Design of additive homomorphic encryption with multiple message spaces for secure and practical storage services over encrypted data

Abstract

Homomorphic encryption scheme is one of the useful tools for handling encrypted information in storage services. However, most of existing schemes have not been used in practical applications due to their inefficiency or lack of functionalities. For example, fully homomorphic encryption, which can provide arbitrary operations, is inefficient. On the other hand, other homomorphic encryptions, including additive homomorphic encryptions, which are efficient enough to be used in practice, are limited in operations for practical applications. In this paper, we devise a message-encoding technique which can split a message space of an additive homomorphic encryption into multiple sub-spaces for different messages. Our technique guarantees that we can deal with multiple sets of data (each data set is assigned to each sub-space), so that multiple data can be computed at once in an additive manner. Using our new technique, we construct two additive homomorphic encryptions with valuable properties. The first one is an additive homomorphic encryption scheme which can be used for evaluating some statistical information, such as the mean and the variance. To give a concrete scheme, we apply our 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 give two modifications of the first application to improve its practicality. As the second application of our technique, we propose an additive homomorphic encryption scheme which can support the functionality of error detection in homomorphic operations. The second scheme is also designed based on Paillier’s scheme. Note that one of the remarkable advantages of our technique is that it can be applied to any additive homomorphic encryption for supporting the above-mentioned functionalities.