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Homomorphic encryption is a form of encryption where a specific algebraic operation performed on the plaintext is equivalent to another (possibly different) algebraic operation performed on the cipher text. A multiplicative homomorphic cryptosystem has an encryption function E that satisfies the following property:

E(M1) * E(M2) = E(M1*M2)

where M1 and M2 are messages. Prove that EIGamal cryptosystem is multiplicative homomorphic.

Hint: (a,b) * (c,d) = (a * c, b * d).

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What have you tried? If this is homework, tag it as such. –  lhf Sep 25 '12 at 23:23
We ask that homework not be the only tag, so I restored number-theory and added cryptography. It would be good to define ElGamal encryption. You could define what $(a,b)$ is in this scheme. As the encryption is based in group theory, that is an important fact. –  Ross Millikan Sep 26 '12 at 3:06
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