What Mathematical Problem Is the Security of ECDSA Based Upon?

The security of the Elliptic Curve Digital Signature Algorithm (ECDSA) is based on the mathematical difficulty of the Elliptic Curve Discrete Logarithm Problem (ECDLP). This problem states that given a base point G and a point Q on an elliptic curve, it is computationally infeasible to find the integer 'k' (the private key) such that Q = k G. The immense difficulty of solving for 'k' is what makes the private key secure.