{"id":"https://openalex.org/W4411066691","doi":"https://doi.org/10.3934/amc.2025025","title":"On the second-order zero differential properties of several classes of power functions over finite fields","display_name":"On the second-order zero differential properties of several classes of power functions over finite fields","publication_year":2025,"publication_date":"2025-06-05","ids":{"openalex":"https://openalex.org/W4411066691","doi":"https://doi.org/10.3934/amc.2025025"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2025025","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2025025","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=68416d02b924fa00d9d41295","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/data/article/export-pdf?id=68416d02b924fa00d9d41295","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101667791","display_name":"Huan Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huan Zhou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101507366","display_name":"Xiaoni Du","orcid":"https://orcid.org/0000-0003-3997-7196"},"institutions":[{"id":"https://openalex.org/I68986083","display_name":"Northwest Normal University","ror":"https://ror.org/00gx3j908","country_code":"CN","type":"education","lineage":["https://openalex.org/I68986083"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoni Du","raw_affiliation_strings":["College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China","institution_ids":["https://openalex.org/I68986083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111819227","display_name":"Xingbin Qiao","orcid":"https://orcid.org/0009-0007-0356-4054"},"institutions":[{"id":"https://openalex.org/I68986083","display_name":"Northwest Normal University","ror":"https://ror.org/00gx3j908","country_code":"CN","type":"education","lineage":["https://openalex.org/I68986083"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xingbin Qiao","raw_affiliation_strings":["College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China","institution_ids":["https://openalex.org/I68986083"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069058569","display_name":"Wenping Yuan","orcid":"https://orcid.org/0000-0002-1469-4395"},"institutions":[{"id":"https://openalex.org/I68986083","display_name":"Northwest Normal University","ror":"https://ror.org/00gx3j908","country_code":"CN","type":"education","lineage":["https://openalex.org/I68986083"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenping Yuan","raw_affiliation_strings":["College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China","institution_ids":["https://openalex.org/I68986083"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05311482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"0","first_page":"10","last_page":"22"},"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9994999766349792,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9979000091552734,"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/mathematics","display_name":"Mathematics","score":0.9379907846450806},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.7011610269546509},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6694393157958984},{"id":"https://openalex.org/keywords/zero-order","display_name":"Zero order","score":0.5143314599990845},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4861607253551483},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4689314663410187},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4395594000816345},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40989190340042114},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.23809781670570374},{"id":"https://openalex.org/keywords/first-order","display_name":"First order","score":0.23460063338279724},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0481128990650177}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9379907846450806},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.7011610269546509},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6694393157958984},{"id":"https://openalex.org/C2993784581","wikidata":"https://www.wikidata.org/wiki/Q8069600","display_name":"Zero order","level":3,"score":0.5143314599990845},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4861607253551483},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4689314663410187},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4395594000816345},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40989190340042114},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.23809781670570374},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.23460063338279724},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0481128990650177},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2025025","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2025025","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=68416d02b924fa00d9d41295","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2025025","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2025025","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=68416d02b924fa00d9d41295","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411066691.pdf","grobid_xml":"https://content.openalex.org/works/W4411066691.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W52191336","https://openalex.org/W1471103927","https://openalex.org/W1477086080","https://openalex.org/W1528065150","https://openalex.org/W1629301835","https://openalex.org/W1990605160","https://openalex.org/W2091168784","https://openalex.org/W2795355075","https://openalex.org/W3088488979","https://openalex.org/W3212857473","https://openalex.org/W4200466424","https://openalex.org/W4225327596","https://openalex.org/W4233487466","https://openalex.org/W4401184024","https://openalex.org/W4402228574","https://openalex.org/W4406597719","https://openalex.org/W4407254452","https://openalex.org/W4410416973"],"related_works":["https://openalex.org/W2792321351","https://openalex.org/W2011296092","https://openalex.org/W4403194573","https://openalex.org/W2351616133","https://openalex.org/W2359538068","https://openalex.org/W3104605355","https://openalex.org/W2887319909","https://openalex.org/W2061019404","https://openalex.org/W4404311502","https://openalex.org/W2108277181"],"abstract_inverted_index":{"The":[0,209],"Feistel":[1,17,58,89],"Boomerang":[2],"Connectivity":[3],"Table":[4,195],"(FBCT)":[5],"is":[6,61,115,124],"an":[7],"important":[8],"cryptanalytic":[9],"technique":[10],"on":[11],"analysing":[12],"the":[13,16,30,38,44,50,57,62,76,88,93,152,160,166,192,198,215,223],"resistance":[14],"of":[15,32,43,67,78,80,92,154,165,197,211,225,230],"network-based":[18],"ciphers":[19],"to":[20,37,221],"power":[21,94,167],"attacks":[22],"such":[23],"as":[24],"differential":[25,41,65,163,226],"and":[26,56,99,119,134,182,214,227,235],"boomerang":[27,59,90,228],"attacks.":[28],"Moreover,":[29],"coefficients":[31],"FBCT":[33],"are":[34,143],"closely":[35],"related":[36],"second-order":[39,63,161],"zero":[40,64,162],"spectrum":[42],"function":[45,168,199],"$":[46,48,68,96,98,100,102,106,110,114,120,129,133,135,137,139,141,146,169,171,173,175,179,181,183,200,202,206],"F(x)":[47,69],"over":[49,83,103,145,172,203],"finite":[51,84,104,204],"fields":[52,105,205],"with":[53,138,176],"even":[54],"characteristic":[55,178],"uniformity":[60,66,91,164],"$.":[70,122,148,188,208],"In":[71],"this":[72],"paper,":[73],"by":[74,158],"calculating":[75],"number":[77],"solutions":[79],"specific":[81],"equations":[82],"fields,":[85],"we":[86,150,190],"determine":[87],"functions":[95],"x^{2^m+3}":[97],"x^{2^m+5}":[101,136],"\\mathbb{F}_{2^n}":[107,147],"$,":[108],"where":[109],"n":[111,187],"=":[112],"2m":[113],"a":[116],"positive":[117],"integer":[118],"m>2":[121],"It":[123],"worth":[125],"noting":[126],"that":[127],"both":[128],"x^{2^m":[130],"+":[131],"3}":[132],"m":[140],"odd":[142,177],"permutations":[144],"Furthermore,":[149],"extend":[151],"work":[153],"Eddahmani":[155],"et":[156],"al.":[157],"discussing":[159],"x^{p^{k}+1}":[170],"\\mathbb{F}_{p^n}":[174],"p":[180],"1\\leq":[184],"k":[185],"<":[186],"And":[189],"give":[191],"Difference":[193],"Distribution":[194],"(DDT)":[196],"x^4":[201],"\\mathbb{F}_{3^n}":[207],"computation":[210],"these":[212],"entries":[213],"cardinalities":[216],"in":[217],"each":[218],"table":[219],"aims":[220],"facilitate":[222],"analysis":[224],"cryptanalysis":[229],"S-boxes":[231],"when":[232],"studying":[233],"distinguishers":[234],"trails.":[236]},"counts_by_year":[],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}