{"id":"https://openalex.org/W1480297755","doi":"https://doi.org/10.1007/3-540-36178-2_1","title":"Analysis of Bernstein\u2019s Factorization Circuit","display_name":"Analysis of Bernstein\u2019s Factorization Circuit","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1480297755","doi":"https://doi.org/10.1007/3-540-36178-2_1","mag":"1480297755"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-36178-2_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-36178-2_1","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-36178-2_1.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-36178-2_1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109240185","display_name":"Arjen K. Lenstra","orcid":null},"institutions":[{"id":"https://openalex.org/I135458274","display_name":"Citigroup","ror":"https://ror.org/032xgdx47","country_code":"US","type":"other","lineage":["https://openalex.org/I135458274"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Arjen K. Lenstra","raw_affiliation_strings":["Citibank, N.A. and Technische Universiteit Eindhoven, 1 North Gate Road, Mendham, NJ, 07945-3104, USA"],"affiliations":[{"raw_affiliation_string":"Citibank, N.A. and Technische Universiteit Eindhoven, 1 North Gate Road, Mendham, NJ, 07945-3104, USA","institution_ids":["https://openalex.org/I135458274"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009126679","display_name":"Adi Shamir","orcid":"https://orcid.org/0000-0002-5422-905X"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Adi Shamir","raw_affiliation_strings":["Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087405501","display_name":"Jim Tomlinson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jim Tomlinson","raw_affiliation_strings":["99 E. 28th St., Bayonne, NJ, 07002-4912, USA"],"affiliations":[{"raw_affiliation_string":"99 E. 28th St., Bayonne, NJ, 07002-4912, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049555551","display_name":"Eran Tromer","orcid":"https://orcid.org/0000-0002-8884-9564"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Eran Tromer","raw_affiliation_strings":["Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel","institution_ids":["https://openalex.org/I53964585"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5109240185"],"corresponding_institution_ids":["https://openalex.org/I135458274"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":4.5351,"has_fulltext":true,"cited_by_count":37,"citation_normalized_percentile":{"value":0.94847248,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9997000098228455,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6836429238319397},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.5420759916305542},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.513359010219574},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5110400915145874},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5014157295227051},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.49953341484069824},{"id":"https://openalex.org/keywords/integer-factorization","display_name":"Integer factorization","score":0.46171995997428894},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4519866704940796},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.44937849044799805},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4274359345436096},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.42490968108177185},{"id":"https://openalex.org/keywords/sieve","display_name":"Sieve (category theory)","score":0.41459769010543823},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34977781772613525},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14861029386520386},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.11820143461227417},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.09334450960159302},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.06903982162475586}],"concepts":[{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6836429238319397},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.5420759916305542},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.513359010219574},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5110400915145874},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5014157295227051},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.49953341484069824},{"id":"https://openalex.org/C119677069","wikidata":"https://www.wikidata.org/wiki/Q4846249","display_name":"Integer factorization","level":4,"score":0.46171995997428894},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4519866704940796},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.44937849044799805},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4274359345436096},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.42490968108177185},{"id":"https://openalex.org/C17732976","wikidata":"https://www.wikidata.org/wiki/Q7511782","display_name":"Sieve (category theory)","level":2,"score":0.41459769010543823},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34977781772613525},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14861029386520386},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11820143461227417},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.09334450960159302},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.06903982162475586},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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/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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/3-540-36178-2_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-36178-2_1","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-36178-2_1.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/5819297e-0172-4409-8a45-50b6abef92af","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/5819297e-0172-4409-8a45-50b6abef92af","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lenstra, A K, Shamir, A, Tomlinson, J & Tromer, E 2002, Analysis of Bernstein's factorization circuit. in Y Zheng (ed.), Advances in Cryptology - ASIACRYPT 2002 (Proceedings 8th International Conference on the Theory and Application of Cryptology and Information Security, Queenstown, New Zealand, December 1-5, 2002). Lecture Notes in Computer Science, vol. 2501, Springer, Berlin, pp. 1-26. https://doi.org/10.1007/3-540-36178-2_1","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:infoscience.tind.io:149708","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/149708","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://infoscience.epfl.ch/record/149708","raw_type":"Text"},{"id":"pmh:tue:oai:pure.tue.nl:publications/5819297e-0172-4409-8a45-50b6abef92af","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/5819297e-0172-4409-8a45-50b6abef92af","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Advances in Cryptology - ASIACRYPT 2002 (Proceedings 8th International Conference on the Theory and Application of Cryptology and Information Security, Queenstown, New Zealand, December 1-5, 2002), 1 - 26","raw_type":"info:eu-repo/semantics/conferencepaper"}],"best_oa_location":{"id":"doi:10.1007/3-540-36178-2_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-36178-2_1","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-36178-2_1.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1480297755.pdf","grobid_xml":"https://content.openalex.org/works/W1480297755.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1531371507","https://openalex.org/W1596482432","https://openalex.org/W1865936578","https://openalex.org/W1976150119","https://openalex.org/W1993840452","https://openalex.org/W1994376122","https://openalex.org/W1998079848","https://openalex.org/W1999862709","https://openalex.org/W2012216209","https://openalex.org/W2019806661","https://openalex.org/W2071483197","https://openalex.org/W2175859306","https://openalex.org/W2179025976","https://openalex.org/W2179504188","https://openalex.org/W2286477783","https://openalex.org/W2918128759","https://openalex.org/W3194229933"],"related_works":["https://openalex.org/W1553416833","https://openalex.org/W2794559785","https://openalex.org/W4386505801","https://openalex.org/W2950631682","https://openalex.org/W2191903507","https://openalex.org/W2286463884","https://openalex.org/W2054570290","https://openalex.org/W2951079798","https://openalex.org/W2022996787","https://openalex.org/W4295997284"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
