Ciphertext-to-Ciphertext Addition

CKKS’s ciphertext-to-ciphertext addition scheme is exactly the same as BFV’s ciphertext-to-ciphertext addition scheme (Summary D-2.4 in §D-2.4).

$⟨$ Summary D-3.3 $⟩$ CKKS Ciphertext-to-Ciphertext Addition

${𝖱𝖫𝖶𝖤}_{S, σ} (Δ M^{⟨ 1 ⟩}) + {𝖱𝖫𝖶𝖤}_{S, σ} (Δ M^{⟨ 2 ⟩})$

$= (A^{⟨ 1 ⟩}, B^{⟨ 1 ⟩}) + (A^{⟨ 2 ⟩}, B^{⟨ 2 ⟩})$

$= (A^{⟨ 1 ⟩} + A^{⟨ 2 ⟩}, B^{⟨ 1 ⟩} + B^{⟨ 2 ⟩})$

$= {𝖱𝖫𝖶𝖤}_{S, σ} (Δ (M^{⟨ 1 ⟩} + M^{⟨ 2 ⟩}))$