The RSA encryption algorithm has become one of the most important public-key encryption schemes in today's computing world. A vital performance boosting operation is the implementation of the Chinese Remainder Theorem to increase the speed of decryption. However, there are rumors and findings that suggest that this execution method, while providing significant performance benefits, is highly susceptible to side channel attacks that may reveal the private keys to an attacker. This would render the encryption useless, and allow the attacker access to important data. We will be researching these attacks on the Chinese Remainder Theorem and whether or not there exists a method of protecting against these attacks.