We gave two talks, at the schools Escola Pia and Petit Plançó in Olot, introducing the students to the world of cryptography. Cryptography is the part of mathematics (and computer science) that deals with secret communications, that is, the transmission of messages that can only be “understood” by authorized participants and are not comprehensible to third parties. Most of the student had not heard about this before, but they could easily think of situations where we have a need for this, for example when we do online shopping and we send our credit card number through the internet.

We started with a little bit of history of the subject, whose origins can be traced back at least to the Third Century BC in Greece (at that time the main use of cryptography was in war time). We explained some simple ciphers, such as the scytale, Cesar’s cipher and Vigenere’s cipher, and also some attacks and how to break them. The students were pretty active, and actually some of them managed to figure out ways of breaking these ciphers. We took the chance to talk about “arithmetic modulo n”, which is used in many practical cryptosystems and is usually not taught at secondary school.

All in all, the students were receptive to these ideas, and showed curiosity for understanding how information is ciphered in our day-to-day digital communications, for example in Whatsapp messages or in applications such as Facebook.