The CKKS fully homomorphic encryption (FHE) scheme enables computations on vectors of approximate complex numbers. A moderate precision of ≈ 20 bits often suffices but, in many applications, a higher precision is required for functionality and/or security. Indeed, to obtain IND-CPA-D security [Li-Micciancio; Eurocrypt'21], secure threshold-FHE [Asharov et al; Eurocrypt'12] and circuit privacy [Gentry; STOC'09], all known approaches require a precision that supports noise flooding. This may lead to a precision of ≈ 80 bits, or more. High-precision CKKS is hard to achieve, notably because of bootstrapping. The main difficulty is modulus consumption: every homomorphic multiplication consumes some, out of an overall modulus budget. Unfortunately, in high precision, most known bootstrapping algorithms consume so much modulus that one needs to increase the parameters to increase the budget. The state-of-the-art approach, Meta-BTS [Bae et al; CCS'22], performs moderate-precision bootstrapping several times to enable high-precision bootstrapping, with similar modulus consumption as the base bootstrapping it builds upon. It however damages latency.

A recent security model for fully homomorphic encryption (FHE), called IND-CPAD security and introduced by Li and Micciancio [Eurocrypt'21], strengthens IND-CPA security by giving the attacker access to a decryption oracle for ciphertexts for which it should know the underlying plaintexts. This includes ciphertexts that it (honestly) encrypted and those obtained from the latter by evaluating circuits that it chose. Li and Micciancio singled out the CKKS FHE scheme for approximate data [Asiacrypt'17] by giving an IND-CPAD attack on it and claiming that IND-CPA security and IND-CPAD security coincide for exact FHE schemes.