Perform computations on encrypted data without decrypting
E(a) × E(b) = E(a + b) — multiplying ciphertexts adds plaintexts!
Public key for encryption, private for decryption
Client encrypts with public key
Server operates on ciphertext
Client decrypts final answer
Process patient data without exposing sensitive health information
Credit scoring and fraud detection on encrypted transactions
Tally votes without revealing individual ballots
Partially Homomorphic: Supports one operation (either add OR multiply). Examples: RSA (multiply), Paillier (add).
Somewhat Homomorphic: Limited number of both operations before noise grows too large.
Fully Homomorphic (FHE): Unlimited operations of any type. First practical scheme: Gentry (2009).
Trade-off: HE is 1000x-1000000x slower than unencrypted computation. Active research is improving performance.