## Cryptology ePrint Archive: Report 2011/642

Constructing differentially 4-uniform permutations over $\mbf_{2^{2m}}$ from quadratic APN permutations over $\mbf_{2^{2m+1}}$

Yongqiang Li and Mingsheng Wang

Abstract: In this paper, by means of the idea proposed in \cite{carlet4uniformpermu}, differentially 4-uniform permutations with the best known nonlinearity over $\mbf_{2^{2m}}$ can be constructed by using quadratic APN permutations over $\mbf_{2^{2m+1}}$. Special emphasis is given for the Gold functions. The algebraic degree of the constructions and their compositional inverse is also investigated. One of the constructions and its compositional inverse have both algebraic degree $m+1$ over $\mbf_2^{2m}$.

Category / Keywords: secret-key cryptography / Permutation, Differential uniformity, Nonlinearity, Algebraic degree