Re: [TLS] Twist security for brainpoolp256r1

[Watson Ladd <[e-mail]>]

On Thu, Nov 13, 2014 at 1:21 AM, Manuel Pégourié-Gonnard
<[e-mail]> wrote:
> On 13/11/2014 07:35, Oleg Gryb wrote:
>> Thanks, very helpful. Just to summarize yours and Manuel's notes in regard of
>> quadratic non-residue, or non-quadratic twists (as they are called in other
>> emails), they can be used as a source of malicious EC points to run
>> invalid-curve attacks on the original curves, but since all implementations
>> compliant with X9* standards including openssl must have point-on-curve
>> validation, invalid-curve attacks and small-group attacks become irrelevant
>> when it comes to brainpoool's openssl implementation.
>
> The situation is actually a bit more complex. Here is a version that's still a
> bit simplified but closer to the truth: let's say there are two kinds of
> protocols (or curve representations):
>
> 1. Those who use both coordinates of the points.
> 2. Those who use only the x coordinate.

The coordinates used on the wire do not determine the calculations
used by an implementation. An interoperable implementation of TLS
could use the Brier-Joyce ladder on x-coordinates only, and take a
randomly chosen square root for use as the y-coordinate, validating
signatures through a different method. This would be of interest in
certain side-channel attack scenarios, as the Brier-Joyce ladder is
easier to protect.

Most implementations don't do this, so the rest of your email is correct.

Sincerely,
Watson Ladd