Using Cryptology to Teach Fundamental Ideas of Mathematics

Resumo

Cryptology is a very old science and until a few decades it was a science for government, military, secret services, and spies. Nowadays, cryptology is almost everywhere in our lives. This article reports on an epistemological analysis of the question: “Is it possible to teach fundamental ideas of mathematics by using cryptography?” In a first step fundamental ideas of mathematics, which are the basic guidelines for mathematical education are discussed. For the analysis a set of fundamental ideas of mathematics is developed e.g. algorithm, functional dependence, modelling, number, measuring, and ordering. In a second step connections between the set of fundamental ideas and various techniques of cryptology are shown. Some outstanding examples for this part of the analysis are the Fleissner grille or the Diffie-Hellman key exchange.