Structured Groebner basis search in a 40-dimensional self-equivalence subspace of functions over F_{2^8} yields 566 quadratic APN functions in six classes, four of which are absent from prior databases of millions of instances.
Differentially uniform mappings for cryptography
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Parametrization of APN exponents in char 3 with proofs that two binomial classes have boomerang uniformity 0 and a third class has uniformity 1 for odd n >= 5.
Under the condition that at most one x with χ(x)=χ(x+1)=1 satisfies (x+1)^r - x^r = b for each b, the binomial F_r(x) = x^r + x^{r+(q-1)/2} is locally-APN with boomerang uniformity ≤2 over F_q (q≡3 mod 4), plus spectra for F_3, F_{(2q-1)/3} and F_2 (p=3).
citing papers explorer
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Quadratic APN Functions in Dimension 8 via Gr\"obner Basis Search in a Self-Equivalence Subspace
Structured Groebner basis search in a 40-dimensional self-equivalence subspace of functions over F_{2^8} yields 566 quadratic APN functions in six classes, four of which are absent from prior databases of millions of instances.
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On APN Exponents and the Differential and Boomerang Properties of Binomials in Characteristic 3
Parametrization of APN exponents in char 3 with proofs that two binomial classes have boomerang uniformity 0 and a third class has uniformity 1 for odd n >= 5.
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Locally-APN Binomials with Low Boomerang Uniformity in Odd Characteristic
Under the condition that at most one x with χ(x)=χ(x+1)=1 satisfies (x+1)^r - x^r = b for each b, the binomial F_r(x) = x^r + x^{r+(q-1)/2} is locally-APN with boomerang uniformity ≤2 over F_q (q≡3 mod 4), plus spectra for F_3, F_{(2q-1)/3} and F_2 (p=3).