Data encryption is vital in protecting the information that we send over the internet on a daily basis. This paper will explore two of the most commonly used public key encryption algorithms today: RSA and elliptic curve. These algorithms draw from mathematical areas such as Number Theory to make it nearly impossible using our current technology to decrypt ciphered messages without the necessary keys. We provide a basic outline of the process of encoding and encrypting through the use of these two algorithms. We also explore how data compression algorithms, such as Huffman's Text Compression algorithm, affect encryption.