FHE over the Integers

This is a fully homomorphic encryption relying only on modular arithmetic. The authors first create an somewhat homomorphic scheme which is bootstrappable and then apply Gentry's technique to construct a fully homomorphic scheme.

One of the main advantages of this scheme represents its conceptual simplicity. The security of the scheme is reduced to the approximate gcd problem over the integers, that is, given a list of integers that are near-multiples of an unknown integer d , find d .