Homomorphic Ciphertext-to-Plaintext Addition

D-1.3 Homomorphic Ciphertext-to-Plaintext Addition

TFHE’s ciphertext-to-plaintext addition (where $λ$ is a constant to add) uses LWE’s ciphertext-to-plaintext addition scheme, which is equivalent to GLWE’s ciphertext-to-plaintext addition scheme (§C-2) with $n = 1$ .

$⟨$ Summary D-1.3 $⟩$ TFHE Ciphertext-to-Plaintext Addition

${𝖫𝖶𝖤}_{\vec{s}, σ} (Δ m + e) + Δ λ$

$= (\vec{a}, b) + Δ λ$

$= (\vec{a}, b + Δ λ)$

$= {𝖫𝖶𝖤}_{\vec{s}, σ} (Δ (m + λ) + e)$

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