# Are all homomorphic encryption schemes based on latticed-based schemes?

PALISADE offers a pool of Homomorphic Encryption schemes and it is stated that "PALISADE is a general lattice cryptography library ...". My question is rather simple: are all homomorphic encryption schemes based on lattice-based cryptography?

• If you want compact ciphertexts, but not necessarily the ability to evaluate arbitrary functions, then there are many homomorphic encryption schemes around. (Textbook) RSA is multiplicatively homomorphic. The additive variant of ElGamal is additively homomorphic when the plaintexts are small enough. Goldwasser-Micali is homomorphic for the XOR operation. Paillier is additively homomorphic over $$\mathbb{Z}_n$$. BGN allows to evaluate degree-two polynomials, provided that the plaintext remains small. In addition, there are generic techniques to boost these limited homomorphisms (e.g. boosting degree-1 to a subclass of degree-2 polynomials), see e.g. this work.