# University of Michigan Math and Science Scholars

Cryptography and Number Theory

A question many researchers in pure mathematics are often being asked is what their work is useful for. One great mathematician, G. H. Hardy had said that his field, Number Theory, is completely useless, yet, in spite of that (or maybe for this very reason), he thought it the most beautiful in all of mathematics. Little did he know that exactly thirty years after his death Number Theory became central to the new breakthrough algorithm for ciphering messages invented by Ron Rivest, Adi Shamir, and Leonard Adleman, and called RSA after their names. This algorithm was key to the development of the internet, online banking, and modern economy. And so two thousand years after its inception, Number Theory became essential to the world. In this course, we will see why ancient mathematicians have found Number Theory and prime numbers so captivating, and we will understand how RSA works. In the process, we will crack a few encrypted messages and invent some new ways of ciphering them. The course meetings will be interactive.