Re: [Cfrg] Rerun: Elliptic Curves - preferred curves around 256bit work factor (ends on March 3rd)

Watson Ladd <watsonbladd@gmail.com> Wed, 25 February 2015 16:53 UTC

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Date: Wed, 25 Feb 2015 08:53:04 -0800
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From: Watson Ladd <watsonbladd@gmail.com>
To: Phillip Hallam-Baker <phill@hallambaker.com>
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Subject: Re: [Cfrg] Rerun: Elliptic Curves - preferred curves around 256bit work factor (ends on March 3rd)
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On Wed, Feb 25, 2015 at 8:22 AM, Phillip Hallam-Baker
<phill@hallambaker.com> wrote:
> Do we have figures for performance of these versus RSA2048?
>
> Yes, we get a reversal of the public/private speed advantage on signature.
> And that in itself is a huge win on the server side
>
> RSA signature verification takes 0.16 ms on a reasonably current machine
> (signature is 6ms)
>
> http://www.cryptopp.com/benchmarks.html

That benchmark is one measurement, on one processor, with no
indication that it was done properly.
>
> How much faster/slower one curve is over another matters much less to me
> than whether the curve is faster or slower than what I am already using. I
> am not going to be using P521 or P448 curves on a constrained device, I will
> go for P255.

What if that constrained device needs to interoperate with the web
PKI, and they decide because of how important they are they must use
P521?

>
> If we had figures comparing the curve candidates to RSA it would probably be
> illuminating.

http://bench.cr.yp.to/results-encrypt.html
and http://bench.cr.yp.to/results-dh.html

>From these on Titian0, we see that ronald1024 encryption takes 41188
cycles, and Curve25519 shared secret agreement 161708 cycles, nearly 4
times as much. But ronald1024 decryption consumes seven times as many
cycles as Curve25519 shared secret agreement.

This pattern holds across processors.  Of course, ronald1024 is a
wrapper around OpenSSL: it's very possible that extensive optimization
could improve those numbers somewhat.

But I was comparing 1024 bit RSA. To properly ensure adequate security
3072 bits is closer to the mark, and here the encryption time exceeds
that of Curve25519.

A simple google search would have found SUPERCOP, where I got these
numbers from.

Sincerely,
Watson Ladd

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