Alice and Bob use DHKE $($Diffie Hellman Key Exchange$)$ to exchange a secret key. They both agree to choose $19$ as a large prime to use the multiplicative group mod $19$ as the basis of his cryptographic system. They also choose the $3$ as a generator to be used as $3$ is primitive element of $19.$

$1.$Bob chooses $7$ as his private key $($exponent$).$ Generate the public key that Bob has to send to Alice

a$)4$

b$)11$

c$)2$

d$)15$

Answer $1$ Question $4$

b

$2.$ Alice chooses $2$ as her private key. Generate public key that Alice has to send to Bob.

a$)9$

b$)10$

c$)7$

d$)3$

Answer $2$ Question $4$

d

$3.$ What is the shared secret key that they agree on$?$

a$)11$

b$)12$

c$)10$

d$)4$

Answer $3$ Question $4$

a