This problem is about ElGamal encryption and signature schemes. $(30$ points$)$

$($a$)$ Let $p=151$ and $g=2$ be a generator of $Z_{151}^{**}.$ Assume that the public key is

$(p,g,32)$ and the secret key $(p,g,20).$ Encrypt the plaintext $m=25$ and decrypt

the ciphertext $(56,13).$

$($b$)$ Use the secret key as the signing key to sign the message $m=25.$ The randomly

chosen $k$ is $11.$ You don't need to do hashing before signing.