{"id":"https://openalex.org/W2573088679","doi":"https://doi.org/10.3233/978-1-60750-002-5-192","title":"New Results on the Algebraic Immunity of Boolean Functions","display_name":"New Results on the Algebraic Immunity of Boolean Functions","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2573088679","doi":"https://doi.org/10.3233/978-1-60750-002-5-192","mag":"2573088679"},"language":"en","primary_location":{"id":"doi:10.3233/978-1-60750-002-5-192","is_oa":false,"landing_page_url":"https://doi.org/10.3233/978-1-60750-002-5-192","pdf_url":null,"source":{"id":"https://openalex.org/S4210202636","display_name":"NATO science for peace and security series. D, Information and communication security","issn_l":"1874-6268","issn":["1874-6268","1879-8292"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"NATO Science for Peace and Security Series - D: Information and Communication Security","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/A5116320388","display_name":"Rizomiliotis Panagiotis","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Rizomiliotis Panagiotis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5116320388"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2891,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.62770401,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T11130","display_name":"Coding theory and cryptography","score":0.9919000267982483,"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":0.9919000267982483,"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/T14228","display_name":"Religion and Sociopolitical Dynamics in Nigeria","score":0.9375,"subfield":{"id":"https://openalex.org/subfields/3300","display_name":"General Social Sciences"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.5046108961105347},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.48136287927627563},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4006492793560028},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3631207346916199},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3336535394191742},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.268595427274704},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2677180767059326},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.053259193897247314}],"concepts":[{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.5046108961105347},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.48136287927627563},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4006492793560028},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3631207346916199},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3336535394191742},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.268595427274704},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2677180767059326},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.053259193897247314}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/978-1-60750-002-5-192","is_oa":false,"landing_page_url":"https://doi.org/10.3233/978-1-60750-002-5-192","pdf_url":null,"source":{"id":"https://openalex.org/S4210202636","display_name":"NATO science for peace and security series. D, Information and communication security","issn_l":"1874-6268","issn":["1874-6268","1879-8292"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"NATO Science for Peace and Security Series - D: Information and Communication Security","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.46000000834465027}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"The":[0,20,104,121],"algebraic":[1,24,39,54,116],"immunity":[2,25,117],"AI(f)":[3,102,118],"of":[4,15,18,23,41,52,60,72,75,80,90,95,129,132],"a":[5,27,87,96],"Boolean":[6,31,97],"function":[7,98],"f":[8,76,81,99],"is":[9,68,106,119],"defined":[10,56],"as":[11,57,127],"the":[12,42,50,58,69,91,115,130],"minimum":[13,70],"degree":[14,71],"all":[16,73,109],"annihilators":[17,74],"f.":[19],"high":[21],"value":[22,122],"consists":[26],"necessary":[28],"condition":[29],"for":[30],"functions":[32],"used":[33],"in":[34],"stream":[35],"ciphers":[36],"to":[37],"resist":[38],"attacks.":[40],"two":[43],"values.":[44],"In":[45],"this":[46],"paper,":[47],"we":[48],"introduce":[49,86],"notion":[51],"extended":[53],"immunity(f)":[55],"maximum":[59],"pAI(f)":[61,67],"and":[62],"pAI(f":[63],"&amp;target;":[64,78,82],"1),":[65],"where":[66,113],"(pAI(f":[77],"1)":[79],"1":[83],"respectively).":[84],"We":[85],"lower":[88,111],"bound":[89,105],"r-th":[92],"order":[93],"nonlinearity":[94],"with":[100,134],"given":[101],"and(f).":[103],"tighter":[107],"than":[108],"known":[110],"bounds,":[112],"only":[114],"used.":[120],"of(f)":[123],"can":[124],"be":[125],"computed":[126],"part":[128],"calculation":[131],"AI(f),":[133],"no":[135],"extra":[136],"computational":[137],"cost.":[138]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
