How does elliptic curve cryptography work?

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How does elliptic curve cryptography work?

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[This is an elliptic curve.](https://blog.cloudflare.com/content/images/image00.png)

You can start with a couple points on the curve and use them to create lines that will lead you to additional points on the curve. You can also find new points by looking for its mirror opposite the X-axis. And you can do this several times, [like a ball bouncing around.](https://blog.cloudflare.com/content/images/image02.gif)

But in reality we only deal with whole numbers (integers) and any parts of the curve that would extend off our screen we just wrap around, and [it looks like this.](https://blog.cloudflare.com/content/images/image06.png)

It makes the bouncing ball game [look like this.](https://blog.cloudflare.com/content/images/image01.gif)

This translates to a cryptographic scheme the curve itself and your starting points represent the inputs (the key and message) and after all that bouncing around you arrive at your encrypted message.