On pedagogically sound examples in public-key cryptography

Pencil-and-paper exercises in public-key cryptography are important in learning the subject. It is desirable that a student doing such an exercise does not get the right answer by a wrong method. We therefore seek exercises that are sound in the sense that a student who makes one of several common errors will get a wrong answer. Such exercises are difficult to construct by hand. This paper considers how to do so automatically, and describes software developed for this purpose, covering several popular cryptosystems (RSA, Diffie-Hellman, Massey-Omura, ElGamal, Knapsack). We also introduce diagnostic exercises, in which all error paths lead to different answers, so that the answer given by the student may suggest the nature of their error. These too can be generated automatically by our software.