{"id":"https://openalex.org/W4416364109","doi":"https://doi.org/10.1145/3798129.3800796","title":"Average Hardness of SIVP for Module Lattices of Fixed Rank","display_name":"Average Hardness of SIVP for Module Lattices of Fixed Rank","publication_year":2026,"publication_date":"2026-06-09","ids":{"openalex":"https://openalex.org/W4416364109","doi":"https://doi.org/10.1145/3798129.3800796"},"language":null,"primary_location":{"id":"doi:10.1145/3798129.3800796","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3798129.3800796","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 58th Annual ACM Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1145/3798129.3800796","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034476970","display_name":"Koen de Boer","orcid":null},"institutions":[{"id":"https://openalex.org/I2802557195","display_name":"United Nations University \u2013 Maastricht Economic and Social Research Institute on Innovation and Technology","ror":"https://ror.org/053zwxr79","country_code":"NL","type":"facility","lineage":["https://openalex.org/I2802557195","https://openalex.org/I4210104502"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Koen de Boer","raw_affiliation_strings":["Unaffiliated, Maastricht, Netherlands","Sans affiliation (France)"],"raw_orcid":"https://orcid.org/0009-0001-2024-637X","affiliations":[{"raw_affiliation_string":"Unaffiliated, Maastricht, Netherlands","institution_ids":["https://openalex.org/I2802557195"]},{"raw_affiliation_string":"Sans affiliation (France)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089233826","display_name":"Aurel Page","orcid":"https://orcid.org/0000-0002-1247-4970"},"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/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]},{"id":"https://openalex.org/I4210166017","display_name":"Institut de Math\u00e9matiques de Bordeaux","ror":"https://ror.org/05m3r1b84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I15057530","https://openalex.org/I4210141950","https://openalex.org/I4210160189","https://openalex.org/I4210166017"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Aurel Page","raw_affiliation_strings":["Inria - Univ. Bordeaux - CNRS - Bordeaux INP - IMB - UMR 5251, Bordeaux, France","IMB - Institut de Math\u00e9matiques de Bordeaux (351 cours de la Lib\u00e9ration 33405 TALENCE CEDEX - France)","CANARI - Analyse cryptographique et arithm\u00e9tique (200, avenue de la Vieille Tour \r\n33405 Talence cedex - France)"],"raw_orcid":"https://orcid.org/0000-0002-1247-4970","affiliations":[{"raw_affiliation_string":"Inria - Univ. Bordeaux - CNRS - Bordeaux INP - IMB - UMR 5251, Bordeaux, France","institution_ids":["https://openalex.org/I4210166017","https://openalex.org/I15057530","https://openalex.org/I4210160189","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"IMB - Institut de Math\u00e9matiques de Bordeaux (351 cours de la Lib\u00e9ration 33405 TALENCE CEDEX - France)","institution_ids":["https://openalex.org/I4210166017"]},{"raw_affiliation_string":"CANARI - Analyse cryptographique et arithm\u00e9tique (200, avenue de la Vieille Tour \r\n33405 Talence cedex - France)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102814338","display_name":"Radu Toma","orcid":"https://orcid.org/0000-0002-4899-7095"},"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/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210091437","display_name":"Sorbonne Paris Cit\u00e9","ror":"https://ror.org/001z21q04","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210091437"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Radu Toma","raw_affiliation_strings":["Sorbonne Univ. - Univ. Paris Cit\u00e9 - CNRS - IMJ-PRG, Paris, France","UPCit\u00e9 - Universit\u00e9 Paris Cit\u00e9 (85 boulevard Saint-Germain\r\n75006 Paris - France)","SU - Sorbonne Universite\u0301 (21 rue de l\u2019\u00c9cole de m\u00e9decine - 75006 Paris - France)"],"raw_orcid":"https://orcid.org/0000-0002-4899-7095","affiliations":[{"raw_affiliation_string":"Sorbonne Univ. - Univ. Paris Cit\u00e9 - CNRS - IMJ-PRG, Paris, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I204730241","https://openalex.org/I4210091437","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"UPCit\u00e9 - Universit\u00e9 Paris Cit\u00e9 (85 boulevard Saint-Germain\r\n75006 Paris - France)","institution_ids":["https://openalex.org/I4210091437","https://openalex.org/I204730241"]},{"raw_affiliation_string":"SU - Sorbonne Universite\u0301 (21 rue de l\u2019\u00c9cole de m\u00e9decine - 75006 Paris - France)","institution_ids":["https://openalex.org/I39804081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071198706","display_name":"Benjamin Wesolowski","orcid":"https://orcid.org/0000-0003-1249-6077"},"institutions":[{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]},{"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/I4210160577","display_name":"Unit\u00e9 de Math\u00e9matiques Pures et Appliqu\u00e9es","ror":"https://ror.org/05n21n105","country_code":"FR","type":"facility","lineage":["https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210160577"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Benjamin Wesolowski","raw_affiliation_strings":["ENS de Lyon - CNRS - UMPA - UMR 5669, Lyon, France","CNRS - Centre National de la Recherche Scientifique (France)","ENS de Lyon - \u00c9cole normale sup\u00e9rieure de Lyon (15 parvis Ren\u00e9 Descartes - BP 7000 - 69342 Lyon Cedex 07 - France)"],"raw_orcid":"https://orcid.org/0000-0003-1249-6077","affiliations":[{"raw_affiliation_string":"ENS de Lyon - CNRS - UMPA - UMR 5669, Lyon, France","institution_ids":["https://openalex.org/I4210160577","https://openalex.org/I113428412","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CNRS - Centre National de la Recherche Scientifique (France)","institution_ids":["https://openalex.org/I1294671590"]},{"raw_affiliation_string":"ENS de Lyon - \u00c9cole normale sup\u00e9rieure de Lyon (15 parvis Ren\u00e9 Descartes - BP 7000 - 69342 Lyon Cedex 07 - France)","institution_ids":["https://openalex.org/I113428412"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01145047,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"814","last_page":"822"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9528999924659729,"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":0.9528999924659729,"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":0.011500000022351742,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.007000000216066837,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/ideal","display_name":"Ideal (ethics)","score":0.5823000073432922},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5300999879837036},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4668999910354614},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.44909998774528503},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.43650001287460327},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4124000072479248},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.40779998898506165},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.37470000982284546},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.36890000104904175}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8296999931335449},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5823000073432922},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5702999830245972},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5300999879837036},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4668999910354614},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.44909998774528503},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.43650001287460327},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4124000072479248},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.40779998898506165},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.37470000982284546},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.36890000104904175},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.364300012588501},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.36059999465942383},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.35409998893737793},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.3483000099658966},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3402000069618225},{"id":"https://openalex.org/C137660015","wikidata":"https://www.wikidata.org/wiki/Q6497083","display_name":"Lattice-based cryptography","level":5,"score":0.3294999897480011},{"id":"https://openalex.org/C2778283813","wikidata":"https://www.wikidata.org/wiki/Q4927106","display_name":"Bloch space","level":3,"score":0.3188999891281128},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31029999256134033},{"id":"https://openalex.org/C168482242","wikidata":"https://www.wikidata.org/wiki/Q6497128","display_name":"Lattice problem","level":3,"score":0.29980000853538513},{"id":"https://openalex.org/C153782549","wikidata":"https://www.wikidata.org/wiki/Q175116","display_name":"Discrete space","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C3087436","wikidata":"https://www.wikidata.org/wiki/Q1386603","display_name":"Secret sharing","level":3,"score":0.2791000008583069},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2653999924659729},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.25760000944137573},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.2529999911785126},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.2529999911785126},{"id":"https://openalex.org/C2779014939","wikidata":"https://www.wikidata.org/wiki/Q6510239","display_name":"Learning with errors","level":3,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3798129.3800796","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3798129.3800796","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 58th Annual ACM Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2511.13659","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.13659","pdf_url":"https://arxiv.org/pdf/2511.13659","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.1145/3798129.3800796","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3798129.3800796","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 58th Annual ACM Symposium on Theory of Computing","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G155594237","display_name":null,"funder_award_id":"ANR-20-CE40-0010","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2511063094","display_name":null,"funder_award_id":"101034255","funder_id":"https://openalex.org/F4320320217","funder_display_name":"Marie Curie"},{"id":"https://openalex.org/G2970831653","display_name":null,"funder_award_id":"ANR-22-PNCQ-0002","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G358896284","display_name":null,"funder_award_id":"101116169","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G5071914031","display_name":null,"funder_award_id":"101054336","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G516181419","display_name":null,"funder_award_id":"ANR-21-CE94-0003","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5463327868","display_name":null,"funder_award_id":"ANR-22-PETQ-0008","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320217","display_name":"Marie Curie","ror":"https://ror.org/02aqv1x10"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,17,42],"problem":[1,13],"of":[2,19,33,44,64],"finding":[3,45],"short":[4,46],"vectors":[5,47],"in":[6,14,48],"Euclidean":[7],"lattices":[8,21,23],"is":[9,32,58,60],"a":[10,29,56],"central":[11],"hard":[12],"complexity":[15],"theory.":[16,41],"case":[18],"module":[20],"(i.e.,":[22],"which":[24],"are":[25],"also":[26],"modules":[27],"over":[28],"number":[30,40],"ring)":[31],"particular":[34],"interest":[35],"for":[36],"cryptography":[37],"and":[38,71],"computational":[39],"hardness":[43],"the":[49,53,62],"asymptotic":[50],"regime":[51],"where":[52],"rank":[54],"(as":[55],"module)":[57],"fixed":[59],"supporting":[61],"security":[63],"quantum-resistant":[65],"cryptographic":[66],"standards":[67],"such":[68],"as":[69],"ML-DSA":[70],"ML-KEM.":[72]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-11-19T00:00:00"}