The CKKS FHE Scheme

In this chapter, we describe the CKKS FHE scheme in detail. The CKKS scheme supports operations on real numbers, and thus, is the preferred scheme for implementing privacy-preserving machine learning applications. We would like to note that the original CKKS scheme (Cheon et al. 2017) supports homomorphic computations over the real numbers, but its implementation could not employ core optimization techniques based on the Residue Number System (RNS) decomposition (see Section 2.2.1) and the Number Theoretic Transform (NTT) (see Section 2.2.3). Consequently, Cheon et al. (2019) proposed a full RNS variant of the CKKS FHE scheme that is optimal for implementation on a standard computer system. They introduced a new structure of the ciphertext modulus which allows using both the RNS decomposition of cyclotomic polynomials and the NTT conversion on each of the RNS components.