A few decades ago (fortunately, just in time for the Information Age) it was discovered that it is possible for two people who have never met to communicate with one another in a way that is secure against eavesdropping. It is remarkable that this is possible in the absence of shared private information, such as the key to a classical cryptosystem. The security of these so-called public-key protocols lies in the computational infeasibility of finding the key, rather than in secrecy. The number theoretic ideas used by these protocols were first discovered hundreds of years ago by pure mathematicians, but have become one of the most important areas of active research in applied mathematics. In this talk we'll describe public-key cryptography via the RSA algorithm, which can be applied to both secure communication and identity verification.