Simpler and Faster BFV Bootstrapping for Arbitrary Plaintext Modulus from CKKS

Bootstrapping is currently the only known method for constructing fully homomorphic encryptions. In the BFV scheme specifically, bootstrapping aims to reduce the error of a ciphertext while preserving the encrypted plaintext. The existing BFV bootstrapping methods follow the same pipeline, relying on the evaluation of a digit extraction polynomial to annihilate the error located in the least significant digits. However, due to its strong dependence on performance, bootstrapping could only utilize a limited form of plaintext modulus, such as a power of a small prime number.