![]() While mathematicians have always been interested in elliptic curves (there is currently a million dollar prize out for a solution to one problem about them), its use in cryptography was not suggested until 1985. 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, classifying their algebraic structure for most important fields. It was not until the mid 19th century that the general question of whether addition always makes sense was answered by Karl Weierstrass. So we’re in a perfect position to feast on the main course: how do we use elliptic curves to actually do cryptography? HistoryĪs 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. We implemented finite field arithmetic and connected it to our elliptic curve code. So far in this series we’ve seen elliptic curves from many perspectives, including the elementary, algebraic, and programmatic ones. ![]()
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