Re: [Cfrg] draft-black-rpgecc-00-.txt [was: Consensus and a way forward]

Adam Langley <> Mon, 01 December 2014 14:17 UTC

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From: Adam Langley <>
To: Robert Ransom <>
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Subject: Re: [Cfrg] draft-black-rpgecc-00-.txt [was: Consensus and a way forward]
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On Sun, Nov 30, 2014 at 7:33 PM, Robert Ransom <> wrote:
> Third, you appear to be arguing that ECDH operations would not use the
> Montgomery curve *isomorphic* to the Edwards curve in your Internet
> draft, but use a *different* Montgomery curve (PinkBikeShed) which is
> merely *isogenous* to the curve that you are proposing, in order to
> reduce the modifications required to make the many existing
> independent, interoperable implementations of Curve25519 operate on
> your curve.  This would *slightly* reduce the technical disadvantage
> of your proposal compared to Curve25519, but would clearly not
> eliminate it.  If you do intend to propose PinkBikeShed for ECDH,
> rather than the Montgomery curve isomorphic to the one specified in
> your Internet draft, then that needs to be stated explicitly in your
> draft.

Yes, I agree. The draft should specify the Montgomery curve and the
isogeny maps. I also very much hope that the CFRG doesn't just specify
curves, but also will provide detailed guidance about their use --
that's also missing from the draft at the moment.

> Interesting suggestion.
> Both 89747 and 121665 are 17 bits long (they are between 2^17 and 2^18
> - 1), and 89747 has a slightly greater Hamming weight than 121665 (10
> rather than 9); I would expect any performance improvement on due to
> that change in curve parameter to be quite small and only applicable
> to a very few implementation strategies.  Have you done any
> benchmarking to quantify the performance improvement that you are
> claiming as a technical benefit of PinkBikeShed?

I've not done any benchmarking, it's just a guess. But the Edward's d
parameter for the curve isomorphic to Curve25519 isn't 121665, it's
+/- 121665/121666 [, section 2].
That value doesn't have a small representation so I think that the
PinkBikeShed curve does get to use a multiplication by a small
constant in place of a multiplication by a large constant. That might
be a small help.

> Do you believe that that possible performance improvement is a
> sufficiently large technical benefit over Curve25519 to outweigh the
> technical disadvantages of your proposal that you were aware of at the
> time that you submitted it?

No. I think the prevalence of Curve25519 alone is enough that the CFRG
should adopt it. PinkBikeShed isn't what I want, but it's close and
it's something that I can live with in order to move forward.



Adam Langley