ICDM: An Encryption That Supports Unlimited Times Homomorphic Arithmetic Operations on Encrypted Data

With the development of cloud computing, privacy has become the key problem of cloud security. The homomorphic encryption is an ideal way to protect users' privacy in cloud computing. But some of the existing homomorphic encryption schemes have less usability, and some are inefficient. There lacks of practical homomorphic encryption schemes in cloud computing at present. CESVMC is a scheme supposed to solve the problem. CESVMC ensures that after calculating the user's encrypted data and returning the cipher result to user by the service provider, the user can decrypt the cipher result and get the right service result. But CESVMC only supports multiplication or division operation once. Meanwhile, to decrypt the cipher text, user needs to tell which type of operation has been done to the cipher text. All these constrain the usability of CESVMC in cloud computing. To solve these problems, an improved CESVMC (ICDM) is proposed. In encryption algorithm, the information of plaintext and the operation type are hidden in a diagonal matrix. Then the diagonal matrix is encrypted by using an invertible matrix as secret key. In decryption algorithm, ICDM chooses the right encryption method by reading the sign of the operation type without any manual interventions. Besides, the arithmetic operations on cipher text correspond to the arithmetic operations on matrix. Security analysis indicates ICDM is IND-CPA. And the experiments show ICDM can support unlimited times arithmetic operations homomorphically after partly lowering efficiency and adding the cipher text length. Thus, it can fit privacy-preserving in cloud computing better.