{"id":"https://openalex.org/W26461435","doi":"https://doi.org/10.1007/978-3-642-39059-3_9","title":"Better Lattice Constructions for Solving Multivariate Linear Equations Modulo Unknown Divisors","display_name":"Better Lattice Constructions for Solving Multivariate Linear Equations Modulo Unknown Divisors","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W26461435","doi":"https://doi.org/10.1007/978-3-642-39059-3_9","mag":"26461435"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-39059-3_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-39059-3_9","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5102969111","display_name":"Atsushi Takayasu","orcid":"https://orcid.org/0000-0002-9310-6976"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Atsushi Takayasu","raw_affiliation_strings":["The University of Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"The University of Tokyo, Japan","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000629127","display_name":"Noboru Kunihiro","orcid":"https://orcid.org/0000-0003-1822-7476"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Noboru Kunihiro","raw_affiliation_strings":["The University of Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"The University of Tokyo, Japan","institution_ids":["https://openalex.org/I74801974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102969111"],"corresponding_institution_ids":["https://openalex.org/I74801974"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":4.4129,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.94898377,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"118","last_page":"135"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":1.0,"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":1.0,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994999766349792,"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/univariate","display_name":"Univariate","score":0.7484763860702515},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5601323246955872},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.4985954761505127},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4933835566043854},{"id":"https://openalex.org/keywords/cryptanalysis","display_name":"Cryptanalysis","score":0.4705900251865387},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.46284621953964233},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4576493799686432},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41211003065109253},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3810310959815979},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3265668749809265},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.24607375264167786},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16259706020355225},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08652591705322266}],"concepts":[{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.7484763860702515},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5601323246955872},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.4985954761505127},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4933835566043854},{"id":"https://openalex.org/C181149355","wikidata":"https://www.wikidata.org/wiki/Q897511","display_name":"Cryptanalysis","level":3,"score":0.4705900251865387},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.46284621953964233},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4576493799686432},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41211003065109253},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3810310959815979},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3265668749809265},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.24607375264167786},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16259706020355225},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08652591705322266},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-39059-3_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-39059-3_9","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W10068438","https://openalex.org/W55292937","https://openalex.org/W94103598","https://openalex.org/W185651473","https://openalex.org/W1489183424","https://openalex.org/W1490771242","https://openalex.org/W1497981337","https://openalex.org/W1549588538","https://openalex.org/W1550863203","https://openalex.org/W1553510179","https://openalex.org/W1749471906","https://openalex.org/W1817126074","https://openalex.org/W1932252878","https://openalex.org/W1948403713","https://openalex.org/W2001896591","https://openalex.org/W2019689629","https://openalex.org/W2070423893","https://openalex.org/W2101040389","https://openalex.org/W2103702084","https://openalex.org/W2103832773","https://openalex.org/W2107475014","https://openalex.org/W2141040012","https://openalex.org/W2144862055","https://openalex.org/W2153886246","https://openalex.org/W2156030242","https://openalex.org/W2159181323","https://openalex.org/W3125094869"],"related_works":["https://openalex.org/W1828158523","https://openalex.org/W2049578243","https://openalex.org/W2000145235","https://openalex.org/W2122079181","https://openalex.org/W1985848810","https://openalex.org/W2889939530","https://openalex.org/W3121881699","https://openalex.org/W2748838164","https://openalex.org/W2066015000","https://openalex.org/W2912721996"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":6}],"updated_date":"2026-01-15T23:16:33.117629","created_date":"2025-10-10T00:00:00"}