{"id":"https://openalex.org/W1604127192","doi":"https://doi.org/10.1007/978-3-642-13013-7_5","title":"Implicit Factoring with Shared Most Significant and Middle Bits","display_name":"Implicit Factoring with Shared Most Significant and Middle Bits","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1604127192","doi":"https://doi.org/10.1007/978-3-642-13013-7_5","mag":"1604127192"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-13013-7_5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-642-13013-7_5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-642-13013-7_5.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%2F978-3-642-13013-7_5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107405594","display_name":"Jean\u2010Charles Faug\u00e8re","orcid":null},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Jean-Charles Faug\u00e8re","raw_affiliation_strings":["UPMC, Universit\u00e9 Paris 06, LIP6, 4, place Jussieu, 75252, Paris, Cedex 5, France"],"affiliations":[{"raw_affiliation_string":"UPMC, Universit\u00e9 Paris 06, LIP6, 4, place Jussieu, 75252, Paris, Cedex 5, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I204730241"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040382220","display_name":"Rapha\u00ebl Marinier","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Rapha\u00ebl Marinier","raw_affiliation_strings":["INRIA, Centre Paris-Rocquencourt, SALSA Project-team, 4, place Jussieu, 75252, Paris, Cedex 5, France"],"affiliations":[{"raw_affiliation_string":"INRIA, Centre Paris-Rocquencourt, SALSA Project-team, 4, place Jussieu, 75252, Paris, Cedex 5, France","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085614648","display_name":"Gu\u00e9na\u00ebl Renault","orcid":"https://orcid.org/0000-0002-7050-9975"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210159731","display_name":"Laboratoire de Recherche en Informatique de Paris 6","ror":"https://ror.org/05krcen59","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210159245","https://openalex.org/I4210159731"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Gu\u00e9na\u00ebl Renault","raw_affiliation_strings":["CNRS, UMR 7606, LIP6, 4, place Jussieu, 75252, Paris, Cedex 5, France"],"affiliations":[{"raw_affiliation_string":"CNRS, UMR 7606, LIP6, 4, place Jussieu, 75252, Paris, Cedex 5, France","institution_ids":["https://openalex.org/I4210159731","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5107405594"],"corresponding_institution_ids":["https://openalex.org/I204730241","https://openalex.org/I39804081"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":2.2603,"has_fulltext":true,"cited_by_count":34,"citation_normalized_percentile":{"value":0.89208633,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"70","last_page":"87"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9995999932289124,"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/moduli","display_name":"Moduli","score":0.8028577566146851},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6079582571983337},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5946020483970642},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5025019645690918},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5009558200836182},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47228342294692993},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.45168787240982056},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.43220287561416626},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4288523197174072},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4242808520793915},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.37814509868621826},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2634900212287903},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2449844479560852},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10243317484855652},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09862589836120605}],"concepts":[{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.8028577566146851},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6079582571983337},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5946020483970642},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5025019645690918},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5009558200836182},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47228342294692993},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.45168787240982056},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.43220287561416626},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4288523197174072},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4242808520793915},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.37814509868621826},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2634900212287903},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2449844479560852},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10243317484855652},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09862589836120605},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/978-3-642-13013-7_5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-642-13013-7_5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-642-13013-7_5.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:CiteSeerX.psu:10.1.1.167.4927","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.167.4927","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-calfor.lip6.fr/%7Ejcf/Papers/SCC2010c.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.187.9104","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.187.9104","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-salsa.lip6.fr/%7Ejcf/Papers/pkc2010b.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.402.6966","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.402.6966","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-polsys.lip6.fr/~renault/ressources_rech/FMR_PKC2010.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01288914v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01288914","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"In 13th International Conference on Practice and Theory in Public Key Cryptography -- PKC 2010, May 2010, Paris, France. pp.70-87, &#x27E8;10.1007/978-3-642-13013-7_5&#x27E9;","raw_type":"Conference papers"},{"id":"pmh:oai:HAL:hal-01288918v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01288918","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":"SCC '10: the 2nd International Conference on Symbolic Computation and Cryptography, Jun 2010, London, United Kingdom. pp.197-201","raw_type":"Conference papers"}],"best_oa_location":{"id":"doi:10.1007/978-3-642-13013-7_5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-642-13013-7_5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-642-13013-7_5.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/W1604127192.pdf","grobid_xml":"https://content.openalex.org/works/W1604127192.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W141781985","https://openalex.org/W1485280854","https://openalex.org/W1499237070","https://openalex.org/W1532770887","https://openalex.org/W1544369918","https://openalex.org/W1766548092","https://openalex.org/W1961022628","https://openalex.org/W1976677460","https://openalex.org/W1988524997","https://openalex.org/W2006155502","https://openalex.org/W2026499134","https://openalex.org/W2041258513","https://openalex.org/W2103832773","https://openalex.org/W2119819322","https://openalex.org/W2147906334","https://openalex.org/W2155178472","https://openalex.org/W2160639384","https://openalex.org/W2168676717","https://openalex.org/W2179025976","https://openalex.org/W2477242951","https://openalex.org/W2490262601","https://openalex.org/W2493993829","https://openalex.org/W2495148038","https://openalex.org/W2503514047","https://openalex.org/W2505860479","https://openalex.org/W2561675875","https://openalex.org/W3097986274","https://openalex.org/W4245046265","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2306553012","https://openalex.org/W4251417359","https://openalex.org/W2381059884","https://openalex.org/W4229993731","https://openalex.org/W2372756075","https://openalex.org/W1979193983","https://openalex.org/W2220405813","https://openalex.org/W1821795854","https://openalex.org/W2374111230","https://openalex.org/W2941119120"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
