A Generalization of Paillier\u27s Public-Key System With Fast Decryption

Paillier\u27s scheme is a homomorphic public key encryption scheme which is widely used in practical. For instance, Paillier\u27s scheme can be used in the data aggregation in smart grid. Damg$\mathring{a}$rd and Jurik generalized Paillier\u27s scheme to reduce the ciphertext expansion factor. However, the decryption scheme of Damg$\mathring{a}$rd and Jurik\u27s scheme is more complicated than Paillier\u27s original scheme. In this paper, we propose a new generalization of Paillier\u27s scheme and all the Paillier\u27s schemes to our knowledge are special cases of our scheme. We propose a very simple decryption algorithm which is more efficient than other generalization algorithms. We prove that our generalized Paillier\u27s scheme is IND-CPA secure. Our generalized Paillier\u27s scheme can be used in smart grid instead of Paillier\u27s scheme for higher flexibility