English

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}
}

Comments

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R2 v1 2026-06-28T10:22:06.462Z