$(60$ pts$)$ We consider a DES$-$based encryption scheme, which operates on $16-$

bit blocks of plaintext and uses sub$-$key of length $12.$ A sketch of the

encryption with first$-$round is given in figure $1$:

Figure $1$:

Consider the following bit sequence as the input data:

$1111000000001111$

$($a$)$ Describe L$\_(1)$ and R$\_(1)$ with respect to R$\_(0),$R$\_(1)$ and K$\_(1).$

$($b$)$ The $16$ bits of the input are first reorganized by the following initial

permutation $($IP$).$

That is the permuted input has bit $8$ of the input as its first bit, bit $13$ as its second

bit and so on$.$

$($i$)$ Write down the permuted input.

$($ii$)$ Compute the inverse permutation namely IP$^(-1).$

$($c$)$ Let the $16$ bits of the permuted input block consist of an $8$ bit block L

followed by an $8$ bit block R$.$ The internal structure of the cipher function

ff in figure $1$S denotes the substitution function which takes a block of $3$ bits and

yields a block of $2$ bits. Function is given with a table which contains the

decimal representations.

$($ex: $(101)2=5,$ so from the table, $5$ corresponds to $3$ which is $(11)2.)$

Write down the output bit sequence with a given sub$-$key K$1=101101100010.$

$($e$)$ Write down L$1$ and R$1$ as a bit sequence.

$($f$)$ Combine L$1$ and R$1$ into $16-$bits bit sequence and apply the inverse

permutation $($IP$^(-1)).$