We describe Shamir's secret sharing scheme and explain how it can be used for secure and redundant cryptocurrency storage. We include samples of individual and group assignments that can be used in an upper-division cryptology class for students who are familiar with modular arithmetic. It takes about one class to cover Shamir's secret sharing,…

This article describes the author's experience designing and implementing an inquiry-based learning (IBL) pedagogical approach to an upper-division undergraduate cryptology course. The author shares the course goals and how the IBL style supports their achievement. The article concludes with sample activities -- in-class exercises that touch on…

The Miller-Rabin test is a useful probabilistic method for finding large primes. In this paper, we explain the method in detail and give three variations on this test. These variations were originally developed as student projects to supplement a course in error correcting codes and cryptography.

We present a concrete situation where there is a difference between the theoretical security of a cipher and its limitations when implemented in practice. Specifically, when entering a PIN, smudges on the keypad substantially reduce its security. We show how the number of possible keys in the presence of the "smudge attack" can be…

We present a detailed description of a Cryptography and Computer Security course that has been offered at Knox College for the last 15 years. While the course is roughly divided into two sections, Cryptology and Computer Security, our emphasis here is on the Cryptology section. The course puts the cryptologic material into its historical context…

Ciphers based on rotor machines were the state-of-the-art in the mid-1900s, with arguably the most famous being the German Enigma. We have found that students have great interest in the Enigma and its cryptanalysis, so we created our own rotor cipher that is simulated with shifting tables and can be cryptanalyzed. Ours and the historic rotor…

We consider the use of projects in math courses as a mechanism for promoting coding, communication, and interdisciplinary application of math skills. Final projects play an important role, but we also discuss several alternate types of projects. We describe a model that incorporates projects at all stages across the undergraduate mathematics…

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…

Prospective teachers and cryptography students use programming, statistics and guile to enrich both their courses.

This paper describes a framework for identifying, classifying, and coding student proofs, modified from existing proof-grading rubrics. The framework includes 20 common errors, as well as categories for interpreting the severity of the error. The coding scheme is intended for use in a classroom context, for providing effective student feedback. In…

We describe two short group projects for finite mathematics students that incorporate matrices and linear programming into fictional consulting requests presented as a letter to the students. The students are required to use mathematics to decrypt secret messages in one project involving matrix multiplication and inversion. The second project…

At the suggestion of a colleague, I read "The Code Book", [32], by Simon Singh to get a basic introduction to the RSA encryption scheme. Inspired by Singh's book, I designed a Ball State University Honors Colloquium in Mathematics for both majors and non-majors, with material coming from "The Code Book" and many other sources. This course became…

In order to get undergraduates interested in mathematics, it is necessary to motivate them, give them good reasons to spend time on a subject that requires hard work, and, if possible, involve them in undergraduate research. This article discusses how cryptography can be used for all these purposes. In particular, a special topics course on…