder_award_id":"0703850","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322676","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2114535050.pdf","grobid_xml":"https://content.openalex.org/works/W2114535050.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W586135738","https://openalex.org/W1485481031","https://openalex.org/W1486898453","https://openalex.org/W1493612669","https://openalex.org/W1495407274","https://openalex.org/W1562630396","https://openalex.org/W1569612250","https://openalex.org/W1592482282","https://openalex.org/W1751074114","https://openalex.org/W1778545302","https://openalex.org/W1969869350","https://openalex.org/W1979485530","https://openalex.org/W1984772295","https://openalex.org/W2005317356","https://openalex.org/W2019816098","https://openalex.org/W2046569422","https://openalex.org/W2073916736","https://openalex.org/W2084836129","https://openalex.org/W2094556471","https://openalex.org/W2111310412","https://openalex.org/W2112566740","https://openalex.org/W2149528579","https://openalex.org/W2331953275","https://openalex.org/W2488422562","https://openalex.org/W3123250145","https://openalex.org/W4246140522"],"related_works":["https://openalex.org/W1555245969","https://openalex.org/W2321282558","https://openalex.org/W2299507895","https://openalex.org/W1900540279","https://openalex.org/W4300200155","https://openalex.org/W4300498183","https://openalex.org/W2577600644","https://openalex.org/W1544736259","https://openalex.org/W2012392278","https://openalex.org/W2656095712"],"abstract_inverted_index":{"Abstract":[0],"In":[1,30],"this":[2],"paper":[3],"we":[4,32],"investigate":[5],"the":[6,10,19,40],"asymptotic":[7],"effectiveness":[8],"of":[9],"Gaudry\u2013Hess\u2013Smart":[11],"Weil":[12],"descent":[13],"attack":[14],"and":[15,36],"its":[16],"generalization":[17],"to":[18,44],"discrete":[20],"logarithm":[21],"problem":[22],"for":[23],"elliptic":[24],"curves":[25],"over":[26],"characteristic-two":[27],"finite":[28],"fields.":[29],"particular":[31],"obtain":[33],"nontrivial":[34],"lower":[35],"upper":[37],"bounds":[38],"on":[39],"smallest":[41],"possible":[42],"genus":[43],"which":[45],"it":[46],"can":[47],"lead.":[48]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2016-06-24T00:00:00"}
