Classification of quadratic APN functions with coefficients in $$\mathbb {F}_2$$ in dimension 10

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 $$\frac{2^n}{n^2}$$ . 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 with coefficients in $$\mathbb {F}_{2}$$ over $$\mathbb {F}_{2^{11}}$$ , and conjecture that they form 6 CCZ-inequivalent classes which also correspond to known APN functions.