Cryptography

We will see a simple application of elementary number theory: public key cryptography. The RSA protocol relies on only very elementary facts and yet has tremendous impact (the three authors of RSA won the Turing award in 2002).

📄️ RSA

The setting is that Alice wants to send a message to Bob while making sure that the message cannot be read by an eavesdropper (Eve).

📄️ Fermat's little theorem

Consider modular arithmetic under modulo $m$. We fix number $a$ so that ${\sf gcd}(a,m)=1$.