GGH Encryption Algorithm
The Goldreich–Goldwasser–Halevi (GGH) lattice-based cryptosystem is an asymmetric cryptosystem based on lattices. There is also a GGH signature scheme.
The Goldreich–Goldwasser–Halevi (GGH) cryptosystem makes use of the fact that the closest vector problem can be a hard problem. It was published in 1997 and uses a trapdoor one-way function that is relying on the difficulty of lattice reduction. The idea included in this trapdoor function is that, given any basis for a lattice, it is easy to generate a vector which is close to a lattice point, for example taking a lattice point and adding a small error vector. But to return from this erroneous vector to the original lattice point a special basis is needed.
The GGH encryption scheme was cryptanalyzed in 1999 by Phong Q. Nguyen.