Thank Fermat For Your Online Security

You might not know it, but Pierre de Fermat — a lawyer and mathematician — created a little theorem that makes sure that the Web site that you connect to is the right one. With this, when you connect to a Web site, the site provides its public key and signs a message with the associated private key. Your browser will then check the signature against the public key, ad if it checks out, you will be allowed to connect to the Web site. Otherwise, these days, the browser will give you a warning that the site cannot be trusted. It is crypto magic!

While elliptic curve cryptography is typically used for the key exchange method these days (such as with ECDH — Elliptic Curve Diffie Hellman), it is normally RSA that is used to provide the public key and create the signature.

Most people think it was Leonhard Euler who helped solve the puzzle of finding a trapdoor in public key encryption. But, it was actually Fermat’s Little Theorem which provided the solution to the problem [here]:

With Fermat’s Little Theorem, we have:

and where p is a prime number. The basic method for encrypting and also signing is [here]: