Malleability of homomorphic encryption El Gamal is a malleable homomorphic encryption system, so is Rabin. Are all homomorphic encryption systems malleable? Or are there any that are not malleable?
Thanks!
The answer may depend on your exact definitions of "homomorphic" and "malleable", but I'll give it a shot.

Basically, homomorphic encryption denotes that, given encryptions $E_k(x)$ and $E_k(y)$ of some values $x$ and $y$, it is possible to obtain an encryption of $x\ast y$ under $k$ from $E_k(x)$ and $E_k(y)$, where $\ast$ is some binary operation, without knowledge of the key $k$. Typically, $\ast$ is the usual addition or multiplication on (bounded) integers, but the attack actually works for almost arbitrary operations (namely, there must be a pair $(x,y)$ such that $x\ast y\notin\{x,y\}$): Assume that an attacker knows $x$ and $y$ along with their encryptions $E_k(x)$ and $E_k(y)$. He may then compute $E_k(x)\mathbin{\hat\ast}E_k(y)$, where $\hat\ast$ denotes the "lifted" version of $\ast$, to obtain a ciphertext $\zeta$. By specification, $\zeta$ decrypts to $x\ast y$, which was assumed different from both $x$ and $y$. Hence, the attacker has obtained a ciphertext ($\zeta$) corresponding to a plaintext ($x\ast y$) he knows but whose ciphertext he has not observed before.

Therefore, any homomorphic encryption scheme is malleable.