How Does the Discrete Logarithm Problem Relate to ECDSA’s Security?

The Discrete Logarithm Problem (DLP) is the underlying mathematical challenge that secures many public-key cryptosystems. In ECDSA, the equivalent is the Elliptic Curve Discrete Logarithm Problem (ECDLP).

The security of the private key rests entirely on the assumption that solving the ECDLP is computationally infeasible. If an efficient solution to the ECDLP were found, an attacker could easily derive the private key from the public key, compromising all ECDSA-secured assets.