an:06309137
Zbl 1319.94077
Li, Yongqiang; Wang, Mingsheng
Constructing differentially 4-uniform permutations over \(\mathrm{GF}(2^{2m})\) from quadratic APN permutations over \(\mathrm{GF}(2^{2m+1})\)
EN
Des. Codes Cryptography 72, No. 2, 249-264 (2014).
00333355
2014
j
94A60 06E30 11T06
permutation; differential uniformity; nonlinearity; algebraic degree
Summary: In this paper, by means of the idea proposed by \textit{C. Carlet} [ACISP 2011, Lect. Notes Comput. Sci. 6812, 1--15 (2011; Zbl 1279.94060)], differentially 4-uniform permutations with the best known nonlinearity over \(\mathbb{F}_{2^{2m}}\) are constructed using quadratic APN permutations over \(\mathbb{F}_{2^{2m+1}}\). 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 \(\mathbb{F}_2^{2m}\).
Zbl 1279.94060