Low-Complexity Ciphertext Multiplication for CKKS Homomorphic Encryption

Homomorphic encryption (HE) allows direct computations on ciphertexts and is a key enabler of privacy-preserving cloud computing. The CKKS algorithm is among the most popular HE schemes and a ciphertext consists of a pair of polynomials with very large coefficients. The complexity of large coefficients can be greatly reduced by using the residue number system (RNS). However, the relinearization and rescaling that follow the coefficient multiplication in every ciphertext multiplication have even higher complexities. This brief proposes reformulations of the relinearization and rescaling using RNS representation. A novel integer division method is developed to enable the combination and simplification of all involved computations. Constants are pre-multiplied to reduce the number of required multipliers. As a result, the complexity of the ciphertext multiplication is greatly reduced. For an example case, the proposed design leads to 18% less silicon area and 42% shorter latency compared to prior work.