$($b$)$ Consider a Feistel cipher composed of $16$ rounds with a block length of $128$

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bits and a key length of $128$ bits. Suppose that, for a given $k,$ the key scheduling algorithm determines values for the first $8$ round keys, $k_1,k_2,$dots, $k_8,$ and then sets $k_9=k_8,k_{10}=k_7,k_{11}=k_6,$dots,$k_{16}=k_1$

Suppose you have a ciphertext $c.$ Explain how, with access to an encryption result, you can decrypt $\text{'}c\text{'}$ and determine the plain text $\text{'}m\text{'}$ using just a single expression.

Implement the Stream Cipher RC$4$ algorithm for the State vector $S=83-$bits text $C.$