ABSTRACT
One of the more striking “real world” applications of number theory is the study of cryptography, which concerns itself with secret communications. The ability to decipher such communications can have striking global consequences; the decipherment of the famous Zimmerman telegram (a 1917 communication from the German Foreign Office to the German ambassador in Mexico), for example, played a significant role in the decision of the United States to enter World War I. This chapter gives an introduction to this area of mathematics, emphasizing the role that number theory plays in it. The idea of “wrapping around” to the beginning of the alphabet suggests modular arithmetic, and indeed it is easy to see how to formalize this mathematically. Essentially, the RSA method depends for its validity on this rule of thumb: multiplying is easy, factoring is hard.
