We construct a simple public-key encryption scheme that supports polynomially many additions and one multiplication, similarly to the cryptosystem of Boneh, Goh, and Nissim (BGN). Security is based on the hardness of learning with errors (LWE), which is known to be as hard as certain worst-case lattice problems. Some features of our cryptosystem include support for large message space, an easy way of achieving formula-privacy, and a better message-to-ciphertext expansion ratio than BGN. Also, it offers an easy way of multiplying two encrypted polynomials.
At Eurocrypt'10, Gentry, Halevi and Vaikuntanathan REF proposed a FHE scheme based on the Learning With Error (LWE) problem.
A Simple BGN-type Cryptosystem from LWE
Proceedings of Eurocrypt 2010, LNCS 6110
Computer Science