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1

So in general ElGamal encryption is only homomorphic wrt. multiplication. However with a few tweeks one can transform ElGamal to exponential ElGamal (and I guess that is what you are referring to). The main difference between ElGamal and exponential ElGamal is that instead of a message: $m$ you have to encrypt $g^{m}$. On decryption that means that one has ...


3

In the most common variant of Paillier encryption with public modulus $n$, any plaintext in $[0,n)$ can be encrypted and decrypted (though sometime the interval is slightly reduced, or centered on zero). To be secure, Pailler encryption needs $n$ to have unknown factorization. That means like at least 1024-bit $n$ (with 2048-bit or more highly recommendable)....


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