Question $5(20$ points$)$

Questions about DES:

$(1)$ Please discuss why $C_0=C_{16},D_0=D_{16}$ in key schedule. $(8$ points$)$

$(2)$ 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 E$-$finnction for round $2(1-1,2)$ is defined as $f(R,k_i)=(2iR{k}_i)$ mod $15,$ where $R$ is a plaintext $($right halo, le is a key that $k_1=6,k_2=13$ and plaintext is $10110110.$

What is the ciphertext after the first round? $(6$ points$)$

ii$.$ What is the ciphertext after the second round? $(6$ points$)$