In Matsui's paper (Linear Cryptanalysis Method for DES cipher), lemma 1.
- $NS(a, b)$ is even
- if $a=1,32$,or $33$, then $NS(a,b)=32$ for all $b$
He said that the following lemma is now trivial from the definition of S-boxes.
- But I can't prove this lemma. How can I prove this lemma?