Algebraická teorie S-boxů

The thesis focuses on an algebraic description of S-boxes by the special type of quadratic equations, defined as biaffine equations. Biaffine equations satisfying S-boxes of higher order may not even exist. However, the special type of S-boxes en- ables to find such equations also for S-boxes of higher order. The S-box in the block cipher Rijndael, composed of the inverse function and the affine transformation, is an example of such special type of S-boxes. The thesis proves that a number of biaffine equations satisfying an S-box of this type does not depend on the affine function. The thesis also proves that for every S-box of order n formed by the in- verse function there exist at least 3n − 1 biaffine equations satisfying this S-box.