High processing time and implementation complexity of the fully homomorphic encryption schemes intrigued cryptographers to extend partially homomorphic encryption schemes to allow homomorphic computation for larger classes of polynomials. In this thesis, we study several public key and partially homomorphic schemes and discuss a recent technique for boosting linearly homomorphic encryption schemes. Further, we implement this boosting technique on CGS linearly homomorphic encryption scheme to allow one single multiplication as well as arbitrary number of additions on encrypted plaintexts. We provide MAGMA source codes for the implementation of the CGS scheme along with the boosted CGS scheme. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2017. / FAU Electronic Theses and Dissertations Collection