The paper deals with nonlinear transformations of well-known symmetric block algorithms such as AES, Kuznyechik, SM4, BelT, and Kalyna. A brief description of the substitution boxes for these algorithms is given. The properties of nonlinearity of the described substitution boxes are investigated with the calculation of the corresponding values. Based on the property of nonlinearity, a method for generating a dynamic substitution box is proposed. The purpose of this method is to generate dynamic substitution boxes (S-boxes) that change depending on the values of some parameter obtained from the secret key of the algorithm. Considering that linear and differential cryptanalysis uses known substitution boxes, the main advantage of the new method is that S-boxes are randomly key-dependent and unknown. Experiments were also carried out to implement this method. The resulting dynamic substitution boxes were tested for nonlinearity and the results were compared with the original nonlinearity values of the same substitution boxes.