Consider a message authentication code that uses our familiar five$-$

bit block cipher from Module $3$ with key $(P,k)=(L{S}_1,27)$ in cipher

block chaining $($CBC$)$ mode.

If the initial value is $IV=01011,$ find the authentication tag for the

message

$x=0110101110$

$($a$)$ If we want to enable each pair of people in a $259-$member or$-$

ganization to communicate securely with their own shared symmetric

key, how many of these keys must be created?

$($b$)$ If the organization instead uses a key distribution center $($KDC$),$

how many keys must be created?

Suppose we want to enable each pair of people in an organization

to communicate securely with their own shared symmetric key, and we

have the capacity to create one thousand keys. What is the largest

number of people that can be accommodated?