"To be fair I should mention that there's one standard NIST curve using a nice prime, namely 2^521 - 1; but the sheer size of this prime makes it much slower than NIST P-256."
(Rant: All these years later, we're all still doing penance for the fact that Schnorr signatures were patented and so everyone used ECDSA instead. It's an absolute garbage fire of a signature scheme and should be abandoned yesterday for many reasons, e.g., no real proof of security, terrible footguns like this.)
EdDSA, which is essentially deterministic Schnorr, does solve the problem.
Also, the use of P-521 didn't specifically cause the vulnerability, but the bad interaction between SHA512 and P-521 did play a role. It is unfortunate that nature conspired against us to make 2^511 - 1 a composite number. The fact that you have to go up to 521 bits to get a Mersenne prime whereas the natural target length for a hash output is 512 bits is the fatal interaction here.
(And indeed, nature could have been kinder to us and given us a Mersenne between 127 and 521...)
Isn’t it kind of the point to just roll random numbers? When would you calculate?
Never heard of (which probably demonstrates that I know pretty much nothing about cryptography?), so seeing a name spelled like "Schn...r" in this context makes at least me think of an entirely different luminary in the area. Thought it was a typo at first.