In this paper we construct a pseudorandom number generator using only worst-case hardness assumptions for standard lattice problems. With a common technique, we can then build a stream cipher by combining the generated pseudorandom sequence with the plaintext. Moreover, as an option to gain efficiency both in terms of speed and memory, we suggest the use of ideal lattices in the construction. Currently, there is no known attack that could exploit this choice. Our implementation for Graphics Processing Units leverages from the parallelism inherent in lattice schemes and reaches performances comparable to the fastest known constructions that enjoy security proofs. This is a preview of subscription content, log in via an institutio