{"id":"https://openalex.org/W3047472941","doi":"https://doi.org/10.1007/s00145-022-09430-6","title":"Non-commutative Ring Learning with Errors from Cyclic Algebras","display_name":"Non-commutative Ring Learning with Errors from Cyclic Algebras","publication_year":2022,"publication_date":"2022-07-01","ids":{"openalex":"https://openalex.org/W3047472941","doi":"https://doi.org/10.1007/s00145-022-09430-6","mag":"3047472941"},"language":"en","primary_location":{"id":"doi:10.1007/s00145-022-09430-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00145-022-09430-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00145-022-09430-6.pdf","source":{"id":"https://openalex.org/S190936789","display_name":"Journal of Cryptology","issn_l":"0933-2790","issn":["0933-2790","1432-1378"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Cryptology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00145-022-09430-6.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014521583","display_name":"Charles. Grover","orcid":null},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Charles Grover","raw_affiliation_strings":["Imperial College London, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Imperial College London, London, UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045978150","display_name":"Andrew R. Mendelsohn","orcid":"https://orcid.org/0000-0003-4735-7157"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Andrew Mendelsohn","raw_affiliation_strings":["Imperial College London, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Imperial College London, London, UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065795716","display_name":"Cong Ling","orcid":"https://orcid.org/0000-0001-7873-4862"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Cong Ling","raw_affiliation_strings":["Imperial College London, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Imperial College London, London, UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034251584","display_name":"Roope Vehkalahti","orcid":"https://orcid.org/0000-0002-3052-0635"},"institutions":[{"id":"https://openalex.org/I94722563","display_name":"University of Jyv\u00e4skyl\u00e4","ror":"https://ror.org/05n3dz165","country_code":"FI","type":"education","lineage":["https://openalex.org/I94722563"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Roope Vehkalahti","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Jyv\u00e4skyl\u00e4, 40014, Jyv\u00e4skyl\u00e4, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Jyv\u00e4skyl\u00e4, 40014, Jyv\u00e4skyl\u00e4, Finland","institution_ids":["https://openalex.org/I94722563"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065795716"],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":{"value":2780,"currency":"USD","value_usd":2780},"apc_paid":{"value":2780,"currency":"USD","value_usd":2780},"fwci":1.6654,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.85546828,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"35","issue":"3","first_page":null,"last_page":null},"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":0.9901000261306763,"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":0.9898999929428101,"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":0.9619792699813843},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.6721705198287964},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5910230875015259},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.5045548677444458},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.4992825984954834},{"id":"https://openalex.org/keywords/lattice-problem","display_name":"Lattice problem","score":0.44942522048950195},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.42402368783950806},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41002315282821655},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34702152013778687},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2427619993686676}],"concepts":[{"id":"https://openalex.org/C2779014939","wikidata":"https://www.wikidata.org/wiki/Q6510239","display_name":"Learning with errors","level":3,"score":0.9619792699813843},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.6721705198287964},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5910230875015259},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5045548677444458},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4992825984954834},{"id":"https://openalex.org/C168482242","wikidata":"https://www.wikidata.org/wiki/Q6497128","display_name":"Lattice problem","level":3,"score":0.44942522048950195},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.42402368783950806},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41002315282821655},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34702152013778687},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2427619993686676},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00145-022-09430-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00145-022-09430-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00145-022-09430-6.pdf","source":{"id":"https://openalex.org/S190936789","display_name":"Journal of Cryptology","issn_l":"0933-2790","issn":["0933-2790","1432-1378"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Cryptology","raw_type":"journal-article"},{"id":"pmh:oai:jyx.jyu.fi:123456789/82493","is_oa":true,"landing_page_url":"http://urn.fi/URN:NBN:fi:jyu-202208124037","pdf_url":null,"source":{"id":"https://openalex.org/S4306400563","display_name":"Jyv\u00e4skyl\u00e4 University Digital Archive (University of Jyv\u00e4skyl\u00e4)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I94722563","host_organization_name":"University of Jyv\u00e4skyl\u00e4","host_organization_lineage":["https://openalex.org/I94722563"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"research article"}],"best_oa_location":{"id":"doi:10.1007/s00145-022-09430-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00145-022-09430-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00145-022-09430-6.pdf","source":{"id":"https://openalex.org/S190936789","display_name":"Journal of Cryptology","issn_l":"0933-2790","issn":["0933-2790","1432-1378"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6700000166893005,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3047472941.pdf","grobid_xml":"https://content.openalex.org/works/W3047472941.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W31130112","https://openalex.org/W79002783","https://openalex.org/W1550813432","https://openalex.org/W1985439922","https://openalex.org/W1994790157","https://openalex.org/W2001093624","https://openalex.org/W2007466965","https://openalex.org/W2025367213","https://openalex.org/W2074735299","https://openalex.org/W2098217413","https://openalex.org/W2098290658","https://openalex.org/W2105994318","https://openalex.org/W2113333997","https://openalex.org/W2137141767","https://openalex.org/W2140256428","https://openalex.org/W2153331043","https://openalex.org/W2480523195","https://openalex.org/W2494078997","https://openalex.org/W2514587965","https://openalex.org/W2514893051","https://openalex.org/W2515257636","https://openalex.org/W2572660015","https://openalex.org/W2576607980","https://openalex.org/W2578134341","https://openalex.org/W2585166081","https://openalex.org/W2586406865","https://openalex.org/W2612903716","https://openalex.org/W2626019822","https://openalex.org/W2745221265","https://openalex.org/W2768527257","https://openalex.org/W2883882804","https://openalex.org/W2902122749","https://openalex.org/W2903270393","https://openalex.org/W2913851998","https://openalex.org/W2919219291","https://openalex.org/W2962882165","https://openalex.org/W2963519039","https://openalex.org/W2963687969","https://openalex.org/W2970130641","https://openalex.org/W2982322161","https://openalex.org/W2990015051","https://openalex.org/W3100632689","https://openalex.org/W4234106236","https://openalex.org/W4240339612","https://openalex.org/W6602828754"],"related_works":["https://openalex.org/W3029306306","https://openalex.org/W3197081079","https://openalex.org/W2942635421","https://openalex.org/W3209433403","https://openalex.org/W4281964710","https://openalex.org/W2151237818","https://openalex.org/W3089540147","https://openalex.org/W4308298797","https://openalex.org/W1491861813","https://openalex.org/W2315723423"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"Learning":[2],"with":[3,180],"Errors":[4],"(LWE)":[5],"problem":[6,126,146],"is":[7],"the":[8,21,98,101,119,137,140,144,148,164],"fundamental":[9],"backbone":[10],"of":[11,23,43,53,90,100,139,143,150,157,167],"modern":[12],"lattice-based":[13],"cryptography,":[14],"allowing":[15],"one":[16],"to":[17,50,96,106,113,136],"establish":[18],"cryptography":[19],"on":[20,30],"hardness":[22,138],"well-studied":[24],"computational":[25],"problems.":[26],"However,":[27],"schemes":[28],"based":[29],"LWE":[31,37,91,105,108,125,169],"are":[32],"often":[33],"impractical,":[34],"so":[35],"Ring":[36,107,168],"was":[38],"introduced":[39],"as":[40,163],"a":[41,48,63,76,80,87,129,155,186],"form":[42],"\u2018structured\u2019":[44],"LWE,":[45,70,182],"trading":[46],"off":[47],"hard":[49],"quantify":[51],"loss":[52],"security":[54,120],"for":[55,123,190],"an":[56,124],"increase":[57],"in":[58],"efficiency":[59],"by":[60,74,109],"working":[61],"over":[62,79,92],"well-chosen":[64],"ring.":[65,81],"Another":[66],"popular":[67],"variant,":[68],"Module":[69,114,181],"generalizes":[71],"this":[72,83],"exchange":[73],"implementing":[75],"module":[77],"structure":[78,103,112,177],"In":[82],"work,":[84],"we":[85,160],"introduce":[86],"novel":[88],"variant":[89,142,166],"cyclic":[93,111],"algebras":[94],"(CLWE)":[95],"replicate":[97],"addition":[99],"ring":[102,176],"taking":[104],"adding":[110],"LWE.":[115],"We":[116],"show":[117],"that":[118],"reductions":[121],"expected":[122],"hold,":[127],"namely":[128],"reduction":[130],"from":[131],"certain":[132],"structured":[133],"lattice":[134],"problems":[135],"decision":[141],"CLWE":[145,162],"(under":[147],"condition":[149],"constant":[151],"rank":[152],"d).":[153],"As":[154],"contribution":[156],"theoretic":[158],"interest,":[159],"view":[161],"first":[165],"which":[170],"supports":[171],"non-commutative":[172],"multiplication":[173],"operations.":[174],"This":[175],"compares":[178],"favorably":[179],"and":[183],"naturally":[184],"allows":[185],"larger":[187],"message":[188],"space":[189],"error":[191],"correction":[192],"coding.":[193]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2021,"cited_by_count":2}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}