Melissa S. Keranen

The Hamilton-Waterloo Problem with 4-Cycles and a Single Factor of n-Cycles

A 2-factor in a graph G is a 2-regular spanning subgraph of G, and a 2-factorization of G is a decomposition of all the edges of G into edge-disjoint 2-factors. A

RSAvisual: a visualization tool for the RSA cipher

{\{C_{m}^{r}, C_{n}^{s}\}}

AESvisual: A Visualization Tool for the AES Cipher

-factorization of Kυ asks for a 2-factorization of Kυ, where r of the 2-factors consists of m-cycles, and s of the 2-factors consists of n-cycles. This is a case of the Hamilton-Waterloo problem with uniform cycle sizes m and n. If υ is even, then it is a decomposition of Kυ − F where a 1-factor F is removed from Kυ. We present necessary and sufficient conditions for the existence of a

VIGvisual: A Visualization Tool for the Vigenère Cipher

{\{C_{4}^{r}, C_{n}^{1}\}}

Some new Kirkman signal sets

-factorization of Kυ − F.

Orientable Z_n-distance magic labeling of the Cartesian product of many cycles

This paper describes a visualization tool ECvisual that helps students understand and instructors teach elliptic curve based ciphers. This tool permits the user to visualize elliptic curves over the real field and over a finite field of prime order, perform arithmetic operations, do encryption and decryption, and convert plaintext to a point on an elliptic curve. The demo mode of ECvisual can be used for classroom presentation and self-study. With the practice mode, the user may go through steps in finite field computations, encryption, decryption and plaintext conversion. The user may compute the output for each operation check each answer for correctness. This helps students understand the primitive operations and how they are used in an elliptic curve cipher. The opportunity for self-study provides an instructor greater flexibility in selecting a lecture pace for this detail-filled material. Classroom evaluation was positive and very encouraging.