Optimal Design of Key Switching Parameters for Efficient CKKS Bootstrapping

Bootstrapping in fully homomorphic encryption depends on a wide range of parameters that significantly influence both performance and precision. Traditionally, these parameters have been selected through empirical methods and heuristic tuning. In this work, we present a comprehensive and rigorous analysis of the error components that accumulate throughout the bootstrapping process. Focusing specifically on the parameters related to key switching, we establish a theoretical framework that supports the systematic and optimal design of these parameters. Our optimized parameter selection enables the attainment of two additional levels in widely used parameter sets, improving the efficiency of bootstrapping without compromising security or precision.