Constructing differentially 4-uniform permutations over GF(22m ) from quadratic APN permutations over GF(22m+1)

作者：Li Y; Wang M^*

来源：Designs, Codes, and Cryptography, 2014, 72(2): 249-264.

DOI：10.1007/s10623-012-9760-9

• Algebraic degree
• Differential uniformity
• Nonlinearity
• Permutation

In this paper, by means of the idea proposed by Carlet (ACISP 1-15, 2011), differentially 4-uniform permutations with the best known nonlinearity over F22m are constructed using quadratic APN permutations over F22m+1. Special constructions are given using the Gold functions. The algebraic degree of the constructions and their compositional inverses is also investigated. One construction and its compositional inverse both have algebraic degree m + 1 over F222m.