Analyzing the influence of linear redundancy in S-boxes on the affine equivalence within XSL-like round functions

We show that S-boxes based on finite field inversion always possess complete linear redundancy. Next, we consider the influence of linear redundancy of S-boxes on the affine equivalence of component functions within XSL-like round functions in the general case. Then, we propose an effective practical approach to test this. Finally, some experimental results on the round functions within the Kuznyechik and AES are presented.