Ciphertext-to-Plaintext Multiplication

D-2.6 Ciphertext-to-Plaintext Multiplication

BFV’s ciphertext-to-plaintext multiplication uses RLWE’s ciphertext-to-plaintext multiplication scheme with the sign of the $A \cdot S$ term flipped in the encryption and decryption formula. Specifically, this is equivalent to the alternative GLWE version’s (§B-4.4) ciphertext-to-plaintext multiplication scheme (§C-3) with $k = 1$ .

$⟨$ Summary D-2.6 $⟩$ BFV Ciphertext-to-Plaintext Multiplication

${𝖱𝖫𝖶𝖤}_{S, σ} (Δ M + E) \cdot Λ$

$= (A, B) \cdot Λ$

$= (A \cdot Λ, B \cdot Λ)$

$= {𝖱𝖫𝖶𝖤}_{S, σ} (Δ (M \cdot Λ) + Λ E)$

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