Dodrant-homomorphic encryption for cloud databases using table lookup

Users of large commercial databases increasingly want to outsource their database operations to a cloud service providers, but guaranteeing the privacy of data in an outsourced database has become the major obstacle to this move. Encrypting all data solves the privacy issue, but makes many operations on the data impossible in the cloud, unless the service provider has the capacity to decrypt data temporarily. Homomorphic encryption would solve this issue, but despite great and on-going progress, it is still far from being operationally feasible. In 2015, we presented what we now call dodrant-homomorphic encryption, a method that encrypts numeric values deterministically using the additively homomorphic Paillier encryption and uses table lookup in order to implement multiplications. We discuss here the security implications of determinism and discuss options to avoid these pitfalls.