alt Hacker News> See for example the many problems of NIST P-224/P-256/P-384 ECC curves
What are those problems exactly? The whitepaper from djb only makes vague claims about NSA being a malicious actor, but after ~20 years no known backdoors nor intentional weaknesses has been reliably proven?
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It would be wise for people to remember that it’s worth doing basic sanity checks before making claims like no backdoors from the NSA. strong encryption has been restricted historically so we had things like DES and 3DES and Crypto AG. In the modern internet age juniper has a bad time with this one https://www.wired.com/2013/09/nsa-backdoor/.
Usually it’s really hard to distinguish intent, and so it’s possible to develop plausible deniability with committees. Their track record isn’t perfect.
With WPA3 cryptographers warned about the known pitfall of standardizing a timing sensitive PAKE, and Harkin got it through anyway. Since it was a standard, the WiFi committee gladly selected it anyway, and then resulted in dragonbleed among other bugs. The techniques for hash2curve have patched that
They're vulnerable to "High-S" malleable signatures, while ed25519 isn't. No one is claiming they're backdoored (well, some people somewhere probably are), but they do have failure modes that ed25519 doesn't which is the GP's point.
in the NIST Curve arena, I think DJB's main concern is engineering implementation - from an online slide deck he published:
We’re writing a document “Security dangers of the NIST curves”
Focus on the prime-field NIST curves
DLP news relevant to these curves? No
DLP on these curves seems really hard
So what’s the problem?
Answer: If you implement the NIST curves, chances are you’re doing it wrong
Your code produces incorrect results for some rare curve points
Your code leaks secret data when the input isn’t a curve point
Your code leaks secret data through branch timing
Your code leaks secret data through cache timing
Even more trouble in smart cards: power, EM, etc.
Theoretically possible to do it right, but very hard
Can anyone show us software for the NIST curves done right?
As I understand it, a big issue is that they are really hard to implement correctly. This means that backdoors and weaknesses might not exist in the theoretical algorithm, but still be common in real-world implementations.
On the other hand, Curve25519 is designed from the ground up to be hard to implement incorrectly: there are very few footguns, gotchas, and edge cases. This means that real-world implementations are likely to be correct implementations of the theoretical algorithm.
This means that, even if P-224/P-256/P-384 are on paper exactly as secure as Curve25519, they could still end up being significantly weaker in practice.