Geodesic
A method of construction of differentially $4$-uniform permutations over $V_{m}$ for even $m$
Diskretnaya Matematika, Tome 31 (2019) no. 2, pp. 69-76

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A generalization of the method of C. Carlet for constructing differentially 4-uniform permutations of binary vector spaces in even dimension $2k$ is suggested. It consists in restricting APN-functions in $2k+1$ variables to a linear manifold of dimension $2k$. The general construction of the method is proposed and a criterion for its applicability is established. Power permutations to which this construction is applicable are completely described and a class of suitable not one-to-one functions is presented.
Keywords: vector space, binary vector, finite field, transformation, permutation, differential uniformity, nonlinearity. 
@article{DM_2019_31_2_a5,
     author = {S. A. Davydov and I. A. Kruglov},
     title = {A method of construction of differentially $4$-uniform permutations over $V_{m}$ for even $m$},
     journal = {Diskretnaya Matematika},
     pages = {69--76},
     publisher = {mathdoc},
     volume = {31},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2019_31_2_a5/}
}
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S. A. Davydov; I. A. Kruglov. A method of construction of differentially $4$-uniform permutations over $V_{m}$ for even $m$. Diskretnaya Matematika, Tome 31 (2019) no. 2, pp. 69-76. http://geodesic.mathdoc.fr/item/DM_2019_31_2_a5/