A short summary:
- Paillier encryption is based on some fancy residuosity math assumption and is additively homomorphic: E(m_1) * E(m_2) = E(m_1 + m_2). Provides more or less the same homomorphic functionality as ElGamal encryption but is based on a different assumption which might be handy for diversifying security
- CryptDB allows performing computations on encrypted data and uses Paillier encryption as one of the encryption types to support homomorphic queries. CryptDB’s onion encryption that uses multiple types of encryption providing different guarantees allows to find a compromise between:
- privacy (more operations on encrypted data → less privacy),
- customizability (does the query require the operation, e.g., ordering of the entries or addition, to be performed at all?),
- and performance (is it fast enough to be used in real world systems?)