{"id":"https://openalex.org/W2030944258","doi":"https://doi.org/10.1007/978-3-540-39887-5_20","title":"Linear Approximations of Addition Modulo 2 n","display_name":"Linear Approximations of Addition Modulo 2 n","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2030944258","doi":"https://doi.org/10.1007/978-3-540-39887-5_20","mag":"2030944258"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-39887-5_20","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-540-39887-5_20","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-540-39887-5_20.pdf","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":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-540-39887-5_20.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049708338","display_name":"Johan Wall\u00e9n","orcid":null},"institutions":[{"id":"https://openalex.org/I2800229700","display_name":"Helsinki Institute of Physics","ror":"https://ror.org/01x2x1522","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I2800229700","https://openalex.org/I63548447","https://openalex.org/I94722563","https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Johan Wall\u00e9n","raw_affiliation_strings":["Laboratory for Theoretical Computer Science, Helsinki University of Technology, P.O.Box 5400, FIN-02015 HUT, Espoo, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Theoretical Computer Science, Helsinki University of Technology, P.O.Box 5400, FIN-02015 HUT, Espoo, Finland","institution_ids":["https://openalex.org/I2800229700"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049708338"],"corresponding_institution_ids":["https://openalex.org/I2800229700"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":2.764,"has_fulltext":true,"cited_by_count":60,"citation_normalized_percentile":{"value":0.91048144,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"261","last_page":"273"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9998999834060669,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9998999834060669,"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":0.9995999932289124,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/modulo","display_name":"Modulo","score":0.914596438407898},{"id":"https://openalex.org/keywords/linear-approximation","display_name":"Linear approximation","score":0.5851898193359375},{"id":"https://openalex.org/keywords/approximations-of-\u03c0","display_name":"Approximations of \u03c0","score":0.5605369210243225},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4920887351036072},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48060914874076843},{"id":"https://openalex.org/keywords/correlation-coefficient","display_name":"Correlation coefficient","score":0.4669032692909241},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.46485435962677},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4559711515903473},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4364979565143585},{"id":"https://openalex.org/keywords/carry","display_name":"Carry (investment)","score":0.41447246074676514},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35242223739624023},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.263547420501709},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10454261302947998},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07090327143669128}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.914596438407898},{"id":"https://openalex.org/C160824197","wikidata":"https://www.wikidata.org/wiki/Q2071054","display_name":"Linear approximation","level":3,"score":0.5851898193359375},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.5605369210243225},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4920887351036072},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48060914874076843},{"id":"https://openalex.org/C2780092901","wikidata":"https://www.wikidata.org/wiki/Q3433612","display_name":"Correlation coefficient","level":2,"score":0.4669032692909241},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.46485435962677},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4559711515903473},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4364979565143585},{"id":"https://openalex.org/C2776299755","wikidata":"https://www.wikidata.org/wiki/Q432449","display_name":"Carry (investment)","level":2,"score":0.41447246074676514},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35242223739624023},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.263547420501709},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10454261302947998},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07090327143669128},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-39887-5_20","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-540-39887-5_20","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-540-39887-5_20.pdf","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":{"id":"doi:10.1007/978-3-540-39887-5_20","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-540-39887-5_20","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-540-39887-5_20.pdf","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2030944258.pdf","grobid_xml":"https://content.openalex.org/works/W2030944258.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W68065621","https://openalex.org/W380217570","https://openalex.org/W1485064528","https://openalex.org/W1504341594","https://openalex.org/W1526619693","https://openalex.org/W1546257376","https://openalex.org/W1596830200","https://openalex.org/W1601793793","https://openalex.org/W1607372077","https://openalex.org/W1926480282","https://openalex.org/W1964723977","https://openalex.org/W1979802565","https://openalex.org/W2024729203","https://openalex.org/W2053679678","https://openalex.org/W2105451999","https://openalex.org/W2137326899","https://openalex.org/W2144931885","https://openalex.org/W2172632525","https://openalex.org/W2241203062","https://openalex.org/W2482045774","https://openalex.org/W2485204867","https://openalex.org/W2495889793","https://openalex.org/W2499605333","https://openalex.org/W3142558777","https://openalex.org/W3145042860","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2117548279","https://openalex.org/W2070252991","https://openalex.org/W2807449856","https://openalex.org/W2007109664","https://openalex.org/W1966076495","https://openalex.org/W1966829720","https://openalex.org/W2064780056","https://openalex.org/W170069669","https://openalex.org/W1994648914","https://openalex.org/W2985787798"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}
