Why We Don't Generate Elliptic Curves Every Day

Filippo argues that user-generated cryptographic parameters, such as custom elliptic curves, are unsafe and offer no significant benefit, so modern cryptography is better served by fixed standard parameter sets. He says the old rationale for custom parameters, avoiding a single shared target, no longer fits an era where even one key breaking is considered unacceptable. He also points to the 2015 Logjam attack, where the custom-parameter negotiation added complexity that led to the attack's worst parts, and to a 2020 Windows vulnerability that let attackers fake signatures by controlling custom curves. Generating parameters can also be slow, with openssl dhparam 2048 taking more than 17 seconds on the author's M2 machine, and verifying them is harder still.