Known inifinte families of quadratic APN polynomials over GF(2^n)

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[math]\displaystyle{ N^\circ }[/math] Functions Conditions References
C1-C2 [math]\displaystyle{ x^{2^s+1}+u^{2^k-1}x^{2^{ik}+2^{mk+s}} }[/math] [math]\displaystyle{ n = pk, \gcd(k,3) = \gcd(s,3k) = 1, p \in \{3,4\}, i = sk \mod p, m = p -i, n \ge 12, u \text{ primitive in } \mathbb{F}_{2^n}^* }[/math] [1]
  1. L. Budaghyan, C. Carlet, G. Leander, Two Classes of Quadratic APN Binomials Inequivalent to Power Functions, IEEE Trans. Inform. Theory 54(9), 2008, pp. 4218-4229