Implementation of the fully homomorphic encryption scheme over integers with shorter keys

New researches in the field of homomorphic encryption schemes have made it possible to implement a variety of schemes using different techniques and programming languages. In this paper we describe the implementation of a DGHV scheme variant using Python and the GMPY2 library. This scheme was first proposed in 2010, by van Dijk et al, and later modified into two variants by Coron in 2011 and 2012, which reduced the prohibitive size of the public keys, at the cost of computational power. Besides that, this paper also presents a comparison of these implementations with the previous implementation of Coron´s first variant.