Partial vs Full
Partially homomorphic (Paillier: additions; RSA: multiplications). Fully homomorphic (FHE): both. Gentry 2009 breakthrough.
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Modern FHE schemes
BFV, CKKS (approximate), TFHE. CKKS handles reals — used in ML on encrypted data.
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Bootstrapping
Refresh noisy ciphertext. Expensive (~seconds per bootstrap). Ongoing performance research.
Performance
Encrypted addition: microseconds. Encrypted multiplication: milliseconds. FHE inference on MNIST-scale nets: minutes.