Re: [Cfrg] Progress on curve recommendations for TLS WG

Andy Lutomirski <luto@amacapital.net> Fri, 15 August 2014 18:50 UTC

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From: Andy Lutomirski <luto@amacapital.net>
Date: Fri, 15 Aug 2014 11:50:30 -0700
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To: Watson Ladd <watsonbladd@gmail.com>
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Cc: Dan Brown <dbrown@certicom.com>, "cfrg@irtf.org" <cfrg@irtf.org>
Subject: Re: [Cfrg] Progress on curve recommendations for TLS WG
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On Fri, Aug 15, 2014 at 11:23 AM, Watson Ladd <watsonbladd@gmail.com>; wrote:
>
> On Aug 15, 2014 10:59 AM, "Dan Brown" <dbrown@certicom.com>; wrote:
>>
>> From: Cfrg [mailto:cfrg-bounces@irtf.org] On Behalf Of Watson Ladd
>> > The reason Dan Brown's example isn't convincing is that having only
>> > prime
>> > factors of not that small size is common.
>>
>> Right about it being common: Dickman's function says the chance of the
>> largest
>> prime factor of that size is about 15%.
>>
>> Wrong about it being unconvincing: the severity of the attack is what
>> matters,
>> not how common it is.  Why would anybody care whether it took six or
>> one-million trials to a find a weak 56-bit curve?
>
> What is it convincing of? If it takes 6 trials all randomly generated curves
> are likely to fail. If it's 1 in a million, then rigidity or lack thereof is
> more important to prevent underhandedness.
>
>>
>> Also, I assume that you are not referring to my BARC example, in which the
>> largest prime factor is two.   Maybe BARC is unconvincing for another
>> reason,
>> which is?
>
> The endomorphism ring was shockingly large, NUMS isn't a property of a curve
> but a generation method, etc. Really the only argument was supersingular
> curves, which I admit being mildly convinced by.
>

If CFRG is going to seriously consider random curves, can we at least
generate good random curves?  I don't think it's *that* hard.  Choose
a good algorithm to turn a seed into a curve, and then use something
like H(next week's top NY Times headline, next week's top Al-Jazeera
headline, next week's S&P 500 close, next week's weather, etc...).

The point being that there are lots of degrees of freedom this way,
but no one (not even the NSA) would be able to control enough of them
to select for any property of the curve.

--Andy