Networks are virtual windows to the people which allow remote access to geographically distant resources without having to be physically present. This is achieved by sending data back and forth in the network. But networks are vulnerable because of their inherent characteristic of facilitating remote access. Hence network security plays a vital role in real time environment as it protects loss and misuse of the data in the network. There are many applications and algorithms running behind the scene for providing security while transmitting data in the network. One of the most important components of network security is cryptography and it consists of many algorithms that protect user from the adversary like trapdoor, eavesdroppers, hackers etc. There are many well known algorithms which serves this purposes and each have its own advantages and disadvantages. The aim of this paper is to outline the key concepts involved in two algorithms namely Goldwasser-Micali encryption and most widely used RSA. Some of the metrics used for comparison are encryption time, decryption time and size of cipher text with varying plain text sizes which are the key considerations for choosing an encryption algorithm. The comparison of encryption and decryption time with varying cypher text sizes for both the algorithms using math lab code and preliminary observations are depicted in this paper.