A Homomorphic ElGamal Variant Based on BGN's Method

Homomorphic encryption has numerous applications, which can directly calculate on encrypted data. In this paper, a simple variant of ElGamal is presented which supports arbitrary additions and one multiplication, similarly to the cryptosystem of Boneh, Goh, and Nissim (BGN). The construction adopts a bilinear pairing map to meet the multiplicative homomorphism. A confirmatory example is given to prove this cryptosystems homomorphism. In the additive homomorphic operation aspect, our scheme possesses a higher security than BGN's method. Obviously, it also offers a way of multiplying two cipher texts. Finally, a security analysis is shown to demonstrate that this variant of ElGamal cryptosystem satisfy CPA and IND-CCA security.