{"id":"https://openalex.org/W2117672015","doi":"https://doi.org/10.1007/11779360_11","title":"On the Non-linearity and Sparsity of Boolean Functions Related to the Discrete Logarithm in Finite Fields of Characteristic Two","display_name":"On the Non-linearity and Sparsity of Boolean Functions Related to the Discrete Logarithm in Finite Fields of Characteristic Two","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2117672015","doi":"https://doi.org/10.1007/11779360_11","mag":"2117672015"},"language":"en","primary_location":{"id":"doi:10.1007/11779360_11","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11779360_11","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":"conference-paper","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/A5082952892","display_name":"Nina Brandst\u00e4tter","orcid":null},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"government","lineage":["https://openalex.org/I138211613"]},{"id":"https://openalex.org/I4210158379","display_name":"Johann Radon Institute for Computational and Applied Mathematics","ror":"https://ror.org/05a94k872","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Nina Brandst\u00e4tter","raw_affiliation_strings":["Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstra\u00dfe 69, A-4040, Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstra\u00dfe 69, A-4040, Linz, Austria","institution_ids":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016164029","display_name":"Tanja Lange","orcid":null},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Tanja Lange","raw_affiliation_strings":["Department of Mathematics, Technical University of Denmark, Matematiktorvet \u2013 Bygning 303, DK-2800, Kongens Lyngby, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technical University of Denmark, Matematiktorvet \u2013 Bygning 303, DK-2800, Kongens Lyngby, Denmark","institution_ids":["https://openalex.org/I96673099"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056642780","display_name":"Arne Winterhof","orcid":"https://orcid.org/0000-0002-3863-1110"},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"government","lineage":["https://openalex.org/I138211613"]},{"id":"https://openalex.org/I4210158379","display_name":"Johann Radon Institute for Computational and Applied Mathematics","ror":"https://ror.org/05a94k872","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Arne Winterhof","raw_affiliation_strings":["Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstra\u00dfe 69, A-4040, Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstra\u00dfe 69, A-4040, Linz, Austria","institution_ids":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.7328,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.69139605,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"135","last_page":"143"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","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/T11130","display_name":"Coding theory and cryptography","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/T11435","display_name":"Polynomial and algebraic computation","score":0.9896000027656555,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9842000007629395,"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/discrete-logarithm","display_name":"Discrete logarithm","score":0.9069924354553223},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.8591791391372681},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6964958310127258},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.6193570494651794},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6177459359169006},{"id":"https://openalex.org/keywords/iterated-logarithm","display_name":"Iterated logarithm","score":0.5824121832847595},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.5227532386779785},{"id":"https://openalex.org/keywords/linearity","display_name":"Linearity","score":0.4870064854621887},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47944751381874084},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4793887138366699},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4523712694644928},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4156484603881836},{"id":"https://openalex.org/keywords/character","display_name":"Character (mathematics)","score":0.4144393801689148},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35164564847946167},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34779471158981323},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.25172746181488037},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25002962350845337},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15998387336730957}],"concepts":[{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.9069924354553223},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.8591791391372681},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6964958310127258},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.6193570494651794},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6177459359169006},{"id":"https://openalex.org/C130594498","wikidata":"https://www.wikidata.org/wiki/Q2028293","display_name":"Iterated logarithm","level":3,"score":0.5824121832847595},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.5227532386779785},{"id":"https://openalex.org/C77170095","wikidata":"https://www.wikidata.org/wiki/Q1753188","display_name":"Linearity","level":2,"score":0.4870064854621887},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47944751381874084},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4793887138366699},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4523712694644928},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4156484603881836},{"id":"https://openalex.org/C2780861071","wikidata":"https://www.wikidata.org/wiki/Q1062934","display_name":"Character (mathematics)","level":2,"score":0.4144393801689148},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35164564847946167},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34779471158981323},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.25172746181488037},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25002962350845337},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15998387336730957},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"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/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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":3,"locations":[{"id":"doi:10.1007/11779360_11","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11779360_11","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"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/fa800d86-eec1-41aa-913c-051ef6a784f5","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/fa800d86-eec1-41aa-913c-051ef6a784f5","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e 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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Brandst\u00e4tter, N, Lange, T & Winterhof, A 2006, On the non-linearity and sparsity of Boolean functions related to the discrete logarithm in finite fields of characteristic two. in \u00d8 Ytrehus (ed.), Coding and cryptography international workshop, WCC'05, Bergen, Norway, March 14-18, 2005 : revised selected papers). Lecture Notes in Computer Science, vol. 3969, Springer, Berlin, pp. 135-143. https://doi.org/10.1007/11779360_11","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:tue:oai:pure.tue.nl:publications/fa800d86-eec1-41aa-913c-051ef6a784f5","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/fa800d86-eec1-41aa-913c-051ef6a784f5","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Coding and cryptography international workshop, WCC'05, Bergen, Norway, March 14-18, 2005 : revised selected papers), 135 - 143","raw_type":"info:eu-repo/semantics/conferencepaper"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W574604760","https://openalex.org/W1489774662","https://openalex.org/W1535052429","https://openalex.org/W1551926475","https://openalex.org/W1552757548","https://openalex.org/W1660562555","https://openalex.org/W1746229377","https://openalex.org/W1868652766","https://openalex.org/W2011798878","https://openalex.org/W2021094554","https://openalex.org/W2024900297","https://openalex.org/W2051450362","https://openalex.org/W2067307917","https://openalex.org/W2069148963","https://openalex.org/W2121176021","https://openalex.org/W2168756922","https://openalex.org/W2505065913","https://openalex.org/W2798742957","https://openalex.org/W4289127653"],"related_works":["https://openalex.org/W2514478013","https://openalex.org/W1570515303","https://openalex.org/W2117672015","https://openalex.org/W2469028681","https://openalex.org/W3032525096","https://openalex.org/W2258836937","https://openalex.org/W2031636522","https://openalex.org/W2067307917","https://openalex.org/W2378553768","https://openalex.org/W109915809"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}