In the process of Diffie$-$Hellman key exchange, user Bob can determine his public value B as:

B $=$ a$^$X$\_$B mod n

where X$\_$B $<$ n$,$ n is a prime number, a is a primitive root of n and a $<$ n$.$ Assume Bob wants to

exchange a secret, K$,$ with user Alice.

$(2\mathrm{.}1)$ What is the equation for Alice to calculate her public value, A $?$

$(2\mathrm{.}2)$ What value does Alice send to Bob in the Diffie$-$Hellman exchange?

$(2\mathrm{.}3)$ What is the equation for Bob to calculate the secret, K$\_$B $?$

$(2\mathrm{.}4)$ What value$($s$)$ are public in this Diffie$-$Hellman exchange $($that is$,$ assumed that a malicious user knows them$)?$

$(2\mathrm{.}5)$ What value$($s$)$ should only be known by Alice $($that is$,$ no other users should know them$)?$

$(2\mathrm{.}6)$ Prove that the secret calculated by Alice, K$\_$A $,$ is the same as the secret calculated by BOB, K$\_$B$.$ Show the detailed steps of your proof.