{"title":"Wan-Lidl多项式微分均匀性的界","authors":"Li-An Chen, Robert S. Coulter","doi":"10.1007/s12095-023-00634-6","DOIUrl":null,"url":null,"abstract":"We study the differential uniformity of the Wan-Lidl polynomials over finite fields. A general upper bound, independent of the order of the field, is established. Additional bounds are established in settings where one of the parameters is restricted. In particular, we establish a class of permutation polynomials which have differential uniformity at most 5 over fields of order 3 mod 4, irrespective of the field size. Computational results are also given.","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"469 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bounds on the differential uniformity of the Wan-Lidl polynomials\",\"authors\":\"Li-An Chen, Robert S. Coulter\",\"doi\":\"10.1007/s12095-023-00634-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the differential uniformity of the Wan-Lidl polynomials over finite fields. A general upper bound, independent of the order of the field, is established. Additional bounds are established in settings where one of the parameters is restricted. In particular, we establish a class of permutation polynomials which have differential uniformity at most 5 over fields of order 3 mod 4, irrespective of the field size. Computational results are also given.\",\"PeriodicalId\":10788,\"journal\":{\"name\":\"Cryptography and Communications\",\"volume\":\"469 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-03-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Cryptography and Communications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s12095-023-00634-6\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cryptography and Communications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s12095-023-00634-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Bounds on the differential uniformity of the Wan-Lidl polynomials
We study the differential uniformity of the Wan-Lidl polynomials over finite fields. A general upper bound, independent of the order of the field, is established. Additional bounds are established in settings where one of the parameters is restricted. In particular, we establish a class of permutation polynomials which have differential uniformity at most 5 over fields of order 3 mod 4, irrespective of the field size. Computational results are also given.
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