$($RSA $-$Diffie and Helman $-$Elgamal$)$

Question $2$:

Q$1$: If Alice and Bob agree on a prime $p=23$ and a base $g=5,$ and Alice selects a secret key $a=6,$ while Bob selects

$b=15,$ compute the shared secret key.

Question $3$:

Q$1$: How would you encrypt the message $M=10$ using the public key $(q=23,a=5,y=8)$ Assume a random number

$k=3$ is chosen for encryption. $($using elgamal encryption$)$