Paillier-encrypted databases with fast aggregated queries

The proliferating usage of cloud environments to store databases poses new challenges. Traditional encryption protects the user's data privacy, but prevents the server from executing computations on behalf of the user (client). By contrast, Partially Homomorphic Encryption schemes, such as the Paillier cryptosystem, facilitate some server queries but involve heavy computations that make them relatively slow. This paper shows a simple performance optimization for Paillier encryption. It significantly reduces the server side workload and can be deployed by the server unilaterally, while remaining transparent to the client. Our optimization trades modular multiplications with cheaper Montgomery Multiplications, by converting the database to a favourable format. We explore several techniques to accelerate the relevant Montgomery multiplications on current and future modern processor architectures, and demonstrate the resulting speed-ups by comparing to the current method implemented via the OpenSSL library. For example, on the latest Intel processor (Architecture Codename Skylake) our method speeds up aggregated queries by a factor of 4×.