Optimizations of Brakerski´s fully homomorphic encryption scheme

In this paper, we propose two methods to improve the efficiency of the scheme. Our main optimization is a new method to fulfill the tensor product of vectors, which can significantly reduce the computational overhead in the key switching algorithm, and the basic homomorphic operation is about 40%-50% faster than before by using this method. By truncating the least significant bits from every element of ciphertext vector, another optimization is presented. Using this method, the ciphertext vector can be represented concisely, which can further improve the efficiency.