{"id":"https://openalex.org/W4226062812","doi":"https://doi.org/10.1109/tit.2022.3157810","title":"Two New Families of Quadratic APN Functions","display_name":"Two New Families of Quadratic APN Functions","publication_year":2022,"publication_date":"2022-03-08","ids":{"openalex":"https://openalex.org/W4226062812","doi":"https://doi.org/10.1109/tit.2022.3157810"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3157810","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3157810","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hdl.handle.net/11250/3062133","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073722882","display_name":"Kangquan Li","orcid":"https://orcid.org/0000-0002-6708-2309"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Kangquan Li","raw_affiliation_strings":["College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, China"],"raw_orcid":"https://orcid.org/0000-0002-6708-2309","affiliations":[{"raw_affiliation_string":"College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039613345","display_name":"Yue Zhou","orcid":"https://orcid.org/0000-0003-4134-4240"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yue Zhou","raw_affiliation_strings":["College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100341684","display_name":"Chunlei Li","orcid":"https://orcid.org/0000-0002-3792-769X"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Chunlei Li","raw_affiliation_strings":["Department of Informatics, University of Bergen, Bergen, Norway"],"raw_orcid":"https://orcid.org/0000-0002-3792-769X","affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071414491","display_name":"Longjiang Qu","orcid":"https://orcid.org/0000-0003-3506-5501"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Longjiang Qu","raw_affiliation_strings":["College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, China"],"raw_orcid":"https://orcid.org/0000-0003-3506-5501","affiliations":[{"raw_affiliation_string":"College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, China","institution_ids":["https://openalex.org/I170215575"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5073722882"],"corresponding_institution_ids":["https://openalex.org/I170215575"],"apc_list":null,"apc_paid":null,"fwci":1.2486,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.82626447,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"68","issue":"7","first_page":"4761","last_page":"4769"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"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":0.9997000098228455,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9764999747276306,"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/T12505","display_name":"Peptidase Inhibition and Analysis","score":0.9614999890327454,"subfield":{"id":"https://openalex.org/subfields/2730","display_name":"Oncology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.6343289613723755},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47744685411453247},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45230722427368164},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3695979118347168},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3583782911300659},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.16596081852912903},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.150092214345932}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6343289613723755},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47744685411453247},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45230722427368164},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3695979118347168},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3583782911300659},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.16596081852912903},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.150092214345932}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2022.3157810","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3157810","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:bora.uib.no:11250/3062133","is_oa":true,"landing_page_url":"https://hdl.handle.net/11250/3062133","pdf_url":null,"source":{"id":"https://openalex.org/S4306401716","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:bora.uib.no:11250/3062133","is_oa":true,"landing_page_url":"https://hdl.handle.net/11250/3062133","pdf_url":null,"source":{"id":"https://openalex.org/S4306401716","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4380357292","display_name":null,"funder_award_id":"2019JJ30030","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G4486442923","display_name":null,"funder_award_id":"311646/O70","funder_id":"https://openalex.org/F4320323299","funder_display_name":"Norges Forskningsr\u00e5d"},{"id":"https://openalex.org/G4882583639","display_name":null,"funder_award_id":"62172427","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G503565750","display_name":null,"funder_award_id":"247742/O70","funder_id":"https://openalex.org/F4320323299","funder_display_name":"Norges Forskningsr\u00e5d"},{"id":"https://openalex.org/G6087505638","display_name":null,"funder_award_id":"62171479","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6816960198","display_name":null,"funder_award_id":"62032009","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null},{"id":"https://openalex.org/F4320323299","display_name":"Norges Forskningsr\u00e5d","ror":"https://ror.org/00epmv149"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W606334457","https://openalex.org/W1571322537","https://openalex.org/W1587687098","https://openalex.org/W1629301835","https://openalex.org/W1976677460","https://openalex.org/W2000906083","https://openalex.org/W2015894712","https://openalex.org/W2024156986","https://openalex.org/W2024483577","https://openalex.org/W2038924129","https://openalex.org/W2048462185","https://openalex.org/W2087896741","https://openalex.org/W2100083939","https://openalex.org/W2105125691","https://openalex.org/W2113845537","https://openalex.org/W2142619926","https://openalex.org/W2163447078","https://openalex.org/W2300471066","https://openalex.org/W2610262450","https://openalex.org/W2907090938","https://openalex.org/W3007804260","https://openalex.org/W3034599416","https://openalex.org/W3038797792","https://openalex.org/W3122760994","https://openalex.org/W3160379239","https://openalex.org/W3191395119","https://openalex.org/W3198570572","https://openalex.org/W3210873239","https://openalex.org/W4210358954","https://openalex.org/W4226341792","https://openalex.org/W4394034396","https://openalex.org/W6631450893","https://openalex.org/W6787031549","https://openalex.org/W6789043600","https://openalex.org/W6863660097","https://openalex.org/W7028540190"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2504004674","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"In":[0,155],"this":[1],"paper,":[2],"we":[3,143],"present":[4],"two":[5,147,158,162],"new":[6,159],"families":[7,148,160],"of":[8,47,60,101,121],"APN":[9,61,102,124,165],"functions.":[10],"The":[11,67],"first":[12],"family":[13,59,78,100],"is":[14,41],"in":[15,191,198],"bivariate":[16],"form":[17,49,81],"<inline-formula":[18,32,50,68,82,89,113,127,135,168,176],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[19,33,51,69,83,90,114,128,136,169,177],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[20,34,52,70,84,91,115,129,137,170,178],"<tex-math":[21,35,53,71,85,92,116,130,138,171,179],"notation=\"LaTeX\">$\\big":[22],"(x^{3}+xy^{2}+":[23],"y^{3}+xy,":[24],"x^{5}+x^{4}y+y^{5}+xy+x^{2}y^{2}":[25],"\\big)\\,\\,\\vphantom":[26],"{_{\\int":[27,73],"_{\\int":[28,74],"}}}$":[29,75],"</tex-math></inline-formula>":[30,38,56,76,87,95,119,133,141,174,182],"over":[31,88,126,167],"notation=\"LaTeX\">${\\mathbb":[36,93,131,139,172,180],"F}_{2^{m}}^{2}$":[37],".":[39],"It":[40],"obtained":[42],"by":[43,65,104,187,194],"adding":[44],"certain":[45],"terms":[46],"the":[48,80,112,122,146,157],"notation=\"LaTeX\">$\\sum":[54],"_{i}(a_{i}x^{2^{i}}y^{2^{i}},b_{i}x^{2^{i}}y^{2^{i}})$":[55],"to":[57,151],"a":[58,99],"functions":[62,103,125],"recently":[63],"proposed":[64],"G\u00f6lo&gcaron;lu.":[66],"notation=\"LaTeX\">$\\vphantom":[72],"second":[77],"has":[79],"notation=\"LaTeX\">$L(z)^{2^{m}+1}+vz^{2^{m}+1}$":[86],"F}_{{2^{3m}}}$":[94],",":[96,142,183],"which":[97,184],"generalizes":[98],"Bracken":[105],"et":[106],"al.":[107],"from":[108],"2011.":[109],"By":[110],"calculating":[111],"notation=\"LaTeX\">$\\Gamma":[117],"$":[118],"-rank":[120],"constructed":[123],"F}_{2^{8}}$":[132,173],"and":[134,175,189,193,196],"F}_{2^{9}}$":[140,181],"demonstrate":[144],"that":[145],"are":[149],"CCZ-inequivalent":[150],"all":[152],"known":[153,163],"families.":[154],"addition,":[156],"cover":[161],"sporadic":[164],"instances":[166],"were":[185],"found":[186],"Edel":[188],"Pott":[190],"2009":[192],"Beierle":[195],"Leander":[197],"2021,":[199],"respectively.":[200]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
