Cryptography has a tremendous potential to enrich math education. In the first place, it puts

mathematics in a dramatic setting. Children are fascinated by intrigue and adventure. More is at

stake than a grade on a test: if you make a mistake, your agent will be betrayed.

In the second place, cryptography provides a natural way to get students to discover certain key

mathematical concepts and techniques on their own. Too often math teachers present everything

on a silver platter, thereby depriving the children of the joy of discovery. In contrast, if after many

hours the youngsters finally develop a method to break a cryptosystem, then they will be more

likely to appreciate the power and beauty of the mathematics that they have uncovered. Later I

shall describe cryptosystems that the children can break if they rediscover such fundamental

techniques of classical mathematics as the Euclidean algorithm and Gaussian elimination.

In the third place, a central theme in cryptography is what we do not know or cannot do. The

security of a cryptosystem often rests on our inability to efficiently solve a problem in algebra,

number theory, or combinatorics. Thus, cryptography provides a way to counterbalance the

impression that students often have that with the right formula and a good computer any math

problem can be quickly solved.

Finally, cryptography provides an excellent opportunity for interdisciplinary projects. The first

example in the next section shows how this can be done in the middle or even primary grades.