Efficient Bootstrapping for Approximate Homomorphic Encryption with Non-sparse Keys

We present a bootstrapping procedure for the full-RNS variant of the approximate homomorphic-encryption scheme of Cheon et al., CKKS (Asiacrypt 17, SAC 18). Compared to the previously proposed procedures (Eurocrypt 18 & 19, CT-RSA 20), our bootstrapping procedure is more precise, more efficient (in terms of CPU cost and number of consumed levels), and is more reliable and 128-bit-secure. Unlike the previous approaches, it does not require the use of sparse secret-keys. Therefore, to the best of our knowledge, this is the first procedure that enables a highly efficient and precise bootstrapping with a low probability of failure for parameters that are 128-bit-secure under the most recent attacks on sparse R-LWE secrets.