Message Integrity. $[10$ Points$]$

For message integration, Hashed Message Authentication Code $($HMAC$)$ can be used.

$($a$)[2$ Points$]$ For a message $$four score and seven years ago$,$ what would be the size

of HMAC when SHA$-256$ is used?

$($b$)[2$ Points$]$ For a message $$four$,$ what would be the size of HMAC when SHA$-256$ is

used?

$($c$)[2$ Points$]$ If Alice wants to send a message M to Bob and ensure that the message is

received intact $($that is$,$ M is not modified$),$ what would Alice have to send to Bob?

$($d$)[4$ Points$]$ If Alice wants to send a message M: $$Bob$,$ please transfer $$50$ to my bank

account. Thank you. Alice$$ to Bob but an adversary Trudy modifies the message to

M$$: $$Bob$,$ please transfer $$5000$ to my bank account. Thank you. Alice.$$ How will Bob

know that the original message from Alice has been modified?