# Can Elgamal be made additively homomorphic and how could it be used for E-voting?

Elgamal is a cryptosystem that is homomorphic over multiplication.

1. How can I convert it to an additive homomorphic cryptosystem?
2. How can I use this additive homomorphic Elgamal cryptosystem for E-voting purpose?

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Elgamal can be made additive by encrypting $g^m$ instead of $m$ with traditional Elgamal for some generator $g$ (usually the same one used to generate the public key). This variant is sometimes called exponential Elgamal. The difficulty is decryption: running the standard decryption gives you $g^m$ and recovering $m$ requires you to solve the discrete log. As long as $m$ is small, this can be done algorithmically or with a lookup table.
Can i use elgamal for both additions and multiplication of ciphertexts?I.e: Whenever i want to multiply i compute my message $x$ as $g^x$ and whenever i want to add i compute conventional Elgamal. My plaintext would be small integers in a range of $0 \ldots 2^{32} or 2^{64}$ –  curious Mar 22 '13 at 11:22