Bitcoin gives you the ability to generate a key pair, a public key and a private key. You generate a signature with your private key, and that signature is what you attach to a transaction. It proves to any third party that the transaction was authorized by you, the rightful owner, without you ever having to reveal the key itself.
But what is actually happening underneath that process?
ECDSA — Elliptic Curve Digital Signature Algorithm
The mechanism behind all of it is ECDSA — a digital signature system built on elliptic curve cryptography.
An elliptic curve is defined by the equation y² = x³ + ax + b. Bitcoin fixes the constants at a = 0 and b = 7, which reduces the equation to the one introduced in the last article:
