Let's consider a simplified DES algorithm that requires an $8-$bit plaintext input denoted

as $M$ and a $6-$bit key denoted as $K.$ The components of this algorithm are defined as

follows:

initial permutation IP $=(146)(25)(387).$

a Feistel function $F$ where

$-$Expansion permutation E has the schema $241233.$

The only S$-$Box is S$2$ from the normal DES Feistel function.

$-$P$-$Box has the permutation schema $4123.$

a key schedule defined simply via shifts without additional permutations as: $C_0||D_0=K,$

$K_i=C_{i+1}||D_{i+1},i=0,1,2,$dots where $C_i$ and $D_i$ are both of $3-$bit length and computed by

$C_i=((C_{i-1}2)o+C_{i-1})1$

$D_i=((D_{i-1}1)o+D_{i-1})2$

Let $M=11010101$ and $K=101101.$

$($a$)$ Calculate the sub$-$keys $K0,K1,$ and $K2$ for the initial three rounds.

$($b$)$ Apply three iterations of F to encrypt M$.$ Then, decrypt the resulting ciphertext. Pay

close attention to all intermediate results at each step of the process.