Problem $5$

Consider a Feistel cipher with $8$ letters. Let $f(x_0{x}_1{x}_2{x}_3)=x_1{x}_2{x}_3{x}_4,$ where

$x_4=x_0*x_2+x_1*x_3.$

$($a$)$ Suppose the plaintext $11011100$ was the input of the Feistel cipher which

consists of two rounds. Obtain the ciphertext.

$($b$)$ Using the same Feistel cipher, find the plaintext that produces the ciphertext