In the ElGamal cryptosystem, a plaintext message m is encrypted as E$($m$)=($c$1,$ c$2)$ where c$1=$ gy and c$2=$ m $$ hy$,$ with g being a generator of a group G of order q$,$ y a random integer in $\{1,...,$ q$1\}$ new for each encryption, and hx the recipient$$s public key. Show that ElGamal encryption is multiplicatively homomorphic, that is$,$ given two messages m$1$ and m$2,$ it holds that E$($m$1$m$2)=$ E$($m$1)$E$($m$2).$ Show also that, in general, it is not additively homomorphic, that is$,$ E$($m$1+$m$2)6=$ E$($m$1)+$E$($m$2).$