On APN functions and their derivatives. (arXiv:2305.00582v1 [cs.CR])

We determine a connection between the weight of a Boolean function and the
total weight of its first-order derivatives. The relationship established is
used to study some cryptographic properties of Boolean functions. We establish
a characterization of APN permutations in terms of the weight of the
first-order derivatives of their components. We also characterize APN functions
by the total weight of the second-order derivatives of their components. The
total weight of the first-order and second-order derivatives for functions such
as …

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