There is perhaps no greater application of number theory than its uses in many of the methods of modern cryptography. The fundamental problem in cryptography is for one party, the “sender,” to transmit a message to another party, the “receiver,” in such a way that no other party can gain knowledge of the message. Typically, the sender performs an encryption algorithm that converts the original “plaintext” message into an apparently unintelligible message called the “ciphertext.” If all goes according to plan, only someone with knowledge of the encryption algorithm and the particular key used to produce the ciphertext can make sense of it. To help keep matters straight, we enlist the help of three fictional characters, Samantha, Robert, and Theresa. Samantha will be the individual wishing to send an encrypted message while Robert will be her intended recipient. Theresa represents a third party who is attempting to decipher the contents of the message that Samantha is sending to Robert (against their wishes).