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…

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 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.

Cryptology, or cryptography, is the study of writing and deciphering hidden messages in codes, ciphers, and writings. It is almost as old as writing itself. Ciphers are messages in which letters are rearranged or substituted for other letters or numbers. Codes are messages in which letters are replaced by letter groups, syllables, or sentences.…

Cryptography is the science of hidden or secret writing. More generally, cryptography refers to the science of safeguarding information. Cryptography allows people to use a public medium such as the Internet to transmit private information securely, thus enabling a whole range of conveniences, from online shopping to personally printed movie…

The Hill cipher is the simplest example of a "block cipher," which takes a block of plaintext as input, and returns a block of ciphertext as output. Although it is insecure by modern standards, its simplicity means that it is well suited for the teaching of such concepts as encryption modes, and properties of cryptographic hash functions. Although…

When students learn mathematics, they tend to understand and remember the mathematical processes that they find practical and relevant. It is not surprising then that "Principles and Standards for School Mathematics" (NCTM 2000) encourages teachers to help students discover the relevance of mathematics in their daily lives. To help young people…

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…

The number Pi has a rich and colorful history. The origin of Pi dates back to when Greek mathematicians realized that the ratio of the circumference to the diameter is the same for all circles. One is most familiar with many of its applications to geometry, analysis, probability, and number theory. This paper demonstrates several examples of how…

For the general public, the field of cryptography has recently become famous as the method used to uncover secrets in Dan Brown's fictional bestseller, The Da Vinci Code. But the science of cryptography has been popular for centuries--secret hieroglyphics discovered in Egypt suggest that code-making dates back almost 4,000 years. In today's…