We present an algorithm for a matrix-based Enigma-type encoder based on a variation of the Hill Cipher as an application of 2 × 2 matrices. In particular, students will use vector addition and 2 × 2 matrix multiplication by column vectors to simulate a matrix version of the German Enigma Encoding Machine as a basic example of cryptography. The ideal assumed background is a rudimentary familiarity of matrix multiplication and vector addition, but students who have successfully completed introductory linear algebra, number theory, and discrete mathematics will find this example accessible. Making this connection between these two systems provides a rich field for the introduction of the concepts mentioned above.