In this book we present a practicable probabilistic encryption scheme that is polynomially secure and is efficient. From the theoretical construction it is clear that the proof of Pseudo randomness of the quadratic residue generator is complete if it can be shown that there exists a one-way permutation under the possible assumption that it is infeasible to factor composite integers, and that the least significant bit is hard-core for this permutation. Furthermore, we discuss the implementation of Probabilistic encryption.