The DES $($Data Encryption Standard$)$ algorithm is a symmetric$-$key block cipher

created in the early $1970$s by an IBM team and adopted by the National Institute

of Standards and Technology $($NIST$).$ The algorithm takes the plain text in $64-$bit

blocks and converts them into ciphertext using $48-$bit keys. Simplified DES,

developed by Professor Edward Schaefer of Santa Clara University, is an

educational rather than a secure encryption algorithm

$$ The S$-$DES encryption algorithm takes an $8-$bit block of plaintext

$($example: $10111101)$ and a $10-$bit key as input and produces an $8-$bit

block of ciphertext as output.

$$ The S$-$DES decryption algorithm takes an $8-$bit block of ciphertext and the

same $10-$bit key used to produce that ciphertext as input and produces the

original $8-$bit block of plaintext.

$$ The S$-$DES encryption algorithm takes an $8-$bit block of plaintext

$($example: $10111101)$ and a $10-$bit key as input and produces an $8-$bit

block of ciphertext as output. The S$-$DES decryption algorithm takes an $8-$

bit block of ciphertext and the same $10-$bit key used to produce that

ciphertext as input and produces the original $8-$bit block of plaintext.

Consider the S$-$DES shown on the next page. The keys k$1$ and k$2$ can be derived

using the functions P$10,$ Shift, and P$8.$ Given the below definit