Known infinite families of APN power functions over GF(2^n) html

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The following table provides a summary of all known infinite families of power APN functions of the form F(x) = xd.

Family Exponent Conditions deg(xd) Reference
Gold 2i + 1 gcd(i,n) = 1 2 [1][2]
Kasami 22i - 2i + 1 gcd(i,n) = 1 i + 1 [3][4]
Welch 2t + 3 n = 2t + 1 3 [5]
Niho 2t + 2t/2 - 1, t even n = 2t + 1 (t+2)/2 [6]
2t + 2(3t+1)/2 - 1, t odd t + 1
Inverse 22t - 1 n = 2t + 1 n-1 [2][7]
Dobbertin 24i + 23i + 22i + 2i - 1 n = 5i i + 3 [8]
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