Like other branches of mathematics, number theory has seen many surprising developments in recent years. One of the most surprising is the fact that number theory, long considered the most "useless" of any field of mathematics, has become vital to the development of modern codes and ciphers. As an example, the RSA cryptosystem, developed in the 1970's by Rivest, Shamir, and Adleman, uses some ideas that are very easy to understand. Yet, these ideas underlie large portions of both modern number theory and modern cryptography. We will explore these ideas, and show how they make RSA the first practical "trap door" cipher. This means that anyone can encode a message but only the recipient can decode it!
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