FHE schemes Over Integers

In 2010, one year after Gentry’s original scheme,another SWHEscheme is presented in [Van Dijk et al. 2010] which suggests Gentry’s ingenious bootstrapping method in order to obtain an FHE scheme. The proposed scheme is over integers and the hardness of the scheme is based on the Approximate Greatest Common Divisor (AGCD) problems [Galbraith et al. 2016]. AGCD problems try to recover p from the given set of x_i = pq_i + r_i. The primary motivation behind the scheme is its conceptual simplicity. A symmetric version of the scheme is probably one of the simplest schemes.