  Public-key cryptography has become a popular way to motivate the teaching of
concepts in elementary number theory, abstract algebra, and introduction to
proof courses, as well as in cryptography courses. Unfortunately, many experts
expect quantum computers to make common forms of public-key cryptography
obsolete in the near future. Fortunately, there are several systems being
evaluated to replace RSA and the other systems we currently use. While some of
the systems are too complicated to be good examples in introductory courses,
others are either quite manageable or have simplified versions which are
manageable. This article gives a tour of the main types of systems under
consideration and the teaching resources available for instructors who want to
teach them.
