Construction algorithm of S-box in DES

Abstract

This thesis is concerned with construction of S-box in DES. S-box of DES is mapping from GF (2)$^6$ to GF (2)$^4$ which satisfies some conditions. First, by use of linear permutation in H$_n$(1,m) (n$\ge$6,n-m$\le$2), we construct linear mapping from GF (2)^6$ to GF (2)$^4$ which satisfies the conditions except non-linear property. Then, by composing this linear mapping with transposition of GF (2)$^6$, we construct mapping which satisfies the conditions. By continuing above process, we can construct good S-box.