We give a review of the Smart-Vercauteren fully homomorphic encryp-tion scheme presented in 2010. The scheme follows Craig Gentry’sblueprint of first defining a somewhat homomorphic encryption scheme,and prove that it is bootstrappable. This is then used to create the fullyhomomorphic scheme. Compared to the original paper by Smart andVercauteren, we give a more comprehensive background, and explainsthe concepts of the scheme more in detail. This text is therefore wellsuited for readers who find Smart and Vercauteren’s paper too brief.