{"id":"https://openalex.org/W2770367798","doi":"https://doi.org/10.1109/iwsda.2017.8097084","title":"A lower bound on the second-order nonlinearity of the class of Maiorana-McFarland bent functions","display_name":"A lower bound on the second-order nonlinearity of the class of Maiorana-McFarland bent functions","publication_year":2017,"publication_date":"2017-09-01","ids":{"openalex":"https://openalex.org/W2770367798","doi":"https://doi.org/10.1109/iwsda.2017.8097084","mag":"2770367798"},"language":"en","primary_location":{"id":"doi:10.1109/iwsda.2017.8097084","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iwsda.2017.8097084","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 Eighth International Workshop on Signal Design and Its Applications in Communications (IWSDA)","raw_type":"proceedings-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/A5102013321","display_name":"Qi Gao","orcid":"https://orcid.org/0000-0001-6999-1517"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qi Gao","raw_affiliation_strings":["School of Mathematics, Southwest Jiaotong University, Chengdu, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Southwest Jiaotong University, Chengdu, China","institution_ids":["https://openalex.org/I4800084"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057734478","display_name":"Deng Tang","orcid":"https://orcid.org/0000-0002-8373-9200"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Deng Tang","raw_affiliation_strings":["School of Mathematics, Southwest Jiaotong University, Chengdu, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Southwest Jiaotong University, Chengdu, China","institution_ids":["https://openalex.org/I4800084"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102013321"],"corresponding_institution_ids":["https://openalex.org/I4800084"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1609823,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"54","issue":null,"first_page":"191","last_page":"195"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9976000189781189,"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":0.8507043719291687},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7544785737991333},{"id":"https://openalex.org/keywords/bent-molecular-geometry","display_name":"Bent molecular geometry","score":0.6656714677810669},{"id":"https://openalex.org/keywords/bent-function","display_name":"Bent function","score":0.6577849388122559},{"id":"https://openalex.org/keywords/stream-cipher","display_name":"Stream cipher","score":0.612302839756012},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5910376310348511},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5532073378562927},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5477811098098755},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.496114581823349},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.4779650866985321},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.44695553183555603},{"id":"https://openalex.org/keywords/block-cipher","display_name":"Block cipher","score":0.4414994716644287},{"id":"https://openalex.org/keywords/resist","display_name":"Resist","score":0.4210958480834961},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.41551411151885986},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4118887186050415},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.364702433347702},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24467375874519348},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23503020405769348},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1263067126274109},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11773636937141418},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10678640007972717},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08043289184570312}],"concepts":[{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.8507043719291687},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7544785737991333},{"id":"https://openalex.org/C138211643","wikidata":"https://www.wikidata.org/wiki/Q675211","display_name":"Bent molecular geometry","level":2,"score":0.6656714677810669},{"id":"https://openalex.org/C84185955","wikidata":"https://www.wikidata.org/wiki/Q4890350","display_name":"Bent function","level":3,"score":0.6577849388122559},{"id":"https://openalex.org/C92950451","wikidata":"https://www.wikidata.org/wiki/Q864718","display_name":"Stream cipher","level":3,"score":0.612302839756012},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5910376310348511},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5532073378562927},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5477811098098755},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.496114581823349},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.4779650866985321},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.44695553183555603},{"id":"https://openalex.org/C106544461","wikidata":"https://www.wikidata.org/wiki/Q543151","display_name":"Block cipher","level":3,"score":0.4414994716644287},{"id":"https://openalex.org/C53524968","wikidata":"https://www.wikidata.org/wiki/Q7315582","display_name":"Resist","level":3,"score":0.4210958480834961},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.41551411151885986},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4118887186050415},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.364702433347702},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24467375874519348},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23503020405769348},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1263067126274109},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11773636937141418},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10678640007972717},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08043289184570312},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C2779227376","wikidata":"https://www.wikidata.org/wiki/Q6505497","display_name":"Layer (electronics)","level":2,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/iwsda.2017.8097084","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iwsda.2017.8097084","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 Eighth International Workshop on Signal Design and Its Applications in Communications (IWSDA)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1528065150","https://openalex.org/W1575067221","https://openalex.org/W1607408212","https://openalex.org/W1629301835","https://openalex.org/W1981357736","https://openalex.org/W2004502213","https://openalex.org/W2010368681","https://openalex.org/W2024729203","https://openalex.org/W2033954829","https://openalex.org/W2078699313","https://openalex.org/W2080985333","https://openalex.org/W2090432705","https://openalex.org/W2095563835","https://openalex.org/W2101226255","https://openalex.org/W2129120739","https://openalex.org/W2136370860","https://openalex.org/W2138238405","https://openalex.org/W2159757394","https://openalex.org/W2173356534","https://openalex.org/W2228844744","https://openalex.org/W2398297263","https://openalex.org/W2504274129","https://openalex.org/W2614614073","https://openalex.org/W2920815888","https://openalex.org/W6689217805","https://openalex.org/W6712388466"],"related_works":["https://openalex.org/W2750816313","https://openalex.org/W1488498670","https://openalex.org/W1977927882","https://openalex.org/W257150968","https://openalex.org/W2754515445","https://openalex.org/W3031815368","https://openalex.org/W2139674655","https://openalex.org/W2145471026","https://openalex.org/W2946472959","https://openalex.org/W4390188610"],"abstract_inverted_index":{"Boolean":[0,42,82],"functions":[1,43,125,145],"used":[2],"in":[3,35,49,126],"stream":[4],"ciphers":[5,8],"and":[6,19,31,74,112,152],"block":[7],"should":[9],"have":[10],"high":[11],"second-order":[12,39,62,79,94,122,141],"nonlinearity":[13,40,80,95,123,142],"to":[14,72,76],"resist":[15],"several":[16],"known":[17,117],"attacks":[18,22],"some":[20],"potential":[21],"which":[23,146],"may":[24],"exist":[25],"but":[26],"are":[27],"not":[28],"yet":[29],"efficient":[30],"might":[32],"be":[33],"improved":[34],"the":[36,57,61,78,93,97,121,127,140,144],"future.":[37],"The":[38],"of":[41,60,81,96,99,106,124,129,143],"also":[44,134],"play":[45],"an":[46],"important":[47],"role":[48],"coding":[50],"theory,":[51],"since":[52],"its":[53],"maximal":[54],"value":[55],"equals":[56],"covering":[58],"radius":[59],"Reed-Muller":[63],"code.":[64],"But":[65],"it":[66],"is":[67],"a":[68,89,136],"extremely":[69],"hard":[70],"task":[71],"calculate":[73],"even":[75],"bound":[77,91,138],"functions.":[83,103,132],"In":[84],"this":[85],"paper,":[86],"we":[87,109],"present":[88],"lower":[90,118,137],"on":[92,120,139],"class":[98,128],"Maiorana-McFarland":[100],"(M-M)":[101],"bent":[102,131,149],"As":[104],"applications":[105],"our":[107,162],"bound,":[108],"provide":[110],"simpler":[111],"direct":[113],"proofs":[114],"for":[115],"two":[116],"bounds":[119],"M-M":[130],"We":[133],"derive":[135],"were":[147],"conjectured":[148],"by":[150,157,159],"Canteaut":[151],"whose":[153],"bentness":[154],"was":[155],"proved":[156],"Leander,":[158],"further":[160],"employing":[161],"bound.":[163]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}