Arithmetic and cryptography

Among the unexpected features of recent developments in technology are the connections between classical arithmetic on the one hand, and new methods for reaching a better security of data transmission on the other. We will illustrate this aspect of the subject by showing how modern cryptography is related to our knowledge of some properties of natural numbers. As an example, we explain how prime numbers play a key role in the process which enables you to withdraw safely your money from your bank account using ATM (Automated Teller Machines) with your secret PIN (Personal Identification Number) code.