{"id":"https://openalex.org/W2585166081","doi":"https://doi.org/10.1007/s10623-021-00973-6","title":"LWE from non-commutative group rings","display_name":"LWE from non-commutative group rings","publication_year":2021,"publication_date":"2021-11-24","ids":{"openalex":"https://openalex.org/W2585166081","doi":"https://doi.org/10.1007/s10623-021-00973-6","mag":"2585166081"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-021-00973-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-021-00973-6","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1612.06670","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008004564","display_name":"Qi Cheng","orcid":"https://orcid.org/0000-0003-4336-3082"},"institutions":[{"id":"https://openalex.org/I8692664","display_name":"University of Oklahoma","ror":"https://ror.org/02aqsxs83","country_code":"US","type":"education","lineage":["https://openalex.org/I8692664"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Qi Cheng","raw_affiliation_strings":["School of Computer Science, University of Oklahoma, Norman, OK, 73019, USA","School of Computer Science, University of Oklahoma, Norman, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Oklahoma, Norman, OK, 73019, USA","institution_ids":["https://openalex.org/I8692664"]},{"raw_affiliation_string":"School of Computer Science, University of Oklahoma, Norman, USA","institution_ids":["https://openalex.org/I8692664"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076077208","display_name":"Jun Zhang","orcid":"https://orcid.org/0000-0003-2173-3302"},"institutions":[{"id":"https://openalex.org/I96852419","display_name":"Capital Normal University","ror":"https://ror.org/005edt527","country_code":"CN","type":"education","lineage":["https://openalex.org/I96852419"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Zhang","raw_affiliation_strings":["School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China","School of Mathematical Sciences, Capital Normal University, Beijing, China;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China","institution_ids":["https://openalex.org/I96852419"]},{"raw_affiliation_string":"School of Mathematical Sciences, Capital Normal University, Beijing, China;","institution_ids":["https://openalex.org/I96852419"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103179935","display_name":"Jincheng Zhuang","orcid":null},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]},{"id":"https://openalex.org/I4210132990","display_name":"State Key Laboratory of Cryptology","ror":"https://ror.org/02pn5rj08","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210132990"]},{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jincheng Zhuang","raw_affiliation_strings":["Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Qingdao, China","School of Cyber Science and Technology, Shandong University, Qingdao, 266237, China","School of Cyber Science and Technology, Shandong University, Qingdao, China"],"raw_orcid":"https://orcid.org/0000-0003-1159-7597","affiliations":[{"raw_affiliation_string":"Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Qingdao, China","institution_ids":["https://openalex.org/I4210132990","https://openalex.org/I154099455"]},{"raw_affiliation_string":"School of Cyber Science and Technology, Shandong University, Qingdao, 266237, China","institution_ids":["https://openalex.org/I80143920"]},{"raw_affiliation_string":"School of Cyber Science and Technology, Shandong University, Qingdao, China","institution_ids":["https://openalex.org/I80143920"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5008004564"],"corresponding_institution_ids":["https://openalex.org/I8692664"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.28,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.60876071,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"90","issue":"1","first_page":"239","last_page":"263"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9998000264167786,"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":0.9998000264167786,"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/T11130","display_name":"Coding theory and cryptography","score":0.996999979019165,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9869999885559082,"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/principal-ideal","display_name":"Principal ideal","score":0.853069543838501},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.635864794254303},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.6144900321960449},{"id":"https://openalex.org/keywords/learning-with-errors","display_name":"Learning with errors","score":0.5872747898101807},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5119863152503967},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5097448229789734},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.5090627074241638},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.5002026557922363},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.4940343499183655},{"id":"https://openalex.org/keywords/principal","display_name":"Principal (computer security)","score":0.4852697551250458},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.4362012445926666},{"id":"https://openalex.org/keywords/lattice-problem","display_name":"Lattice problem","score":0.4286684989929199},{"id":"https://openalex.org/keywords/group-ring","display_name":"Group ring","score":0.4270443320274353},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42438822984695435},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4173547327518463},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3442279100418091},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2192646861076355},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19558224081993103},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.17107132077217102},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.11179861426353455},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.05603840947151184}],"concepts":[{"id":"https://openalex.org/C78766492","wikidata":"https://www.wikidata.org/wiki/Q44382","display_name":"Principal ideal","level":3,"score":0.853069543838501},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.635864794254303},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6144900321960449},{"id":"https://openalex.org/C2779014939","wikidata":"https://www.wikidata.org/wiki/Q6510239","display_name":"Learning with errors","level":3,"score":0.5872747898101807},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5119863152503967},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5097448229789734},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.5090627074241638},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.5002026557922363},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.4940343499183655},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.4852697551250458},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4362012445926666},{"id":"https://openalex.org/C168482242","wikidata":"https://www.wikidata.org/wiki/Q6497128","display_name":"Lattice problem","level":3,"score":0.4286684989929199},{"id":"https://openalex.org/C76572486","wikidata":"https://www.wikidata.org/wiki/Q2602722","display_name":"Group ring","level":3,"score":0.4270443320274353},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42438822984695435},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4173547327518463},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3442279100418091},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2192646861076355},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19558224081993103},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.17107132077217102},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.11179861426353455},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.05603840947151184},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10623-021-00973-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-021-00973-6","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1612.06670","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1612.06670","pdf_url":"https://arxiv.org/pdf/1612.06670","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2585166081","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1612.06670","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1612.06670","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1612.06670","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1612.06670","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1612.06670","pdf_url":"https://arxiv.org/pdf/1612.06670","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.41999998688697815,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G4740114680","display_name":null,"funder_award_id":"11971321","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5345224189","display_name":null,"funder_award_id":"CCF-1900820","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8579884243","display_name":null,"funder_award_id":"CCF-1409294","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8737206796","display_name":null,"funder_award_id":"11826102","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W74973629","https://openalex.org/W76319470","https://openalex.org/W599875224","https://openalex.org/W634784785","https://openalex.org/W1489262079","https://openalex.org/W1499766499","https://openalex.org/W1546333190","https://openalex.org/W1675339804","https://openalex.org/W1936753088","https://openalex.org/W1985439922","https://openalex.org/W1992282993","https://openalex.org/W2001093624","https://openalex.org/W2007466965","https://openalex.org/W2013089668","https://openalex.org/W2038761522","https://openalex.org/W2058785578","https://openalex.org/W2061949491","https://openalex.org/W2098290658","https://openalex.org/W2106970188","https://openalex.org/W2122973102","https://openalex.org/W2142048307","https://openalex.org/W2152783950","https://openalex.org/W2152926062","https://openalex.org/W2167236842","https://openalex.org/W2168676717","https://openalex.org/W2403700287","https://openalex.org/W2407361721","https://openalex.org/W2514587965","https://openalex.org/W2578134341","https://openalex.org/W2605112356","https://openalex.org/W2612903716","https://openalex.org/W2626019822","https://openalex.org/W2950780165","https://openalex.org/W2990927541","https://openalex.org/W3028867652","https://openalex.org/W3029104462","https://openalex.org/W3112612024","https://openalex.org/W3158888163"],"related_works":["https://openalex.org/W3047472941","https://openalex.org/W2098290658","https://openalex.org/W2921629858","https://openalex.org/W3158888163","https://openalex.org/W2883034031","https://openalex.org/W2883036095","https://openalex.org/W2397608281","https://openalex.org/W2076166285","https://openalex.org/W3115534942","https://openalex.org/W31130112","https://openalex.org/W2802997679","https://openalex.org/W3209433403","https://openalex.org/W2578134341","https://openalex.org/W3028681291","https://openalex.org/W57039937","https://openalex.org/W2912572442","https://openalex.org/W2988963440","https://openalex.org/W2796472420","https://openalex.org/W3022480174","https://openalex.org/W924029577"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
