ECDSA signing and verification visualized step by step
Given public key Q = k * G (where k is the private key and G is the generator point), finding k requires solving the Elliptic Curve Discrete Logarithm Problem. With a 256-bit key, there are ~10^77 possible values - more than atoms in the observable universe. Point multiplication is a one-way trapdoor function: easy to compute forward, computationally infeasible to reverse.