{"id":"https://openalex.org/W2989959564","doi":"https://doi.org/10.1007/978-3-030-34578-5_3","title":"Middle-Product Learning with Rounding Problem and Its Applications","display_name":"Middle-Product Learning with Rounding Problem and Its Applications","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2989959564","doi":"https://doi.org/10.1007/978-3-030-34578-5_3","mag":"2989959564"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-34578-5_3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-34578-5_3","pdf_url":null,"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":"green","oa_url":"https://hal.science/hal-02880043","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054438923","display_name":"Shi Bai","orcid":"https://orcid.org/0000-0002-0746-3054"},"institutions":[{"id":"https://openalex.org/I63772739","display_name":"Florida Atlantic University","ror":"https://ror.org/05p8w6387","country_code":"US","type":"education","lineage":["https://openalex.org/I63772739"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Shi Bai","raw_affiliation_strings":["Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, USA","institution_ids":["https://openalex.org/I63772739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017987811","display_name":"Katharina Boudgoust","orcid":"https://orcid.org/0000-0002-3971-9368"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I56067802","display_name":"Universit\u00e9 de Rennes","ror":"https://ror.org/015m7wh34","country_code":"FR","type":"education","lineage":["https://openalex.org/I56067802"]},{"id":"https://openalex.org/I2802519937","display_name":"Institut de Recherche en Informatique et Syst\u00e8mes Al\u00e9atoires","ror":"https://ror.org/00myn0z94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I2802519937","https://openalex.org/I28221208","https://openalex.org/I4210127572","https://openalex.org/I4210159245","https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Katharina Boudgoust","raw_affiliation_strings":["Univ Rennes, CNRS, IRISA, Rennes, France"],"affiliations":[{"raw_affiliation_string":"Univ Rennes, CNRS, IRISA, Rennes, France","institution_ids":["https://openalex.org/I2802519937","https://openalex.org/I56067802","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018995566","display_name":"Dipayan Das","orcid":"https://orcid.org/0000-0002-7681-1868"},"institutions":[{"id":"https://openalex.org/I155837530","display_name":"National Institute of Technology Durgapur","ror":"https://ror.org/04ds0jm32","country_code":"IN","type":"education","lineage":["https://openalex.org/I155837530"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Dipayan Das","raw_affiliation_strings":["Department of Mathematics, National Institute of Technology, Durgapur, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Institute of Technology, Durgapur, India","institution_ids":["https://openalex.org/I155837530"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089430087","display_name":"Adeline Roux-Langlois","orcid":"https://orcid.org/0000-0003-0617-9606"},"institutions":[{"id":"https://openalex.org/I2802519937","display_name":"Institut de Recherche en Informatique et Syst\u00e8mes Al\u00e9atoires","ror":"https://ror.org/00myn0z94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I2802519937","https://openalex.org/I28221208","https://openalex.org/I4210127572","https://openalex.org/I4210159245","https://openalex.org/I56067802"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I56067802","display_name":"Universit\u00e9 de Rennes","ror":"https://ror.org/015m7wh34","country_code":"FR","type":"education","lineage":["https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Adeline Roux-Langlois","raw_affiliation_strings":["Univ Rennes, CNRS, IRISA, Rennes, France"],"affiliations":[{"raw_affiliation_string":"Univ Rennes, CNRS, IRISA, Rennes, France","institution_ids":["https://openalex.org/I2802519937","https://openalex.org/I56067802","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090845413","display_name":"Weiqiang Wen","orcid":"https://orcid.org/0000-0001-5272-2572"},"institutions":[{"id":"https://openalex.org/I2802519937","display_name":"Institut de Recherche en Informatique et Syst\u00e8mes Al\u00e9atoires","ror":"https://ror.org/00myn0z94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I2802519937","https://openalex.org/I28221208","https://openalex.org/I4210127572","https://openalex.org/I4210159245","https://openalex.org/I56067802"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I56067802","display_name":"Universit\u00e9 de Rennes","ror":"https://ror.org/015m7wh34","country_code":"FR","type":"education","lineage":["https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Weiqiang Wen","raw_affiliation_strings":["Univ Rennes, CNRS, IRISA, Rennes, France"],"affiliations":[{"raw_affiliation_string":"Univ Rennes, CNRS, IRISA, Rennes, France","institution_ids":["https://openalex.org/I2802519937","https://openalex.org/I56067802","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003284833","display_name":"Zhenfei Zhang","orcid":"https://orcid.org/0000-0003-2692-6242"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhenfei Zhang","raw_affiliation_strings":["Algorand, Boston, USA"],"affiliations":[{"raw_affiliation_string":"Algorand, Boston, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5054438923"],"corresponding_institution_ids":["https://openalex.org/I63772739"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.5513,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.70912791,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"55","last_page":"81"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","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/T10237","display_name":"Cryptography and Data Security","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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9958999752998352,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/learning-with-errors","display_name":"Learning with errors","score":0.95074462890625},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.6659269332885742},{"id":"https://openalex.org/keywords/ciphertext","display_name":"Ciphertext","score":0.6598877906799316},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5759730339050293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5111234784126282},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.48578742146492004},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4221554100513458},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.3874187171459198},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36369433999061584},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32199588418006897},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2752164602279663},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2616598606109619}],"concepts":[{"id":"https://openalex.org/C2779014939","wikidata":"https://www.wikidata.org/wiki/Q6510239","display_name":"Learning with errors","level":3,"score":0.95074462890625},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.6659269332885742},{"id":"https://openalex.org/C93974786","wikidata":"https://www.wikidata.org/wiki/Q1589480","display_name":"Ciphertext","level":3,"score":0.6598877906799316},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5759730339050293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5111234784126282},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.48578742146492004},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4221554100513458},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.3874187171459198},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36369433999061584},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32199588418006897},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2752164602279663},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2616598606109619},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-030-34578-5_3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-34578-5_3","pdf_url":null,"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:HAL:hal-02880043v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02880043","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":"Asiacrypt 2019 - 25th Annual International Conference on the Theory and Application of Cryptology and Information Security, Dec 2019, Kobe, Japan. &#x27E8;10.1007/978-3-030-34578-5_3&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-02880043v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02880043","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":"Asiacrypt 2019 - 25th Annual International Conference on the Theory and Application of Cryptology and Information Security, Dec 2019, Kobe, Japan. &#x27E8;10.1007/978-3-030-34578-5_3&#x27E9;","raw_type":"Conference papers"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7099999785423279}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W38127577","https://openalex.org/W151792660","https://openalex.org/W190530026","https://openalex.org/W1491861813","https://openalex.org/W1546634390","https://openalex.org/W1614548964","https://openalex.org/W1760474993","https://openalex.org/W1974169366","https://openalex.org/W1985439922","https://openalex.org/W2007466965","https://openalex.org/W2026653933","https://openalex.org/W2048685209","https://openalex.org/W2058785578","https://openalex.org/W2061949491","https://openalex.org/W2089477764","https://openalex.org/W2098290658","https://openalex.org/W2122882636","https://openalex.org/W2261941747","https://openalex.org/W2293813270","https://openalex.org/W2398538644","https://openalex.org/W2412886904","https://openalex.org/W2465263483","https://openalex.org/W2494078997","https://openalex.org/W2514587965","https://openalex.org/W2552357046","https://openalex.org/W2555933408","https://openalex.org/W2571657973","https://openalex.org/W2575853501","https://openalex.org/W2739600916","https://openalex.org/W2795036470","https://openalex.org/W2796314191","https://openalex.org/W2886641005","https://openalex.org/W2953258282","https://openalex.org/W2961104175","https://openalex.org/W3104192529","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2963103512","https://openalex.org/W2765793266","https://openalex.org/W2739694080","https://openalex.org/W2550942574","https://openalex.org/W2195479001","https://openalex.org/W2315723423","https://openalex.org/W4221138287","https://openalex.org/W2944613252","https://openalex.org/W1874619058","https://openalex.org/W3149951253"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
