Cryptology

Abstract

Now that so much information is transmitted over the Internet, it has become very important to develop secure methods of sending and receiving information. Security concerns are widespread because so much personal information is stored on computers. Eavesdroppers try to intercept online transactions, hoping to steal your credit card information or even your identity. Over the years, governments have relayed vital information to allies while attempting to keep enemies from obtaining it. Entire agencies, such as the National Security Agency, employ hundreds of mathematicians to keep their government’s information a secret while trying to intercept and decode information belonging to other governments or groups. This chapter introduces examples of both private key and public key codes, including the RSA public key code.

The problem of distinguishing prime numbers from composites, and of resolving composite numbers into their prime factors, is one of the most important and useful in all of arithmetic.

—Carl Friedrich Gauss, 1777–1855