{"id":"https://openalex.org/W2480841974","doi":"https://doi.org/10.1007/978-3-662-49896-5_19","title":"Structural Lattice Reduction: Generalized Worst-Case to Average-Case Reductions and Homomorphic Cryptosystems","display_name":"Structural Lattice Reduction: Generalized Worst-Case to Average-Case Reductions and Homomorphic Cryptosystems","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2480841974","doi":"https://doi.org/10.1007/978-3-662-49896-5_19","mag":"2480841974"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-662-49896-5_19","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-662-49896-5_19","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042695169","display_name":"Nicolas Gama","orcid":"https://orcid.org/0000-0001-7308-9171"},"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/I195731000","display_name":"Universit\u00e9 de Versailles Saint-Quentin-en-Yvelines","ror":"https://ror.org/03mkjjy25","country_code":"FR","type":"education","lineage":["https://openalex.org/I195731000","https://openalex.org/I277688954"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques Blaise Pascal","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]},{"id":"https://openalex.org/I97565354","display_name":"University of Lausanne","ror":"https://ror.org/019whta54","country_code":"CH","type":"education","lineage":["https://openalex.org/I97565354"]}],"countries":["CH","FR"],"is_corresponding":true,"raw_author_name":"Nicolas Gama","raw_affiliation_strings":["Inpher, Lausanne, Switzerland","Laboratoire de Math\u00e9matiques de Versailles, UVSQ, CNRS, Universit\u00e9 Paris-Saclay, 78035, Versailles, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inpher, Lausanne, Switzerland","institution_ids":["https://openalex.org/I97565354"]},{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques de Versailles, UVSQ, CNRS, Universit\u00e9 Paris-Saclay, 78035, Versailles, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I195731000","https://openalex.org/I277688954","https://openalex.org/I4210155549"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074733198","display_name":"Malika Izabach\u00e8ne","orcid":"https://orcid.org/0000-0003-0216-7958"},"institutions":[{"id":"https://openalex.org/I4210085861","display_name":"Laboratoire d'Int\u00e9gration des Syst\u00e8mes et des Technologies","ror":"https://ror.org/000dbcc61","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131","https://openalex.org/I2738703131","https://openalex.org/I277688954","https://openalex.org/I4210085861","https://openalex.org/I4210117989"]},{"id":"https://openalex.org/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Malika Izabach\u00e8ne","raw_affiliation_strings":["CEA, LIST, 91191, Gif-sur-Yvette Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CEA, LIST, 91191, Gif-sur-Yvette Cedex, France","institution_ids":["https://openalex.org/I2738703131","https://openalex.org/I4210085861"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102661245","display_name":"Phong Q. Nguy\u1ec5n","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["FR","JP"],"is_corresponding":false,"raw_author_name":"Phong Q. Nguyen","raw_affiliation_strings":["CNRS/JFLI and the University of Tokyo, Tokyo, Japan","Inria, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS/JFLI and the University of Tokyo, Tokyo, Japan","institution_ids":["https://openalex.org/I74801974"]},{"raw_affiliation_string":"Inria, Paris, France","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034405994","display_name":"Xiang Xie","orcid":"https://orcid.org/0000-0001-5044-9576"},"institutions":[{"id":"https://openalex.org/I2250955327","display_name":"Huawei Technologies (China)","ror":"https://ror.org/00cmhce21","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250955327"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiang Xie","raw_affiliation_strings":["Huawei Technologies, Shenzhen, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Huawei Technologies, Shenzhen, China","institution_ids":["https://openalex.org/I2250955327"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5042695169"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I195731000","https://openalex.org/I277688954","https://openalex.org/I4210155549","https://openalex.org/I97565354"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":3.3862,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.93321312,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"528","last_page":"558"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9998999834060669,"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":0.9998999834060669,"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":0.993399977684021,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9921000003814697,"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/cryptosystem","display_name":"Cryptosystem","score":0.7178161144256592},{"id":"https://openalex.org/keywords/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.6352951526641846},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.6083973050117493},{"id":"https://openalex.org/keywords/lattice-problem","display_name":"Lattice problem","score":0.6065883636474609},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5780549049377441},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5662572383880615},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.553015947341919},{"id":"https://openalex.org/keywords/lattice-reduction","display_name":"Lattice reduction","score":0.5513319373130798},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5136753916740417},{"id":"https://openalex.org/keywords/lattice-based-cryptography","display_name":"Lattice-based cryptography","score":0.4982872009277344},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4677208960056305},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3031117916107178},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2145155668258667},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.1784786880016327}],"concepts":[{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.7178161144256592},{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.6352951526641846},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.6083973050117493},{"id":"https://openalex.org/C168482242","wikidata":"https://www.wikidata.org/wiki/Q6497128","display_name":"Lattice problem","level":3,"score":0.6065883636474609},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5780549049377441},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5662572383880615},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.553015947341919},{"id":"https://openalex.org/C44274781","wikidata":"https://www.wikidata.org/wiki/Q6497132","display_name":"Lattice reduction","level":4,"score":0.5513319373130798},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5136753916740417},{"id":"https://openalex.org/C137660015","wikidata":"https://www.wikidata.org/wiki/Q6497083","display_name":"Lattice-based cryptography","level":5,"score":0.4982872009277344},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4677208960056305},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3031117916107178},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2145155668258667},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.1784786880016327},{"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/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.0},{"id":"https://openalex.org/C144901912","wikidata":"https://www.wikidata.org/wiki/Q471906","display_name":"Quantum cryptography","level":4,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-3-662-49896-5_19","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-662-49896-5_19","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-01382384v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-01382384","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":"http://ist.ac.at/eurocrypt2016/","raw_type":"Conference papers"},{"id":"pmh:oai:HAL:hal-02177632v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02177632","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":"Advances in Cryptology \u2013 EUROCRYPT 2016, pp.528-558, 2016, &#x27E8;10.1007/978-3-662-49896-5_19&#x27E9;","raw_type":"Book sections"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W17575016","https://openalex.org/W39036742","https://openalex.org/W56544557","https://openalex.org/W74973629","https://openalex.org/W79002783","https://openalex.org/W80562455","https://openalex.org/W149470655","https://openalex.org/W913176383","https://openalex.org/W1498897152","https://openalex.org/W1555176766","https://openalex.org/W1580599221","https://openalex.org/W1589934104","https://openalex.org/W1766548092","https://openalex.org/W1970144139","https://openalex.org/W1981142474","https://openalex.org/W1994790157","https://openalex.org/W2016297799","https://openalex.org/W2025247340","https://openalex.org/W2038761522","https://openalex.org/W2051176401","https://openalex.org/W2058546698","https://openalex.org/W2058785578","https://openalex.org/W2061949491","https://openalex.org/W2065151783","https://openalex.org/W2089477764","https://openalex.org/W2113333997","https://openalex.org/W2140256428","https://openalex.org/W2141040012","https://openalex.org/W2142048307","https://openalex.org/W2151237818","https://openalex.org/W2152926062","https://openalex.org/W2156030242","https://openalex.org/W2159486442","https://openalex.org/W2176745559","https://openalex.org/W2226167778","https://openalex.org/W2480841974","https://openalex.org/W2755136615","https://openalex.org/W3150881812"],"related_works":["https://openalex.org/W2032226069","https://openalex.org/W1597211008","https://openalex.org/W2905116383","https://openalex.org/W2949749387","https://openalex.org/W4385711271","https://openalex.org/W2348168089","https://openalex.org/W2353157311","https://openalex.org/W4384027199","https://openalex.org/W3112306103","https://openalex.org/W2950017356"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}
