{"id":"https://openalex.org/W2936741070","doi":"https://doi.org/10.1109/tit.2019.2910070","title":"Differential Spectrum of Kasami Power Permutations Over Odd Characteristic Finite Fields","display_name":"Differential Spectrum of Kasami Power Permutations Over Odd Characteristic Finite Fields","publication_year":2019,"publication_date":"2019-04-17","ids":{"openalex":"https://openalex.org/W2936741070","doi":"https://doi.org/10.1109/tit.2019.2910070","mag":"2936741070"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2019.2910070","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2910070","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084781221","display_name":"Haode Yan","orcid":"https://orcid.org/0000-0001-8144-3433"},"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":"Haode Yan","raw_affiliation_strings":["School of Mathematics, Southwest Jiaotong University, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Southwest Jiaotong University, Chengdu, China","institution_ids":["https://openalex.org/I4800084"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004913173","display_name":"Zhengchun Zhou","orcid":"https://orcid.org/0000-0002-0228-7119"},"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":"Zhengchun Zhou","raw_affiliation_strings":["School of Mathematics, Southwest Jiaotong University, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0002-0228-7119","affiliations":[{"raw_affiliation_string":"School of Mathematics, Southwest Jiaotong University, Chengdu, China","institution_ids":["https://openalex.org/I4800084"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082041657","display_name":"Jian Weng","orcid":"https://orcid.org/0000-0003-4067-8230"},"institutions":[{"id":"https://openalex.org/I159948400","display_name":"Jinan University","ror":"https://ror.org/02xe5ns62","country_code":"CN","type":"education","lineage":["https://openalex.org/I159948400"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Weng","raw_affiliation_strings":["College of Cyber Security, Jinan University, Guangzhou, China"],"raw_orcid":"https://orcid.org/0000-0003-4067-8230","affiliations":[{"raw_affiliation_string":"College of Cyber Security, Jinan University, Guangzhou, China","institution_ids":["https://openalex.org/I159948400"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080664346","display_name":"Jinming Wen","orcid":"https://orcid.org/0000-0002-8181-0958"},"institutions":[{"id":"https://openalex.org/I159948400","display_name":"Jinan University","ror":"https://ror.org/02xe5ns62","country_code":"CN","type":"education","lineage":["https://openalex.org/I159948400"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinming Wen","raw_affiliation_strings":["College of Cyber Security, Jinan University, Guangzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-8181-0958","affiliations":[{"raw_affiliation_string":"College of Cyber Security, Jinan University, Guangzhou, China","institution_ids":["https://openalex.org/I159948400"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026698531","display_name":"Tor Helleseth","orcid":"https://orcid.org/0000-0003-1290-3541"},"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":"Tor Helleseth","raw_affiliation_strings":["Department of Informatics, University of Bergen, Bergen, Norway"],"raw_orcid":null,"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/A5063335569","display_name":"Qi Wang","orcid":"https://orcid.org/0000-0001-9780-5443"},"institutions":[{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qi Wang","raw_affiliation_strings":["Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, China","institution_ids":["https://openalex.org/I3045169105"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6943,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.88053647,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"65","issue":"10","first_page":"6819","last_page":"6826"},"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":0.9943000078201294,"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":0.9897000193595886,"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/monomial","display_name":"Monomial","score":0.8175487518310547},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5554550290107727},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5416967272758484},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5183433294296265},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46149834990501404},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.43874549865722656},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4352649450302124},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.42412081360816956},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22656464576721191}],"concepts":[{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.8175487518310547},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5554550290107727},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5416967272758484},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5183433294296265},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46149834990501404},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.43874549865722656},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4352649450302124},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.42412081360816956},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22656464576721191}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2019.2910070","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2910070","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1427926582","display_name":null,"funder_award_id":"U1736203","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G23357023","display_name":"\u65b0\u578b\u5dee\u5206\u5747\u5300\u51fd\u6570\u8bbe\u8ba1\u53ca\u5176\u76f8\u5173\u5e8f\u5217\u548c\u7f16\u7801\u7814\u7a76","funder_award_id":"61672028","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2516456528","display_name":null,"funder_award_id":"61672015","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3316746206","display_name":null,"funder_award_id":"61661146003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4515569331","display_name":"\u03b1-\u5f3a\u8870\u51cf\u7a00\u758f\u4fe1\u53f7\u91cd\u6784\u7406\u8bba\u7814\u7a76\u4e0e\u7b97\u6cd5\u8bbe\u8ba1","funder_award_id":"11871248","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4856273086","display_name":null,"funder_award_id":"11801468","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6220089879","display_name":null,"funder_award_id":"61825203","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1050485050","https://openalex.org/W1542020576","https://openalex.org/W1563907129","https://openalex.org/W1587687098","https://openalex.org/W1627303988","https://openalex.org/W1629301835","https://openalex.org/W1654806544","https://openalex.org/W1965411348","https://openalex.org/W1984812887","https://openalex.org/W2000881271","https://openalex.org/W2039170351","https://openalex.org/W2053266393","https://openalex.org/W2083108312","https://openalex.org/W2089277105","https://openalex.org/W2090147850","https://openalex.org/W2095066562","https://openalex.org/W2123695891","https://openalex.org/W2140420535","https://openalex.org/W2140487394","https://openalex.org/W2162542560","https://openalex.org/W2742188599","https://openalex.org/W2761692269"],"related_works":["https://openalex.org/W2399505800","https://openalex.org/W333749553","https://openalex.org/W1966623661","https://openalex.org/W2942288111","https://openalex.org/W2951675266","https://openalex.org/W2469327063","https://openalex.org/W1964258562","https://openalex.org/W2950511598","https://openalex.org/W1955455432","https://openalex.org/W4299961354"],"abstract_inverted_index":{"Functions":[0],"with":[1,46,110],"low":[2,47],"differential":[3,16,34,48,53,75,153],"uniformity":[4,49],"have":[5,55],"important":[6],"applications":[7],"in":[8,130],"cryptography,":[9],"coding":[10],"theory,":[11],"and":[12,50,105,148],"sequence":[13],"design.":[14],"The":[15,66],"spectrum":[17,154],"of":[18,23,33,59,68,77,121,133,155,158],"a":[19,57,142],"cryptographic":[20],"function":[21],"is":[22,71,101,107,123,161],"great":[24],"interest":[25],"for":[26],"estimating":[27],"its":[28],"resistance":[29],"to":[30,72,141],"some":[31],"variants":[32],"cryptanalysis.":[35],"Finding":[36],"power":[37,81,159],"permutations":[38,82,160],"(i.e.,":[39],"monomial":[40],"bijective":[41],"mappings)":[42],"over":[43,61,93],"finite":[44],"fields":[45],"determining":[51],"their":[52],"spectra":[54],"received":[56],"lot":[58],"attention":[60],"the":[62,74,78,131,152],"past":[63],"two":[64],"decades.":[65],"objective":[67],"this":[69,119,156],"paper":[70],"study":[73],"properties":[76],"well-known":[79],"Kasami":[80],"x":[83],"p":[84,100,134],"<sup":[85,89,95],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[86,90,96],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2k</sup>":[87],"-p":[88],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</sup>":[91],"+1":[92],"GF(p":[94],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[97],"),":[98],"where":[99],"an":[102,108,138],"odd":[103],"prime":[104],"k":[106],"integer":[109],"gcd(n,":[111],"k)":[112],"=":[113,135],"1.":[114],"It":[115],"turns":[116],"out":[117],"that":[118],"family":[120,157],"monomials":[122],"differentially":[124],"(p":[125],"+":[126],"1)-uniform.":[127],"Our":[128],"result":[129],"case":[132],"3":[136],"gives":[137],"affirmative":[139],"solution":[140],"recent":[143],"conjecture":[144],"by":[145],"Xu,":[146],"Cao,":[147],"Xu.":[149],"Most":[150],"notably,":[151],"completely":[162],"determined.":[163]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}