Functional Bootstrapping for packed ciphertext via homomorphic LUT evaluation

This paper introduces a new bootstrapping framework for the Fan-Vercauteren (FV) scheme, called the functional bootstrapping, providing more generic and advanced functionality than the ordinary bootstrapping method. More specifically, the functional bootstrapping allows us to evaluate an arbitrary function while removing the error of an input ciphertext. Therefore, we achieve better depth consumption and computational complexity as the evaluation of a circuit can be integrated as part of the functional bootstrapping procedure. In particular, our approach extends the functionality of FV since it is even applicable to functions between different plaintext spaces.