What Are the Risks of Using a Poorly Chosen Elliptic Curve?

Using a poorly chosen elliptic curve can introduce critical vulnerabilities into a financial system. A 'weak curve' might allow for efficient attacks that solve the ECDLP, leading to private key compromise.

Risks include a small key space, special mathematical properties that simplify the problem, or even a 'backdoor' deliberately inserted into the curve parameters. A compromised curve means all digital signatures based on it are insecure.