ElGamal Encryption System Operates as Follows:

$$ Key Generation $($KeyGen$)$: The process starts by selecting a large prime number and a generator of the multiplicative group Zo

The private key is chosen randomly from the set. The public key is then computed as mod, where is made public along with and. The public key is and the private key is

$$ Encryption $($Enc$)$: To encrypt a message m$,$ which is an element of Zp$,$ select a random k from $\{1,2,...,$p$-2\}.$ The ciphertext is then generated as a pair $($C$1,$C$2)$ where

C$1=$g mod p

C$2-$m$-$hmod p

Here c$1$ serves as the ephemeral public key, and c$2$ carries the message encrypted with the derived key h$.$

$.$

Decryption $($Dec$)$: Given the ciphertext $($C$1,$C$2),$ compute the plaintext message using the private key as follows: m$=$c$2-($c$2-1$mod p

Given its key generation, encryption, and decryption processes, explain whether ElGamal is homomorphic under multiplication. Provide a detailed explanation to support your answer.