Secp256k1

Secp256k1 is the name of the elliptic curve used by Bitcoin to implement its public key cryptography. All points on this curve are valid Bitcoin public keys. When a user wishes to generate a public key using their private key, they multiply their private key, a large number, by the Generator Point, a defined point on the secp256k1 curve. Thanks to the Discrete Log Problem, dividing a public key by the Generator Point cannot yield a private key. All elliptic curves are equations with a specific template: _y^2 = x^3 + ax^ + b_. For secp256k1 specifically, _a_ = 0 and _b_ = 7, yielding the equation _y^2 = x^3 + 7_. Because the _y_ component of the equation is squared, secp256k1 is symmetric across the x-axis, and for each value of _x_, there are two values of _y_, one of which is odd while the other is even. This allows public keys to be identified simply by the x-coordinate and the parity of the y-coordinate, saving significant data usage on the blockchain.