Have you ever wondered about the math behind bitcoin’s private and public keys?
Here’s how it works.
Imagine that you have a shoebox.
At the bottom of the box is a piece of graph paper.
Now, you go get a bundle of wire and tangle it up in a big messy ball. Like a bunch of tangled cables.
Now, inside the box you put an ant that will walk the wire and follow your instructions.
Now, you put the ant on its starting point on the wire. Then you pick a random number (say 1,078) and tell it to walk that number of waypoints.
How far to the next waypoint? The ant uses its handy maps app. At each waypoint, the app says how far to go to the next.
The ant starts walking along the wire, up, down, crisscrossing back and forth on the tangled wires in the box. A little while later, the ant completes the 1,078 waypoints and stops. You ask the ant to look down at the graph paper and tell you its position above the grid.
It tells you coordinates, say (15, 9).
That’s it! Your private key is 1078 (number of steps) and your public key is (15, 9).
Someone who has your public key (15, 9) has no idea how many waypoints the ant took to get there.
This is the cool thing about the encryption (maps app). When the ant looks forward, there is only one next waypoint. However, if the ant looks backwards, there are two waypoints that could arrive to where the ant is standing.
This means that for any malicious ant on the public key (15,9) trying to walk back to count the number of waypoints to the starting spot (secret key), there are many forks in the road that the ant must navigate when making the return trip. This makes the journey back impossible to do as a single ant. But maybe not for a vast colony of ants (quantum computer).
The real Bitcoin encryption uses vast distances and seemingly infinite points within a massive mathematical box.
To illustrate the vastness of the true scale, if each ant waypoint was roughly was the width of a human hair, the box would be almost 5 times the Milky Way galaxy (475,000 light years square) and the tangled wire would wrap around the visible universe uncountable trillions of times. It’s uncountable because there are almost as many waypoints for the ant to stop as there are atoms in the universe.
