$(3)($Diffie$-$Hellman key exchange$)$

Start with the prime $p=7$ and the primitive root $g=5.$

$($a$)$ Alice chooses the secret key $a=2.$ Compute the public key A that

Alice sends to Bob.

$($b$)$ Bob chooses the secret key $b=3.$ Compute the public key $B$ that Bob

sends $B$ to Alice.

$($c$)$ Use Diffie$-$Hellman key exchange to compute the secret key that Alice

and Bob share.

$($d$)$ Explain why Diffie$-$Helllman key exchange is a secure system.