Public Keys are computed from Private Keys using Elliptic Curve Cryptography (ECC) over the curve secp256k1:
$$y^2 = x^3 + 7 \pmod p$$
📈 Point Multiplication
Given a generator point $G$ on the curve and your private key scalar $k$, the public key point $K$ is calculated as: $$K = k \cdot G$$
Point multiplication on an elliptic curve is a trapdoor function: easy to calculate $K$, but practically impossible to calculate $k$ given $K$ (Elliptic Curve Discrete Logarithm Problem).
🧠 Today's Key Takeaway
- Public keys are point coordinates on the secp256k1 elliptic curve.
- Elliptic curve multiplication provides cryptographic trapdoor security.
