Diffie Hellman key agreement scheme with python.

So far in this series we’ve seen elliptic curves from many perspectives, including the elementary, algebraic, and programmatic ones. We implemented finite field arithmetic and connected it to our elliptic curve code. So we’re in a perfect position to feast on the main course: how do we use elliptic curves to actually do cryptography?

## History

As the reader has heard countless times in this series, an elliptic curve is a geometric object whose points have a surprising and well-defined notion of addition. That you can add some points on some elliptic curves was a well-known technique since antiquity, discovered by Diophantus. It was not until the mid 19th century that the general question of whether addition always makes sense was answered by Karl Weierstrass. In 1908 Henri Poincaré asked about how one might go about classifying the structure of elliptic curves, and it was not until 1922 that Louis Mordell proved the fundamental theorem of elliptic curves

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