Classification of quadratic APN functions with coefficients in GF(2) for dimensions up to 9.

Almost perfect nonlinear (APN) and almost bent (AB) functions are integral components of modern block ciphers and play a fundamental role in symmetric cryptography. In this paper, we describe a procedure for searching for quadratic APN functions with coefficients in F2 over the finite field F2n and apply this procedure to classify all such functions over F2n with n≤9. We discover two new APN functions (which are also AB) over F29 that are CCZ-inequivalent to any known APN function over this field. We also verify that there are no quadratic APN functions with coefficients in F2 over F2n with 6≤n≤8 other than the currently known ones.