A linear Cramer-Shoup encryption scheme version was proposed by Shacham in 2007. Short Cramer-Shoup encryption scheme was designed by Abdalla et al. in 2014. This scheme is a variant of the Cramer-Shoup encryption scheme that has a smaller size. They proved that it is an IND-PCA secure encryption under DDH and the collisionresistance assumptions. We design a faster version of Short Cramer-Shoup encryption scheme denoted Fast Short Cramer-Shoup encryption. We also, proposed a faster version of linear Cramer-Shoup encryption called Fast Linear Cramer-Shoup. We prove that the Fast Short Cramer-Shoup is IND-PCA secure under DDH and the collision-resistance assumptions. We also, show that our linear encryption is CCA secure under the Linear assumption. Finally we run an evaluation of performances of our schemes.