Advanced Encryption Standard (AES) block cipher system is widely used in cryptographic applications. A nonlinear substitution operation is the main factor of the AES cipher system strength. The purpose of the proposed approach is to generate the random S-boxes changing for every change of the secret key. The fact that the S-boxes are randomly key-dependent and unknown is the main strength of the new approach, since both linear and differential cryptanalysis require known S-boxes. In the paper, we briefly analyze the AES algorithm, substitution S-boxes, linear and differential cryptanalysis, and describe a randomly key-dependent S-box and inverse S-box generation algorithm. After that, we introduce the independency measure of the S-box elements, and experimentally investigate the quality of the generated S-boxes.