Problem $3$

Consider a block cipher with block size $n=3.$ Suppose $K=Z_2^3,$ and let $B_k$ :

$Z_2^3{Z}_2^3$ such that $B_k(x)=k+x.$

$($a$)$ Suppose the block cipher is in output feedback mode. Encrypt $111000101$

when the key is $101$ and the initial state is $s=000.$

$($b$)$ Suppose the block cipher is block chaining. Encrypt $111000101$ when the

key is $101$ and the priming value is $y_0=000.$