Initiation Of Cryptology Thanks To A Scilab™ Project Using Perfect Magic Shuffles

Abstract

Why use Magic for teaching cryptology and algorithmic notions through thanks to Scilab/Matlab programs? During a magic performance, the audience will seek to understand how the trick works once the surprise has worn off. So the teacher can use that in order to interest their students, and a magic trick will lead them to ask how does it work? After discovering the secret, the students could want to create one trick themselves .
I had the idea to use magic shuffles to explain the basis of cryptology in 2016. I presented it during a conference in INSA only for their students [1].
In this article I present the main notions of cryptology as message representation, encrypt function and decrypt function. I discuss about the integrity of the cryptology. In fact, these encrypt/decrypt method is based on the secret of algorithm. We know that this method can no more use for real application. What it is explained can be teach either with a top-bottom method or with a bottom-top method as project pedagogy. All the figures come from Scilab programs.
To be understable by students, I use playing cards and magic shuffles !
• the message is represented by playing cards (as Hearts, Spades, Diamonds and Clubs),
• the encrypt function is the function which describes the Faro shuffle using in many cards trick,
• the decrypt function is not the inverse of the encrypt function but we use a magic property of this shuffle, i.e the idempotency.
The students know the magic trick secret and like that they are able to “perform” a magic representation for their friends and family. After that, if one (or more !) spectator wants to know the secret, they would be able to explain and so enjoy a certain success amount.
So the students have to work hardly on but they think/feel that it isn't work but game ! Sharing a mathematical / informatics / cryptography notions and demonstrations is not easy but becomes it with this approach. Isn't this the aim of all teaching?
Whatever the students will be able to see the impact that originality and creativity have when com-bined with an interest in a professional area. But it isn't enough without trainings !