D-4.4 Ciphertext-to-Plaintext Addition

BGV’s ciphertext-to-plaintext addition scheme is almost the same as BFV’s scheme (Summary D-2.5 in §D-2.5). However, one difference is that it’s not the case that the plaintext polynomial Λ(X) to be added is scaled up by Δ, but it remains as Λ(X).

Summary D-4.4 BGV Ciphertext-to-Plaintext Addition

𝖱𝖫𝖶𝖤S,σ(M + ΔE) + Λ

= (A, B) + Λ

= (A, B + Λ)

= 𝖱𝖫𝖶𝖤S,σ((M + Λ) + ΔE)