Re: [TLS] Using Brainpool curves in TLS

Manuel Pégourié-Gonnard <> Fri, 18 October 2013 16:30 UTC

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Cc: Patrick Pelletier <>, "" <>
Subject: Re: [TLS] Using Brainpool curves in TLS
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On 18/10/2013 17:35, Watson Ladd wrote:
> On Fri, Oct 18, 2013 at 12:22 AM, Manuel Pégourié-Gonnard
>> If I may reformulate my point: twist-security is relevant only for curves
>> suitable for use with schemes where only the x coordinate is transmitted, and no
>> attempt to reconstruct y is needed on the receiving side. Which means, curves
>> for which formulas exist for point multiplication using only the x coordinate.
>> To the best of my knowledge (read: after looking up the explicit formulas
>> database) no such formulas exist for short Weierstrass curves. Let's try with
>> pseudo-code:
> This isn't true: See Brier-Joye ladders. They aren't used because of
> efficency problems, but they
> solve the incompleteness issues.

I stand corrected, I wasn't previously aware of these formulas and missed them
when I checked the EFD page. Thanks for bringing them to my attention.

>> If (has efficient x-only formulas)

Anyway, since I took care to add "efficient" here, this doesn't change the
evaluation of this condition...

>> PS: just kidding (almost?), but one could argue that brainpoolP384r1, as used in
>> TLS for ECDH now, is *less* secure because of twist-security, if people start
>> thinking that they don't need to validate public keys for this curve...
> Invalid curve attacks mean validation on short Weierstraß curves is
> always required.

Which was precisely my point: people should *not* start thinking validation
isn't required (regardless of whether the curve is twist-secure or not), when
they are receiving an (x,y) pair. I'm sorry if that wasn't clear enough from my
messages, I really thought it was.