As the size of the communication through networks and especially through Internet grew, there became a huge need for securing these connections. The symmetric and asymmetric cryptosystems formed a good complementary approach for providing this security. While the asymmetric cryptosystems were a perfect solution for the distribution of the keys used by the communicating parties, they were very slow for the actual encryption and decryption of the data flowing between them. Therefore, the symmetric cryptosystems perfectly filled this space and were used for the encryption and decryption process once the session keys had been exchanged securely. Parallelism is a hot research topic area in many different fields and being used to deal with problems whose solutions take a considerable amount of time. Cryptography is no exception and, computer scientists have discovered that parallelism could certainly be used for making the algorithms for asymmetric cryptosystems go faster and the experimental results have shown a good promise so far. This thesis is based on the parallelization of a famous public-key algorithm, namely RSA.