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by tptacek 202 days ago
He does a motte-and-bailey thing with the P-curves. I don't know if it's intentional or not.

Curve25519 was a materially important engineering advance over the state of the art in P-curve implementations when it was introduced. There was a window of time within which Curve25519 foreclosed on Internet-exploitable vulnerabilities (and probably a somewhat longer period of time where it foreclosed on some embedded vulnerabilities). That window of time has pretty much closed now, but it was real at the time.

But he also does a handwavy thing about how the P-curves could have been backdoored. No practicing cryptgraphy engineer I'm aware of takes these arguments seriously, and to buy them you have to take Bernstein's side over people like Neil Koblitz.

The P-curve backdoor argument is unserious, but the P-curve implementation stuff has enough of a solid kernel to it that he can keep both arguments alive.

1 comments

Quite true, but the Dual_EC backdoor claim is serious. DJB's point that we should design curves with "nothing up my sleeve" is a nice touch.
See, this gets you into trouble, because Bernstein has actually a pretty batshit take on nothing-up-my-sleeve constructions (see the B4D455 paper) --- and that argument also hurts his position on Kyber, which does NUMS stuff!
Link?
There’s also a more approachable set of slides on the topic at https://cr.yp.to/talks/2025.11.14/slides-djb-20251114-safecu...
What do you think of those slides?
I tried a couple searches and I forget which calculator-speak version of "BADASS" Bernstein actually used, but the concept of the paper† is that all the NUMS-style curves are suspect because you can make combinations of mathematical constants say whatever you want them to say (in combination), and so instead you should pick curve constants based purely on engineering excellence, which nobody could ever disagree about or (looks around the room) start huge conspiracy theories over.

as I remember it