Forge Capsule

Homomorphic Encryption: Fully Homomorphic and CKKS Scheme

Homomorphic encryption (HE): compute on encrypted data without decrypting. Partial HE: additive (Paillier) or multiplicative. Fully HE (FHE): arbitrary circuits. Gentry 2009: first FHE construction using ideal lattices. BGV/BFV: integer arithmetic, leveled FHE. CKKS: approximate arithmetic for floating-point (neural network inference). TFHE: gate bootstrapping, fast boolean circuits. Key operations: addition, multiplication, bootstrapping (expensive). Noise management: ciphertext noise grows with operations — bootstrapping refreshes. Applications: private ML inference, secure aggregation, private set intersection. OpenFHE, SEAL (Microsoft), HEAAN libraries. Performance: 1000-10000x overhead vs plaintext.