Exercise $2$: Diffie$-$Hellman key exchange

Reem and Hala want to establish a shared secret key using the Diffie$-$Hellman key exchange protocol. They agree on the following parameters:

Prime number $(q)=11$

Primitive root of $q(a)=6$

Verify if the value of $a=6$ is a primitive root of $q=11.$

Reem chooses her private key $x_R$ as $6,$ and Hala chooses his private key $x_H$ as $5.$

$2.$ Calculate the following:

a$)$ Reem's public key $Y_R.$

b$)$ Hala's public key $Y_H.$

c$)$ The shared secret key $(K)$ that Reem and Hala will derive.

After establishing the shared secret key $($K$)$ using the Diffie$-$Hellman key exchange protocol, Reem and Hala decide to use the Caesar cipher for encrypting their messages. The Caesar cipher is a simple substitution cipher where each letter in the plaintext is shifted a certain number of positions down the alphabet.

The encryption function for the Caesar cipher is as follows:

Enc$(x)=(x+K)mod26$

$x$ is the letter to be encrypted $,$ where $A=0,B=1,$dots,$Z=25.$

$K$ is the shared secret key $)K(25.$

Enc $(x)$ is the encrypted letter.