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Cryptography has become an important topic in undergraduate curricula in mathematics and computer science, not just for its intrinsic interest---``about the most fun you can have with mathematics''\cite{ferg04, but for its current standing as the basis for almost all computer security. From wireless networking to secure email to password protection, cryptographic methods are used to secure information, to protect users, and to protect data. At Victoria University, cryptography has been taught as part of a mathematics and computer science degree for several years. The students all have had at least a year of tertiary mathematics, and some exposure to a computer algebra system (Maple). However, the cost of Maple, and the current licensing agreement, means that students are unable to experiment with the software away from the computer laboratories at the University. For this reason we have decided to investigate the use of open-source computer algebra systems Maxima and Axiom. Although not as full-featured and powerful as the commercial systems Maple and Mathematica, we show they are in fact admirably suited for a subject such as cryptography. In some ways Maxima and Axiom even surpass Maple and Mathematica. Student response to the introduction of these systems has been very positive.