Bootstrapping Small Integers With CKKS

Youngjin Bae, Jaehyung Kim, Damien Stehlé, Elias Suvanto

Abstract: The native plaintexts of the Cheon-Kim-Kim-Song (CKKS) fully homomorphic encryption scheme are vectors of approximations to complex numbers. Drucker et al. [J. Cryptol.’24] have showed how to use CKKS to efficiently perform computations on bits and small bit-length integers, by relying on their canonical embeddings into the complex plane. For small bit-length integers, Chung et al. [IACR eprint’24] recently suggested to rather rely on an embedding into complex roots of unity, to gain numerical stability and efficiency. Both works use CKKS in a black-box manner.