I am reading "The design of Xoodoo and Xoofff". On page 13 there is a collorary related to the component $\chi$ [Algorithm 1, 1].
Corollary 1. For fixed (difference or mask) $a$, the compatible (difference or mask) $b$ values form an affine space of dimension 2 and vice-versa
I am trying to verify this corollary exhaustively. That is I have fixed a $b$ and generated all $a$. Specifically, I took $b=110$. For this value, the corresponding possible $a$'s are $S=\{010, 100, 011, 101\}$. My question is Does $S$ form an affine space of dimension 2? if so, why?
