{"id":"https://openalex.org/W3205542998","doi":null,"title":"Algorithms for Sparse Random 3XOR: The Low-Density Case","display_name":"Algorithms for Sparse Random 3XOR: The Low-Density Case","publication_year":2021,"publication_date":"2021-03-01","ids":{"openalex":"https://openalex.org/W3205542998","mag":"3205542998"},"language":"en","primary_location":{"id":"pmh:oai:HAL:hal-02306917v3","doi":null,"is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-02306917","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.archives-ouvertes.fr/hal-02306917","raw_type":"info:eu-repo/semantics/preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.archives-ouvertes.fr/hal-02306917","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054666119","display_name":"Charles Bouillaguet","orcid":"https://orcid.org/0000-0001-9416-6244","observed_orcids":["https://orcid.org/0000-0001-9416-6244"]},"institutions":[{"id":"https://openalex.org/I4387153239","display_name":"Centre de Recherche en Informatique, Signal et Automatique de Lille","ror":"https://ror.org/05vrs3189","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I2279609970","https://openalex.org/I4387153239","https://openalex.org/I7454413"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bouillaguet, Charles","raw_affiliation_strings":["ALgorithms for coMmunicAtion SecuriTY","Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ALgorithms for coMmunicAtion SecuriTY","institution_ids":[]},{"raw_affiliation_string":"Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189","institution_ids":["https://openalex.org/I4387153239"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071991273","display_name":"Claire Delaplace","orcid":"https://orcid.org/0000-0002-5314-1806","observed_orcids":["https://orcid.org/0000-0002-5314-1806"]},"institutions":[{"id":"https://openalex.org/I4401200318","display_name":"Mod\u00e9lisation, information et syst\u00e8mes","ror":"https://ror.org/05w9qrp28","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4401200318","https://openalex.org/I4647051"]},{"id":"https://openalex.org/I4647051","display_name":"Universit\u00e9 de Picardie Jules Verne","ror":"https://ror.org/01gyxrk03","country_code":"FR","type":"education","lineage":["https://openalex.org/I4647051"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Delaplace, Claire","raw_affiliation_strings":["Mod\u00e9lisation, Information et Syst\u00e8mes - UR UPJV 4290"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mod\u00e9lisation, Information et Syst\u00e8mes - UR UPJV 4290","institution_ids":["https://openalex.org/I4401200318","https://openalex.org/I4647051"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009219098","display_name":"Antoine Joux","orcid":"https://orcid.org/0000-0003-2682-6508","observed_orcids":["https://orcid.org/0000-0003-2682-6508"]},"institutions":[{"id":"https://openalex.org/I4210128801","display_name":"Helmholtz Center for Information Security","ror":"https://ror.org/02njgxr09","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I4210128801"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Joux, Antoine","raw_affiliation_strings":["Helmholtz Center for Information Security [Saarbr\u00fccken]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Helmholtz Center for Information Security [Saarbr\u00fccken]","institution_ids":["https://openalex.org/I4210128801"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.7753999829292297,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.7753999829292297,"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/T11269","display_name":"Algorithms and Data Compression","score":0.05719999969005585,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.02759999968111515,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sparse-vectors","display_name":"sparse vectors","score":0.703000009059906},{"id":"https://openalex.org/keywords/subquadratic-algorithms","display_name":"subquadratic algorithms","score":0.7990000247955322},{"id":"https://openalex.org/keywords/linear-time-algorithms","display_name":"linear-time algorithms","score":0.6579999923706055},{"id":"https://openalex.org/keywords/cryptanalysis","display_name":"cryptanalysis","score":0.5130000114440918},{"id":"https://openalex.org/keywords/hamming-weight","display_name":"Hamming weight","score":0.8180000185966492}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4527556598186493},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33814650774002075}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:HAL:hal-02306917v3","doi":null,"is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-02306917","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.archives-ouvertes.fr/hal-02306917","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:HAL:hal-02306917v4","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-02306917","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2021","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:lilloa.univ-lille.fr:20.500.12210/88788","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.12210/88788","pdf_url":null,"source":{"id":"https://openalex.org/S4306402203","display_name":"LillOA (Universit\u00e9 de Lille (University Of Lille))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210123514","host_organization_name":"Centre d'\u00c9tudes en Civilisations, Langues et Lettres \u00c9trang\u00e8res","host_organization_lineage":["https://openalex.org/I4210123514"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/workingPaper"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-02306917v3","doi":null,"is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-02306917","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.archives-ouvertes.fr/hal-02306917","raw_type":"info:eu-repo/semantics/preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4389043100","https://openalex.org/W3041117036","https://openalex.org/W2798577881","https://openalex.org/W2794563531","https://openalex.org/W2167446192","https://openalex.org/W3040656505","https://openalex.org/W4411489771","https://openalex.org/W7110454426","https://openalex.org/W4401201533","https://openalex.org/W2286119377"],"abstract_inverted_index":{"We":[0,17,41],"present":[1],"algorithms":[2,116],"for":[3,61],"variants":[4],"of":[5,12,21,36,122],"the":[6,44,73,84,92,109,118,123],"3XOR":[7,47],"problem":[8,48],"with":[9,72,104],"lists":[10],"consisting":[11],"random":[13,45],"sparse":[14,46],"$n$-bit":[15,37],"vectors.":[16],"consider":[18],"two":[19],"notions":[20],"sparsity:":[22],"low-density":[23,93],"(each":[24],"bit":[25],"is":[26,39,111],"independently":[27],"biased":[28],"towards":[29],"zero)":[30],"and":[31],"low-weight":[32],"(the":[33],"Hamming":[34],"weight":[35],"vectors":[38],"fixed).":[40],"show":[42],"that":[43],"can":[49],"be":[50],"solved":[51],"in":[52,69,101,125],"strongly":[53],"subquadratic":[54],"time,":[55],"namely":[56],"less":[57,112],"than":[58,113],"$\\\\bigO{N^{2-\\\\epsilon}}$":[59],"operations":[60],"a":[62,95],"constant":[63],"$\\\\epsilon":[64],">":[65],"0$.":[66],"This":[67],"stands":[68],"strong":[70],"contrast":[71],"regular":[74],"case,":[75],"where":[76],"it":[77],"has":[78],"not":[79],"been":[80],"possible":[81],"to":[82],"have":[83],"exponent":[85],"drop":[86],"below":[87],"$2":[88],"-":[89],"o(1)$.":[90],"In":[91],"setting,":[94],"very":[96],"simple":[97],"algorithm":[98],"even":[99],"runs":[100],"linear":[102],"time":[103],"overwhelming":[105],"success":[106],"probability":[107],"when":[108],"density":[110],"$0.0957$.":[114],"Our":[115],"exploit":[117],"randomness":[119],"(and":[120],"sparsity)":[121],"input":[124],"an":[126],"essential":[127],"way.":[128]},"counts_by_year":[],"updated_date":"2026-10-25T09:29:13.331239","created_date":"2021-10-25T00:00:00"}
