Homomorphic Ciphertext-to-Plaintext Multiplication

D-1.4 Homomorphic Ciphertext-to-Plaintext Multiplication

TFHE’s ciphertext-to-plaintext multiplication uses LWE’s ciphertext-to-plaintext multiplication scheme, which is equivalent to GLWE’s ciphertext-to-plaintext multiplication scheme (§C-3) with $n = 1$ .

$⟨$ Summary D-1.4 $⟩$ TFHE Ciphertext-to-Plaintext Multiplication

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

$= (\vec{a}, b) \cdot λ$

$= (λ \cdot \vec{a}, λ \cdot b)$

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

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