Alice$($A$)$ and Bob$($B$)$ use ElGamal encryption system with public key parameters: $q=29,g=2,$ Alice chooses the secret key, $x_A=5.$ Bob chooses the random integer $k=8,$ and wants to encrypt the message $m=15.$ Compute $C=(C_1,C_2).$ Note: $1.$ To be fully graded, provide a detailed solution with all computations included. $2.$ Feel free to make assumptions for any necessary values not explicitly provided in the question.

Note: provide a handwritten, detailed solution with all computations

$7$

i $-$

B

I

U

c

$x_2$

$x^2$