One of the greatest contributions to computer security: Adding Points on an Elliptic Curve

Respecting nP

Beauty is all around us. In nature, and even within the security of our Internet connections. Every single time that you connect to the Internet, there’s a bit of magic that goes on, and it is beautiful in its simplicity, but also in protecting you from others who wish to spy on you.

Your computer generates a random number, and then takes a point on an elliptic curve, and a prime number, and then adds that point to itself, with the number of times that you have generated. Next, you pass that to the server — and who has also done the same thing — and then you take the value received, and then, again, add it to itself by the number your generated. And in the end, both you and the server has the same value. This is now your encryption key, and only you and the server will know it. That is the magic of the ECDH (Elliptic Curve Diffie Hellman) method:

And Elliptic Curve Cryptography (ECC) is also used to create a public key and a private key, and where we can digitally sign for things, and to create your online identity. I will first define the core of ECC: