In this paper we will explore Rabin's cryptosystem, one of the cryptographic algorithm that is similar to RSA developed by Michael O. Rabin based on the quadratic residue problem. We will introduce the background theory, the scheme and the security of Rabin and a basic padding scheme to use for Rabin's system. Also, there is another exploration of picking different type of primes and an algorithm to solve the quadratic residue problem when the prime <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?p%20%5Cnot%20%5Cequiv%203%20%5Cpmod%7B4%7D" data-classname="equation" data-title="" /> and the experiment to measure the performance of that algorithm.