Paper 2019/1491

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

Yuyin Yu and Nikolay Kaleyski and Lilya Budaghyan and Yongqiang Li

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 GF(2) over the finite fields GF(2^n) and apply this procedure to classify all such functions over GF(2^n) with n up to 9. We discover two new APN functions (which are also AB) over GF(2^9) 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 GF(2) over GF(2^n) with n between 6 and 8 other than the currently known ones.