Differentially uniform mappings for cryptography
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Linear cryptanalysis method for DES cipher
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Codes, Bent Functions and Permutations Suitable For DES-likeCryptosystems
Designs, Codes and Cryptography
New Bent Mappings Suitable for Fast Implementation
Fast Software Encryption, Cambridge Security Workshop
On the classification of APN functions up to dimension five
Designs, Codes and Cryptography
A Construction of Differentially 4-Uniform Functions from Commutative Semifields of Characteristic 2
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
On the construction of bent vectorial functions
International Journal of Information and Coding Theory
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
On the construction of highly nonlinear permutations
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Determining the nonlinearity of a new family of APN functions
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
A few more quadratic APN functions
Cryptography and Communications
IEEE Transactions on Information Theory
A new APN function which is not equivalent to a power mapping
IEEE Transactions on Information Theory
Classes of Quadratic APN Trinomials and Hexanomials and Related Structures
IEEE Transactions on Information Theory
Two Classes of Quadratic APN Binomials Inequivalent to Power Functions
IEEE Transactions on Information Theory
New families of quadratic almost perfect nonlinear trinomials and multinomials
Finite Fields and Their Applications
Constructing new APN functions from known ones
Finite Fields and Their Applications
Finite Fields and Their Applications
On the construction of bent vectorial functions
International Journal of Information and Coding Theory
CCZ-equivalence of bent vectorial functions and related constructions
Designs, Codes and Cryptography
On known and new differentially uniform functions
ACISP'11 Proceedings of the 16th Australasian conference on Information security and privacy
A character theoretic approach to planar functions
Cryptography and Communications
PICARO: a block cipher allowing efficient higher-order side-channel resistance
ACNS'12 Proceedings of the 10th international conference on Applied Cryptography and Network Security
Sequences and functions derived from projective planes and their difference sets
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
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We survey the properties of two parameters introduced by C. Ding and the author for quantifying the balancedness of vectorial functions and of their derivatives. We give new results on the distribution of the values of the first parameter when applied to F + L, where F is a fixed function and L ranges over the set of linear functions: we show an upper bound on the nonlinearity of F by means of these values, we determine then the mean of these values and we show that their maximum is a nonlinearity parameter as well, we prove that the variance of these values is directly related to the second parameter. We briefly recall the known constructions of bent vectorial functions and introduce two new classes obtained with Gregor Leander. We show that bent functions can be used to build APN functions by concatenating the outputs of a bent (n, n/2)-function and of some other (n, n/2)-function. We obtain this way a general infinite class of quadratic APN functions. We show that this class contains the APN trinomials and hexanomials introduced in 2008 by L. Budaghyan and the author, and a class of APN functions introduced, in 2008 also, by Bracken et al.; this gives an explanation of the APNness of these functions and allows generalizing them. We also obtain this way the recently found Edel---Pott cubic function. We exhibit a large number of other sub-classes of APN functions. We eventually design with this same method classes of quadratic and non-quadratic differentially 4-uniform functions.