Re: [Cfrg] ECC reboot (Was: When's the decision?)

[Phillip Hallam-Baker <[e-mail]>]

On Thu, Oct 16, 2014 at 2:29 PM, Alyssa Rowan <[e-mail]> wrote:
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> On 16/10/2014 17:08, Paterson, Kenny wrote:
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>> Our first task should be to finalise the requirements that we will
>> use to guide the selection process. I think we are close, with a
>> couple of outstanding issues:
>
> Alright, so let's try to get things in high gear and argue those out…?
>
>> 1. Amount of "wiggle room" that should be permitted.
>
> Broadly: I think what we're aiming for is probably one faster/strong
> curve, and one stronger/fast curve.
>
> Given the strong preferences of some to minimise the number of curves,
> it looks to me like ­≈384 is almost-definitely dropped, leaving us
> with something near ≈256 and something near ≈512.
>
> We seem to be in agreement that wiggle room on ≈256 would include
> fields of 2^255-19 as well as 2^256-189 in scope.
>
> For the paranoid-strong, performance-second ≈512, 2^512-569 very
> obviously falls within scope.

Agree so far.


> I put forth that 2^521-1 also falls within scope. It's not very far
> away, and it's a true Mersenne prime rather than a pseudo-Mersenne,
> and they do not grow on trees - no others fall near our criteria (the
> next lowest is 2^127-1 which is way too small, and the next biggest is
> 2^607-1). They are very attractive - attractive enough for 4 (?)
> independent research groups to independently arrive on E-521, and
> SECG/NIST to have independently picked the same prime years ago for
> secp521r1.

It is a Mersenne but the performance advantage is compromised by it
being larger than 512 bits. That means every memory operation is going
to break stride. Which is a really bad tradeoff for the marginal
improvement in speed.


> [Previous discussion countering this point: Sean Parkinson @ RSA
> suggested stepping over a power of 2 is "only going to hurt
> performance in the future". Phillip Hallam-Baker also thought anything
> that is not less than a clean multiple of a power of two "may cause
> severe performance hits on future architectures", mentioning 512-bit
> memory buses on graphics cards?!

There is a good reason for that. What we call 'graphics cards' are
really just what we used to call a vector unit.

Getting someone to build purpose built ECC accelerators is hard and
expensive. I can buy an nvida card that with a ridiculous number of
cores that I can pretty much program to do anything I like.


Its not just a question of speed, its a question of the amount of
microcode required to implement ECC math as a native function of the
GPU.


> although I'm not convinced that's
> actually primarily relevant to an implementation of a high-strength
> curve. We will, of course, evaluate performance of contenders in Phase
> II, future architectures can be more-or-less anything that works well,
> and performance implications usually aren't anything like so obvious…
> Aren't Mersennes actually particularly _good_ performance-wise?]

That depends on whether you are looking for a reason to include or exclude.

At the ~512 level, what I am looking for is a curve that absolutely
nobody is going to be able to suggest is suspect as being bongoed.
2^512 is a round number that needs no explanation. 2^521 isn't.

The Web PKI will almost certainly be based exclusively on the ~512
level curve. The roots certainly will. So the performance advantage of
issuing end entity ~256 certs would be very small.

Where I think ~256 keys will be used is for ephemeral mix ins. So I
exchange a master session key M with the ~512 bit key, use an
ephemeral ~256 to create a second session key E and then derive my
encryption and authentication keys using a one way function on M and
E. That preserves the ~512 work factor for confidentiality and adds a
~256 work factor for forward secrecy.


So I am willing to be more flexible on ~256 than ~512 because for my
applications the attacker always has to break the ~512.


> I put forth that 2^414-17 and 2^448-2^224-1 might fall outside "wiggle
> room" there, although I do so very reluctantly as I think it's a shame
> to exclude them on that basis if they have otherwise nice properties,
> and they do seem to have very good performance for their strength.

I agree. They are a little faster but we have to give up a lot of
security to get that speed. Its not 64 bits, its a 2^20 reduction in
work factor. I want them bits.


>> 31/10/14 (2 weeks from now): we agree on whatever benchmarking
>> system we're going to use for performance measurements. (Right now,
>> supercop seems like the front runner to me.)

I think a significant performance difference is a tie breaker but not
the best determinant. What I see as being convincing are:

1) Difficulty of screwing up the implementation (see Watson Ladd's post).

2) Legacy deployment.


Given the way that I think we are likely to use ~256 and given the
fact that DJB has established a large user base for the curve already.
I am willing to suggest we just let him win on that one unless there
is at least a 10%, maybe a 20% speed advantage he missed.

For ~512 I want the Platinum level security, whatever it takes.