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Based on her response (at 53:40), I feel like she misunderstood the question. The first response "The nice thing about standards is there's so many to choose fr

by fryguy 12y ago

Based on her response (at 53:40), I feel like she misunderstood the question. The first response "The nice thing about standards is there's so many to choose from" is probably because even if she proposes a curve with a flaw, people could just choose to use Curve25519 or whatever. I feel like they've already addressed the question with their "bada55 curves" page: http://safecurves.cr.yp.to/bada55.html http://safecurves.cr.yp.to/bada55.html

tptacek 12y ago
The subtext of BADA55 is that even curves that are seeded from mathematical constants or from other first-principals rationales still provide a malicious curve generator with leeway to pick from many potential curves, and to steer victims to the weakest of them.
- jeff_marshall 12y ago
  That's true, but if the curve uses a well-studied underlying field where the curves that are vulnerable to cryptanalytic attacks can be avoided (prime fields lead the way here, last time I worked on an ECC implementation ~ 5 years ago), the risk from this threat isn't so great -I'd worry about other aspects of the resulting system first. A quick google search shows DJB and Tanja Lange have some nice analysis of existing curves here: http://safecurves.cr.yp.to/index.html http://safecurves.cr.yp.to/index.html Of course, if the cryptographers generating the curve aren't sharing their knowledge of some new class of weak curves, all bets are off.
- deleted 12y ago
  [deleted]
- nullc 12y ago
  BADA55 curves are not "from mathematical constants or from other first-principals rationales", they're a demonstration that the spec "provably random" construction used for some other curves can be ground to produce very rare characteristics. They all have unjustified high entropy random "seeds", like P-256, which were the product of a computationally expensive search to find curves meeting the BADA55 characteristic. An example of a curve "from mathematical constants or from other first-principals rationales" would be to set parameters to 'trivial values' like 0 or 2^255 and increment until you get the first curve that matches a security test. Some curves, like the curve25519 curve or secp256k1 were constructed this way and this method could not be "BADA55" in the way that P-256 could be.

by fryguy 12y ago

tptacek 12y ago

The subtext of BADA55 is that even curves that are seeded from mathematical constants or from other first-principals rationales still provide a malicious curve generator with leeway to pick from many potential curves, and to steer victims to the weakest of them.

jeff_marshall 12y ago
That's true, but if the curve uses a well-studied underlying field where the curves that are vulnerable to cryptanalytic attacks can be avoided (prime fields lead the way here, last time I worked on an ECC implementation ~ 5 years ago), the risk from this threat isn't so great -I'd worry about other aspects of the resulting system first. A quick google search shows DJB and Tanja Lange have some nice analysis of existing curves here: http://safecurves.cr.yp.to/index.html http://safecurves.cr.yp.to/index.html Of course, if the cryptographers generating the curve aren't sharing their knowledge of some new class of weak curves, all bets are off.
deleted 12y ago
[deleted]
nullc 12y ago
BADA55 curves are not "from mathematical constants or from other first-principals rationales", they're a demonstration that the spec "provably random" construction used for some other curves can be ground to produce very rare characteristics. They all have unjustified high entropy random "seeds", like P-256, which were the product of a computationally expensive search to find curves meeting the BADA55 characteristic. An example of a curve "from mathematical constants or from other first-principals rationales" would be to set parameters to 'trivial values' like 0 or 2^255 and increment until you get the first curve that matches a security test. Some curves, like the curve25519 curve or secp256k1 were constructed this way and this method could not be "BADA55" in the way that P-256 could be.