Homomorphic Encryption Reference
Reference for partial, somewhat, and fully homomorphic encryption schemes enabling computation on ciphertexts.
Taxonomy
Partially homomorphic schemes support one operation type indefinitely (e.g., RSA for multiplication). Somewhat homomorphic schemes support both addition and multiplication but only for limited circuit depth. Fully homomorphic encryption (FHE) supports arbitrary computation on ciphertexts. The breakthrough Gentry scheme uses bootstrapping to refresh ciphertexts and enable unlimited depth.
- partial
- One operation, unlimited depth
- somewhat
- Both ops, limited depth
- fully
- Arbitrary circuits
RSA, PaillierBGV, BFVCKKS, TFHEModern Schemes
CKKS supports approximate arithmetic suitable for machine learning on encrypted data. BGV/BFV perform exact integer arithmetic for counting and comparison. TFHE enables fast bootstrapping for arbitrary Boolean circuits. All FHE schemes remain orders of magnitude slower than plaintext computation, limiting practical deployment to specific privacy-sensitive domains.
- CKKS
- Approximate arithmetic
- BFV/BGV
- Exact integer arithmetic
- TFHE
- Fast Boolean bootstrapping
ML on encrypted datainteger circuitsgate-by-gate