Homomorphic Key Switching

D-1.5 Homomorphic Key Switching

- Reference: TFHE Deep Dive - Part III - Key switching and leveled multiplications [9]

TFHE’s key switching scheme changes an LWE ciphertext’s secret key from $\vec{s}$ to ${\vec{s}}_{^{'}}$ . This scheme is essentially LWE’s key switching scheme. Specifically, this is equivalent to the alternative GLWE version’s (§B-4.4) key switching scheme (§C-5) with $n = 1$ as follows:

$⟨$ Summary D-1.5 $⟩$ TFHE Key Switching

${𝖫𝖶𝖤}_{{\vec{s}}_{^{'}}, σ} (Δ m) = (0, b) + ⟨ {𝖣𝖾𝖼𝗈𝗆𝗉}^{β, l} (\vec{a}), {𝖫𝖾𝗏}_{{\vec{s}}_{^{'}}, σ}^{β, l} (\vec{s}) ⟩$

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