$(1)$ What is the effective key size of DES? $(2$ points$)$

$(2)$ If the input to the $S1$ box is $101000($the lookup table of $S1$ box is shown below$),$

what is the output and why? $(5$ points$)$

$(3)$ Please discuss why $C_0=C_{16},D_0=D_{16}$ in key schedule. $(5$ points$)$

$(4)$ Consider a simple block cipher using $8-$bit block that is based on the Feistel

Structure. It has only two rounds and has no initial or final permutation. The F$-$

function for round $i(i=1,2)$ is defined as

$f_i(R_{i-1},k_i)=5^i{R}_{i-1}{k}_i,$mod$20$

$,$ where $R_{i-1}$ is a plaintext $($right half$),k_i$ is a key that $k_1=10,k_2=3$ and

plaintext is $10100101($i$.$e$.L_0=1010,R_0=0101).$

i$.$ What is the ciphertext after the first round? $(10$ points$)$

ii$.$ What is the ciphertext after the second round? $(10$ points$)$