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.

How Does the Choice of Elliptic Curve Affect the Security of the Signature?
What Are the Risks of Using a Poorly Chosen Elliptic Curve?
What Makes the ECDSA Process “One-Way” and Why Is This Critical for Security?
What Is the Specific Elliptic Curve Standard Commonly Used in Bitcoin?
How Does the Elliptic Curve Digital Signature Algorithm (ECDSA) Relate to Public Key Security?
What Is the Computational Problem That Makes This Derivation Hard?
What Is the Risk to ECDSA from Quantum Computing?
What Is the Discrete Logarithm Problem?

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