In this paper, the authors present an algorithm for Residue Number System (RNS) implementation of RSA cryptography based on an existing RNS division algorithm. The proposed algorithm and that of the state of the art were written in C++ programming language to compare their efficiency with respect to execution time. Experimental results show that their algorithm can encrypt and decrypt text without loss of inherent information and faster than the state of the art. It also offers firm resistance to brute-force and key sensitivity attacks.