De Bello Homomorphico: Investigation of the extensibility of the OpenFHE library with basic mathematical functions by means of common approaches using the example of the CKKS cryptosystem

Cloud computing has become increasingly popular due to its scalability, cost-effectiveness, and ability to handle large volumes of data. However, entrusting (sensitive) data to a third party raises concerns about data security and privacy. Homomorphic encryption is one solution that allows users to store and process data in a public cloud without the cloud provider having access to it. Currently, homomorphic encryption libraries only support addition and multiplication; other mathematical functions must be implemented by the user. To this end, we discuss and implement the division, exponential, square root, logarithm, minimum, and maximum function, using the CKKS cryptosystem of the OpenFHE library. To demonstrate that complex applications can be realized with this extended function set, we have used it to homomorphically realize the Box–Cox transform, which is used in many real-world applications, e.g., time-series forecasts. Our results show how the number of iterations required to achieve a given accuracy varies depending on the function. In addition, the execution time for each function is independent of the input and is in the range of ten seconds on a reference machine. With this work, we provide users with insights on how to extend the original restricted function set of the CKKS cryptosystem of the OpenFHE library with basic mathematical functions.