[Resource Topic] 2024/1778: Construction of quadratic APN functions with coefficients in $\mathbb{F}_2$ in dimensions $10$ and $11$

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Title:
Construction of quadratic APN functions with coefficients in \mathbb{F}_2 in dimensions 10 and 11

Authors: Yuyin Yu, Jingchen Li, Nadiia Ichanska, Nikolay Kaleyski

Abstract:

Yu et al. described an algorithm for conducting computational searches for quadratic APN functions over the finite field \mathbb{F}_{2^n}, and used this algorithm to give a classification of all quadratic APN functions with coefficients in \mathbb{F}_{2} for dimensions n up to 9. In this paper, we speed up the running time of that algorithm by a factor of approximately \frac{n \times 2^n}{n^3}. Based on this result, we give a complete classification of all quadratic APN functions over \mathbb{F}_{2^{10}} with coefficients in \mathbb{F}_{2}. We also perform some partial computations for quadratic APN functions over \mathbb{F}_{2^{11}} with coefficients in \mathbb{F}_{2} , and conjecture that they form 6 CCZ-inequivalent classes which also correspond to known APN functions.

ePrint: https://eprint.iacr.org/2024/1778

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