Re: [CFRG] compact representation and HPKE
Loup Vaillant-David <loup@loup-vaillant.fr> Wed, 10 February 2021 23:12 UTC
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From: Loup Vaillant-David <loup@loup-vaillant.fr>
To: Dan Harkins <dharkins@lounge.org>, cfrg@irtf.org
Date: Thu, 11 Feb 2021 00:11:59 +0100
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Subject: Re: [CFRG] compact representation and HPKE
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On Wed, 2021-02-10 at 04:42 -0800, Dan Harkins wrote: > > For all of these curves, p = 3 mod 4 so doing a modular square root > is just exponentiation to (p + 1)/4. Not sure how onerous an > additional exponentiation is. I've just checked by removing the final inversion from my X25519 implementation (which uses an x-only ladder), the cost is less than 10%. Comparatively even less if you're using a more expensive ladder. > But then Mike Hamburg was saying that one can do a x-only Montgomery > Ladder for these curves if an exponentiation is, indeed, onerous so > there are options to consider. To be checked, but an x-only ladder is likely to be faster on its own. So not only do you gain speed by avoiding an exponentiation, you gain speed by running a faster ladder. While we *may* beat x-only ladders by using a complete addition law and fixed windows, it would be more complex, and require more memory (stack in most implementations). And a naive x-y ladder is about half the speed of the x-only ladder, if not less (assuming constant time implementations). This is horrible for embedded applications. Alternatively, we could recover the y-coordinate *after* performing an x-only ladder. With luck, it might not even cost an additional exponentiation. Still, this feels like an avoidable complication, not worth the single bit of security you could get by recovering the sign of a point. As an implementer, I have a very strong preference for x-only ladders: not only are they fast, they're easiest to implement. Less room for error. Loup.
- [CFRG] compact representation and HPKE Dan Harkins
- Re: [CFRG] compact representation and HPKE John Mattsson
- Re: [CFRG] compact representation and HPKE Richard Barnes
- Re: [CFRG] compact representation and HPKE Mike Hamburg
- Re: [CFRG] compact representation and HPKE Dan Harkins
- Re: [CFRG] compact representation and HPKE Dan Harkins
- Re: [CFRG] compact representation and HPKE John Mattsson
- Re: [CFRG] compact representation and HPKE Michael Scott
- Re: [CFRG] compact representation and HPKE Michael Scott
- Re: [CFRG] compact representation and HPKE Dan Harkins
- Re: [CFRG] compact representation and HPKE Benjamin Beurdouche
- Re: [CFRG] compact representation and HPKE Dan Harkins
- Re: [CFRG] compact representation and HPKE Loup Vaillant-David
- Re: [CFRG] compact representation and HPKE Eric Rescorla
- Re: [CFRG] compact representation and HPKE Christopher Wood
- Re: [CFRG] compact representation and HPKE Paul Hoffman
- Re: [CFRG] compact representation and HPKE Dan Harkins
- Re: [CFRG] compact representation and HPKE Stephen Farrell
- Re: [CFRG] compact representation and HPKE Eric Rescorla
- Re: [CFRG] compact representation and HPKE Stephen Farrell
- Re: [CFRG] compact representation and HPKE Andrey Jivsov
- Re: [CFRG] compact representation and HPKE Mike Hamburg
- Re: [CFRG] compact representation and HPKE Mike Hamburg
- Re: [CFRG] compact representation and HPKE Loup Vaillant-David
- Re: [CFRG] compact representation and HPKE Salz, Rich
- Re: [CFRG] compact representation and HPKE Mike Hamburg
- Re: [CFRG] compact representation and HPKE Stephen Farrell
- Re: [CFRG] compact representation and HPKE Peter Gutmann
- Re: [CFRG] compact representation and HPKE John Mattsson
- Re: [CFRG] compact representation and HPKE Benjamin Lipp
- Re: [CFRG] compact representation and HPKE John Mattsson
- Re: [CFRG] compact representation and HPKE Mike Hamburg
- Re: [CFRG] compact representation and HPKE Salz, Rich
- Re: [CFRG] compact representation and HPKE Dan Harkins
- Re: [CFRG] compact representation and HPKE Karthik Bhargavan
- Re: [CFRG] compact representation and HPKE Richard Barnes
- Re: [CFRG] compact representation and HPKE Eric Rescorla
- Re: [CFRG] compact representation and HPKE Benjamin Beurdouche
- Re: [CFRG] compact representation and HPKE Dan Harkins
- Re: [CFRG] compact representation and HPKE Billy Brumley
- Re: [CFRG] compact representation and HPKE Stanislav V. Smyshlyaev
- Re: [CFRG] compact representation and HPKE Dan Harkins
- Re: [CFRG] compact representation and HPKE Stanislav V. Smyshlyaev
- Re: [CFRG] compact representation and HPKE John Mattsson
- Re: [CFRG] compact representation and HPKE denis bider