On APN functions and their derivatives
Cryptography and Security
2023-05-02 v1
Abstract
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 permutations, bent, partially-bent, quadratic, plateaued and balanced functions is determined.
Keywords
Cite
@article{arxiv.2305.00582,
title = {On APN functions and their derivatives},
author = {Augustine Musukwa},
journal= {arXiv preprint arXiv:2305.00582},
year = {2023}
}
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