$(6)($Knapsack cryptosystem$)$

Consider the superincreasing sequence

$r=(2,5,11,24,49).$

Let $A=10$ and $B=99.$

$($a$)$ Compute the sequence

$M=(M_1,M_2,M_3,M_4,M_5)$

where

$M_i-=A{r}_i,(modB),$ for $i=1,2,3,4,5.$

$($b$)$ Choose the binary plaintext

$x=(1,0,0,1,1)$

and compute the ciphertext $S.$

$($c$)$ The knapsack cryptosystem generated the ciphertext $S^{\text{'}}=26$ from the

plaintext $y.$ Using knapsack decryption, compute the plaintext $y.$