Riv. Mat. Univ. Parma, Vol. 14, No. 2, 2023

Aaron Gaio [a]

A cryptography teaching-learning sequence for high school and the concept of public-key cryptography

Pages: 249-264
Accepted in revised form: 16 October 2023
Mathematics Subject Classification: 97M10, 97C70.
Keywords: cryptography, public-key, education, school.
[a]: University of Trento, Trento, Italy

Abstract: The goal of this paper is to present a teaching-learning sequence about cryptography for high school. Applied discrete mathematics, cryptography in this particular case, is rare to find in the usual school curricula, but can provide good topics for mathematical activities and engage students in a real-world situation. Cryptography is a strongly interdisciplinary subject that would not live without other subjects (most notably, Computer Science, but also Engineering, and so on). Needless to underline the importance of public-key cryptography in the modern world and its application in research and industry and how this contribution can help bridging the gap between school mathematics and the world of research and industry.
The Italian institutional context will be presented, together with a literature review about the teaching and learning of cryptography and discrete mathematics at school. The theoretical framework and methodology used follows the principle of design research and aim at designing and presenting tasks in the model of Realistic Mathematics Education.
After presenting the whole teaching-learning sequence, I will focus on a particular task describing public-key cryptography without the typical use of RSA-like systems.
The teaching-learning sequence and the public-key cryptography activity did respect the principles of RME both in eliciting students' curiosity and interest and in the formation of some initial informal knowledge on the concepts of one-way functions and public-key cryptography that can lead to a more formal mathematical reasoning in future activities.

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