Cryptography has been widely used as a mean to secure message communication. A cryptosystem is made up of a publicly available algorithm and a secretly kept key. The algorithm is responsible for transforming the original message into something unintelligible. The result of losing the key or cracked algorithm can be catastrophic, where all secret communications will be known to adversaries. One way to find the key is by brute-force attacks which try every possible combination of keys. The only way to prevent this is by having the key of sufficiently large enough such that finding the right key cannot be made in a reasonable time frame. However, large key size imposes extra computational works which result in larger energy consumption and thus more heat dissipation to the environment.... Therefore, the selection of key size does not only depends on the required security level, but also factors such as the ability of the processor and the available memory resources. The advent of multi-core technology promises some improvements in the utilization of computational resources. Many reports support the idea that multi-core technology brought a significant improvement over the single core technology. In this study, we investigate this hypothesis on the RSA cryptosystem in relation to the key size. Earlier studies reported multi-core efficiency in normal applications, but the question arises if multi-core architecture remains superior to a single core architecture when dealing with applications involving large integers. From our experimentation, we observe that the higher the number of cores, the better the performance of the encryption and decryption processes. The quad-core technology can smoothly handle operations involving 8192 bits key.