$(6)$ ElGamal public key cryptosystem $($encryption$)$:

Start with the prime $p=13$ and the primitive root $g=2.$

Alice sends Bob the public key $A=3.$

Bob wants to send the message $m=11$ to Alice. He chooses the random

element $k=3.$ Using the ElGamal public key cryptosystem, compute the

pair of numbers $(c_1,c_2)$ that Bob sends to Alice.

Note: Do not work out how Alice computes the plaintext message $m$ from

the ciphertext $(c_1,c_2).$