Classification of quadratic APN functions with coefficients in F2 for dimensions up to 9

Abstract

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.