Quo Vadis CKKS: Comparison of the realization of basic mathematical functions for the homomorphic cryptosystem CKKS using De Bello and polynomial approximations

As data storage and processing increasingly shift to the cloud, the risk of data breaches also rises. One way to address this is using Homomorphic Encryption (HE), which allows for data processing while the data remains encrypted, unlike traditional methods. However, current HE libraries support only addition and multiplication, requiring users to implement other mathematical functions themselves. To this end, we developed and analyzed basic mathematical functions in a previous work. Since polynomial approximations are more common in HE, this paper expands on that by examining and comparing polynomial approximations of these functions with the previously implemented methods. Our findings indicate that while polynomial approximations offer the benefit of low multiplication depth, the previously implemented methods generally outperform them in most scenarios despite their higher computational cost.