{"id":"https://openalex.org/W1822635470","doi":"https://doi.org/10.1142/s0129054115500306","title":"Two Boolean Functions with Five-Valued Walsh Spectra and High Nonlinearity","display_name":"Two Boolean Functions with Five-Valued Walsh Spectra and High Nonlinearity","publication_year":2015,"publication_date":"2015-08-01","ids":{"openalex":"https://openalex.org/W1822635470","doi":"https://doi.org/10.1142/s0129054115500306","mag":"1822635470"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054115500306","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054115500306","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"},"type":"article","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/A5026635882","display_name":"Xiwang Cao","orcid":"https://orcid.org/0000-0002-6950-8588"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiwang Cao","raw_affiliation_strings":["Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu Province 210016, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu Province 210016, P. R. China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034965387","display_name":"Lei Hu","orcid":"https://orcid.org/0000-0002-9920-5342"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Hu","raw_affiliation_strings":["State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100039, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100039, P. R. China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1078,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.90339095,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"26","issue":"05","first_page":"537","last_page":"556"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9987000226974487,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9983999729156494,"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/boolean-function","display_name":"Boolean function","score":0.7735543251037598},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.6617083549499512},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.6045398116111755},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5934146046638489},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5629532933235168},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5352846384048462},{"id":"https://openalex.org/keywords/confusion","display_name":"Confusion","score":0.5031716227531433},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.47725412249565125},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.471633642911911},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46795570850372314},{"id":"https://openalex.org/keywords/boolean-algebra","display_name":"Boolean algebra","score":0.41252508759498596},{"id":"https://openalex.org/keywords/parity-function","display_name":"Parity function","score":0.412234365940094},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.29358798265457153},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22126376628875732},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21862000226974487},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09578129649162292},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08924904465675354}],"concepts":[{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.7735543251037598},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.6617083549499512},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.6045398116111755},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5934146046638489},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5629532933235168},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5352846384048462},{"id":"https://openalex.org/C2781140086","wikidata":"https://www.wikidata.org/wiki/Q557945","display_name":"Confusion","level":2,"score":0.5031716227531433},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.47725412249565125},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.471633642911911},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46795570850372314},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.41252508759498596},{"id":"https://openalex.org/C188183281","wikidata":"https://www.wikidata.org/wiki/Q2898309","display_name":"Parity function","level":4,"score":0.412234365940094},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.29358798265457153},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22126376628875732},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21862000226974487},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09578129649162292},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08924904465675354},{"id":"https://openalex.org/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C11171543","wikidata":"https://www.wikidata.org/wiki/Q41630","display_name":"Psychoanalysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0129054115500306","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054115500306","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.746.7782","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.746.7782","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1406.4567.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322438","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1499506103","https://openalex.org/W1522714351","https://openalex.org/W1540809269","https://openalex.org/W1556690101","https://openalex.org/W1571032422","https://openalex.org/W1964723977","https://openalex.org/W2005235240","https://openalex.org/W2021094554","https://openalex.org/W2070084604","https://openalex.org/W2087838526","https://openalex.org/W2089277105","https://openalex.org/W2090432705","https://openalex.org/W2093311925","https://openalex.org/W2112846031","https://openalex.org/W2123715782","https://openalex.org/W2126085612","https://openalex.org/W2129190177","https://openalex.org/W2138238405","https://openalex.org/W2144580888","https://openalex.org/W2161517294","https://openalex.org/W2164701364","https://openalex.org/W2504274129","https://openalex.org/W2911452795","https://openalex.org/W3151140615","https://openalex.org/W4254374678","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2234833091","https://openalex.org/W98542587","https://openalex.org/W2379318067","https://openalex.org/W2037737738","https://openalex.org/W353786736","https://openalex.org/W2465207115","https://openalex.org/W2107037376","https://openalex.org/W2375859531","https://openalex.org/W4234182517","https://openalex.org/W1993714627"],"abstract_inverted_index":{"For":[0],"cryptographic":[1,29],"systems":[2],"the":[3,28,48,51],"method":[4,55],"of":[5,23,50],"confusion":[6],"and":[7,44],"diffusion":[8],"is":[9,19,64],"used":[10],"as":[11],"a":[12,53],"fundamental":[13],"technique":[14],"to":[15],"achieve":[16],"security.":[17],"Confusion":[18],"reflected":[20],"in":[21],"nonlinearity":[22],"certain":[24],"Boolean":[25,37],"functions":[26,38],"describing":[27],"transformation.":[30],"In":[31,47],"this":[32],"paper,":[33],"we":[34],"present":[35],"two":[36],"which":[39],"have":[40],"low":[41],"Walsh":[42],"spectra":[43],"high":[45],"nonlinearity.":[46],"proof":[49],"nonlinearity,":[52],"new":[54],"for":[56],"evaluating":[57],"some":[58],"exponential":[59],"sums":[60],"over":[61],"finite":[62],"fields":[63],"provided.":[65]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
