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

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Functions Conditions References
C1-C2 , [1]
C3 , [2]
C4 [3]
C5 , [4]
C6 [4]
C7-C9 , [5]
C10 even, and even, [6]
C11 satisfies the conditions in Theorem 3.6 of [7] [7]
C12 , [8]
C13 [9]
  1. L. Budaghyan, C. Carlet, G. Leander. Two classes of quadratic APN binomials inequivalent to power functions. IEEE Trans. Inform. Theory, 54(9), pp. 4218-4229, 2008.
  2. L. Budaghyan and C. Carlet. Classes of Quadratic APN Trinomials and Hexanomials and Related Structures. IEEE Trans. Inform. Theory, vol. 54, no. 5, pp. 2354-2357, May 2008.
  3. L. Budaghyan, C. Carlet, G. Leander. Constructing new APN functions from known ones. Finite Fields and Their Applications, v. 15, issue 2, pp. 150-159, April 2009.
  4. 4.0 4.1 L. Budaghyan, C. Carlet, G. Leander. On a construction of quadratic APN functions. Proceedings of IEEE Information Theory Workshop, ITW’09, pp. 374-378, Taormina, Sicily, Oct. 2009.
  5. C. Bracken, E. Byrne, N. Markin, G. McGuire. A few more quadratic APN functions. Cryptography and Communications 3, pp. 45-53, 2008.
  6. Y. Zhou, A. Pott. A new family of semifields with 2 parameters. Advances in Mathematics, v. 234, pp. 43-60, 2013.
  7. L. Budaghyan, M. Calderini, C. Carlet, R. S. Coulter, I. Villa. Constructing APN Functions through Isotopic Shifts. IEEE Trans. Inform. Theory, early access article.
  8. H. Taniguchi. On some quadratic APN functions. Designs, Codes and Cryptography 87, pp. 1973-1983, 2019.
  9. L. Budaghyan, T. Helleseth, N. Kaleyski. A new family of APN quadrinomials. IEEE Trans. Inf. Theory, early access article.