Practical Additive Homomorphic Encryption for Statistical Analysis over Encrypted Data

Homomorphic encryption scheme is one of useful tools for handling encrypted sensitive information. However, most of existing schemes have not been widely used in practical applications due to their inefficiency. In this paper, we give an additive homomorphic encryption scheme which can be used for evaluating some statistical information, such as the mean and the variance. To compute the information without the multiplicative homomorphism, we devise a message encoding technique and design a new additive homomorphic encryption by applying our encoding technique to Paillier's scheme which supports the additive homomorphism. Note that our scheme is the first additive homomorphic encryption which supports the evaluation of both the mean and the variance of encrypted data. We also propose some modifications of our scheme to improve the practicality. One of remarkable advantages of our message encoding technique is that it can be applied to any additive homomorphic encryption for supporting the above mentioned statistical operations.