This project is designed to refine a course and develop a text in cryptography, the science of designing methods to disguise secret messages. The goal is to provide an innovative alternative in introductory mathematics for beginning nonscience majors as well as students preparing for certification in elementary and high school mathematics. Through this thematic approach, the objective is to sharpen students' critical thinking skills and to stimulate their interest in the use of mathematics in the daily operations of society. This course is serving to replace more traditional beginning courses such as college algebra and trigonometry and finite mathematics, and is appropriate for all entering college students. The course covers classical cipher systems (systems used during the World Wars, for example), modern encryption systems, and error-correcting codes. Some of the topics being presented in the text are substitution ciphers, transposition ciphers, the RSA Algorithm, digital signatures, the Knapsack Algorithm, and one-way functions used for PIN security. Mathematical topics to be presented at the beginning level are modular arithmetic, probability and statistics, matrix arithmetic, number theory, and combinatorics. In an active learning environment utilizing technology, these mathematical tools are used to guide students in breaking and constructing cipher systems, and in determining the strength and utility of ciphers. The radical difference in this course and the "sampler" courses that have been taught in the past is that many mathematical notions can be introduced under the one canopy of cryptography, with its obvious historical significance and its critical modem-day importance. The project is being disseminated via a preliminary manual for the course to selected institutions that are beta testing the materials in classes, presentations at national meetings, and preparation of a text for commercial publication. An experienced evaluation team is providing an intensive evaluation of the project.
