A Restrained Paillier Cryptosystem and Its Applications for Access Control of Common Secret

The modified Paillier cryptosystem has become extremely popular and applied in many fields, owning to its additive homomorphism. This cryptosystem provides weak private keys and a strong private key. A weak private key only can decrypt ciphertexts under the corresponding public key. The strong private key can decrypt all ciphertexts even under different public keys. When the modified Paillier cryptosystem is applied in a system, the member, often the system administrator, has the strong private key and can decrypt all ciphertexts. If this system administrator is attacked or compromised, the security of the application system absolutely break down. Thus, it is important to stop the decryption of the strong private key. To address this issue, we propose an restrained version of the modified Paillier cryptosystem (Restrained-Paillier), by endowing the multiplicative homomorphism. We perform the additive encryption on the multiplicative ciphertext and generate the mixed ciphertext, which can not be decrypted by the strong private key. Based on this Restrained-Paillier, we develop two applications. Firstly, we realize access control of common secret of two owners. In our scheme, only one owner cannot access secret. Secondly, we present three protocols for identity distribution and key management, identity authentication and private key recovery. Security analysis shows that the Restrained-Paillier cryptosystem can resist the chosen plaintext attack. The experimental results illustrate the utility and efficiency of the proposed protocols.