Linear cryptanalysis method for DES cipher
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Finite fields
Characterization of Linear Structures
Designs, Codes and Cryptography
On a Class of Permutation Polynomials over $\mathbb{F}_{2^n}$
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
A note on a class of quadratic permutations over F2n
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
On known and new differentially uniform functions
ACISP'11 Proceedings of the 16th Australasian conference on Information security and privacy
The weights of the orthogonals of the extended quadratic binary Goppa codes
IEEE Transactions on Information Theory
Constructing new APN functions from known ones
Finite Fields and Their Applications
When does G(x )+γTr(H(x)) permute Fpn?
Finite Fields and Their Applications
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Differentially 4-uniform permutations over ${\mathbb F}_{2^{2k}}$, especially those with high nonlinearity and high algebraic degree, are cryptographically significant mappings as they are good choices for the substitution boxes (S-boxes) in many symmetric ciphers. For instance, the currently endorsed Advanced Encryption Standard (AES) uses the inverse function, which is a differentially 4-uniform permutation. However, up to now, there are only five known infinite families of such mappings which attain the known maximal nonlinearity. Most of these five families have small algebraic degrees and only one family can be defined over ${\mathbb F}_{2^{2k}}$ for any positive integer k. In this paper, we apply the powerful switching method on the five known families to construct differentially 4-uniform permutations. New infinite families of such permutations are discovered from the inverse function, and some sporadic examples are found from the others by using a computer. All newly found infinite families can be defined over fields ${\mathbb F}_{2^{2k}}$ for any k and their algebraic degrees are 2k−1. Furthermore, we obtain a lower bound for the nonlinearity of one infinite family.