Private Public key cryptography. 

I barely understand it.

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“In short, the unique s value provides a pathway for getting to the randomly-generated point r.

You can give these two pieces of information to someone else, and starting from the public key point Q they can use the s value to help them get to the random point r. The trick here is that only the person with the corresponding private key d could create a valid pathway to this random point provided by s.

This pathway also has the message hash z encoded in to it, which is what effectively allows us to create signatures for messages; nobody can create the pathways from the public key to a random point on the curve via the message hash without knowing the private key it was created from.”