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Teaching Mathematics and its Applications Advance Access originally published online on June 2, 2006
Teaching Mathematics and its Applications 2007 26(1):2-16; doi:10.1093/teamat/hrl008
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© The Author 2006. Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

A cryptological way of teaching mathematics

Pino Caballero-Gil and Carlos Bruno-Castañeda

Pino Caballero-Gil, Department of Statistics, Operations Research and Computation, Faculty of Maths, University of La Laguna, 38271 La Laguna. Tenerife, Canary Islands, Spain. E-mail: pcaballe{at}ull.es

  Abstract

This work addresses the subject of mathematics education at secondary schools from a current and stimulating point of view intimately related to computational science. Cryptology is a captivating way of introducing into the classroom different mathematical subjects such as functions, matrices, modular arithmetic, combinatorics, equations, statistics and proofs, which usually are recognized as difficult for many students. Special attention is paid here to the concepts of proof and verification through the definition of zero-knowledge cryptographic protocols. Many other different cryptographic and cryptanalytic activities (building and breaking ciphers, respectively) and modern cryptographic applications such as secret-sharing protocols are also proposed as resources for motivating mathematics learning and for achieving a significant improvement in student understanding of several algebraic, analytical and statistical concepts.

Received July 2005. Accepted February 2006.


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