How Does the Elliptic Curve Digital Signature Algorithm (ECDSA) Relate to Public Key Security?

ECDSA is the algorithm used in Bitcoin and many other cryptocurrencies to create digital signatures, which prove ownership of funds without revealing the private key. It relies on the mathematical difficulty of solving the Elliptic Curve Discrete Logarithm Problem.

The security of the public key, and thus the funds, rests entirely on the impossibility of efficiently calculating the private key from the public key.