What Is the Role of the “Elliptic Curve” in the Security of ECDSA?

The security of ECDSA is rooted in the mathematical properties of the elliptic curve over a finite field. Specifically, it relies on the computational difficulty of the Elliptic Curve Discrete Logarithm Problem (ECDLP).

This problem makes it easy to calculate the public key from the private key but extremely hard to do the reverse. The curve parameters are carefully chosen to ensure a high level of cryptographic strength.

This mathematical foundation is what protects the private key.