Homomorphic Key Switching

D-4.9 Homomorphic Key Switching

BGV’s homomorphic key switching scheme changes an RLWE ciphertext’s secret key from $S$ to $S^{'}$ . This scheme is exactly the same as BFV’s key switching scheme (Summary D-2.8 in §D-2.8).

$⟨$ Summary D-4.9 $⟩$ BGV’s Key Switching

${𝖱𝖫𝖶𝖤}_{S^{'}, σ} (M + Δ E) = (0, B) + ⟨ {𝖣𝖾𝖼𝗈𝗆𝗉}^{β, l} (A), {𝖱𝖫𝖾𝗏}_{S^{'}, σ}^{β, l} (S) ⟩$

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