{"id":"https://openalex.org/W2964070865","doi":"https://doi.org/10.1137/17m1154187","title":"On the Secrecy Gain of $\\ell$-Modular Lattices","display_name":"On the Secrecy Gain of $\\ell$-Modular Lattices","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2964070865","doi":"https://doi.org/10.1137/17m1154187","mag":"2964070865"},"language":"en","primary_location":{"id":"doi:10.1137/17m1154187","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1154187","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","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/A5073641250","display_name":"Anne-Maria Ernvall-Hyt\u00f6nen","orcid":"https://orcid.org/0000-0001-7598-8509"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Anne-Maria Ernvall-Hyt\u00f6nen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5016817284","display_name":"Esa V. Vesalainen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Esa V. Vesalainen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073641250"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2607,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.60791169,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"32","issue":"2","first_page":"1441","last_page":"1457"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9945999979972839,"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"}},"topics":[{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9945999979972839,"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":0.9929999709129333,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9889000058174133,"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/counterexample","display_name":"Counterexample","score":0.9280655980110168},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8827883005142212},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6900999546051025},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.587826669216156},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.58741295337677},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5538005828857422},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4873965382575989},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1477503478527069},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1392982304096222}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.9280655980110168},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8827883005142212},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6900999546051025},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.587826669216156},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.58741295337677},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5538005828857422},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4873965382575989},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1477503478527069},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1392982304096222},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"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:10.1137/17m1154187","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1154187","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/b7fea0cc-0e50-4193-bbc4-36ab1aa62f5b","is_oa":false,"landing_page_url":"https://arxiv.org/abs/1708.09239","pdf_url":null,"source":{"id":"https://openalex.org/S4406923060","display_name":"\u00c5bo Akademi University Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Ernvall-Hyt\u00f6nen , A-M &amp; Vesalainen , E 2018 , ' On the secrecy gain of l-modular lattices ' , SIAM Journal on Discrete Mathematics , vol. 32 , no. 2 , pp. 1441\u20131457 . https://doi.org/10.1137/17M1154187","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1708820433","display_name":null,"funder_award_id":"BERC 2014-2017 program","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"},{"id":"https://openalex.org/G3244436707","display_name":null,"funder_award_id":"SEV-2013-0323","funder_id":"https://openalex.org/F4320328444","funder_display_name":"Basque Center for Applied Mathematics"},{"id":"https://openalex.org/G3779338858","display_name":null,"funder_award_id":"2014-2017","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"},{"id":"https://openalex.org/G4252991836","display_name":null,"funder_award_id":"BERC 2014-2017","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G4271410626","display_name":null,"funder_award_id":"303820","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"},{"id":"https://openalex.org/G4373130462","display_name":null,"funder_award_id":"2013-0323","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G5281057304","display_name":null,"funder_award_id":"2014-2017","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G6939876626","display_name":null,"funder_award_id":"SEV-2013-0323","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G7529331022","display_name":null,"funder_award_id":"BERC 2014-2017","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"},{"id":"https://openalex.org/G8296132195","display_name":null,"funder_award_id":"SEV-2013-0323","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"}],"funders":[{"id":"https://openalex.org/F4320321108","display_name":"Academy of Finland","ror":"https://ror.org/05k73zm37"},{"id":"https://openalex.org/F4320321705","display_name":"Eusko Jaurlaritza","ror":"https://ror.org/00pz2fp31"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320322400","display_name":"Magnus Ehrnroothin S\u00e4\u00e4ti\u00f6","ror":"https://ror.org/02cdzet69"},{"id":"https://openalex.org/F4320328444","display_name":"Basque Center for Applied Mathematics","ror":"https://ror.org/03b21sh32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1538720896","https://openalex.org/W1626000505","https://openalex.org/W1993913758","https://openalex.org/W2043769961","https://openalex.org/W2060483042","https://openalex.org/W2132726459","https://openalex.org/W2289880074","https://openalex.org/W2397087910"],"related_works":["https://openalex.org/W4309222106","https://openalex.org/W2012590989","https://openalex.org/W4385681624","https://openalex.org/W4240581084","https://openalex.org/W1734188852","https://openalex.org/W2952569802","https://openalex.org/W2049141591","https://openalex.org/W2950489642","https://openalex.org/W4297939726","https://openalex.org/W4298858221"],"abstract_inverted_index":{"We":[0,80],"show":[1],"that":[2],"for":[3,60,88],"every":[4],"$\\ell>1$,":[5],"there":[6],"is":[7],"a":[8,51,68,83],"counterexample":[9],"to":[10,53,67],"the":[11,33,57,86],"$\\ell$-modular":[12,63,90],"secrecy":[13],"function":[14],"conjecture":[15,35,59],"by":[16,36],"Oggier,":[17],"Sol\u00e9,":[18],"and":[19,38],"Belfiore":[20],"[IEEE":[21,40],"Trans.":[22,41],"Inform.":[23,42],"Theory,":[24,43],"62":[25,44],"(2016),":[26,45],"pp.":[27,46],"5690--5708].":[28],"These":[29],"counterexamples":[30],"all":[31],"satisfy":[32],"modified":[34,58],"Ernvall-Hyt\u00f6nen":[37],"Sethuraman":[39],"4514--4522].":[47],"Furthermore,":[48],"we":[49],"provide":[50,82],"method":[52,87],"prove":[54],"or":[55],"disprove":[56],"any":[61],"given":[62],"lattice":[64],"rationally":[65],"equivalent":[66],"suitable":[69],"amount":[70],"of":[71,73,85],"copies":[72],"$\\mathbb{Z}\\oplus":[74],"\\sqrt{\\ell}\\,\\mathbb{Z}$":[75],"with":[76],"$\\ell":[77],"\\in":[78],"\\{3,5,7,11,23\\}$.":[79],"also":[81],"variant":[84],"strongly":[89],"lattices":[91],"when":[92],"$\\ell\\in":[93],"\\{6,14,15\\}$.":[94]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-16T09:10:04.655348","created_date":"2025-10-10T00:00:00"}
