Re: [Cfrg] ECC mod 8^91+5
"D. J. Bernstein" <djb@cr.yp.to> Wed, 02 August 2017 16:00 UTC
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Date: Wed, 02 Aug 2017 16:00:15 -0000
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From: "D. J. Bernstein" <djb@cr.yp.to>
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Subject: Re: [Cfrg] ECC mod 8^91+5
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Samuel Neves writes: > These formulas do exist, cf. [1] or [2], but they require curves of > _odd_ order, which is not the case here. The complete formulas from https://cr.yp.to/talks/2009.07.17/slides.pdf don't require odd order. Fundamentally, incomplete implementations---and complete implementations with timing leaks from branches between different incomplete formulas--- are not the result of complete formulas failing to exist. They are the result of complete formulas failing to compete with the simplicity and speed of incomplete formulas. This tension is what's nicely resolved by Montgomery curves for DH, and by complete Edwards curves for more general applications. ---Dan
- [Cfrg] ECC mod 8^91+5 Dan Brown
- Re: [Cfrg] ECC mod 8^91+5 David Jacobson
- Re: [Cfrg] ECC mod 8^91+5 Dan Brown
- Re: [Cfrg] ECC mod 8^91+5 Dan Brown
- Re: [Cfrg] ECC mod 8^91+5 Thomas Garcia
- Re: [Cfrg] ECC mod 8^91+5 Ilari Liusvaara
- Re: [Cfrg] ECC mod 8^91+5 Dan Brown
- Re: [Cfrg] ECC mod 8^91+5 Dan Brown
- Re: [Cfrg] ECC mod 8^91+5 Ilari Liusvaara
- Re: [Cfrg] ECC mod 8^91+5 D. J. Bernstein
- Re: [Cfrg] ECC mod 8^91+5 Samuel Neves
- Re: [Cfrg] ECC mod 8^91+5 D. J. Bernstein
- Re: [Cfrg] ECC mod 8^91+5 Dan Brown
- Re: [Cfrg] ECC mod 8^91+5 Dan Brown
- Re: [Cfrg] ECC mod 8^91+5 Paterson, Kenny
- Re: [Cfrg] ECC mod 8^91+5 Hanno Böck
- Re: [Cfrg] ECC mod 8^91+5 Salz, Rich
- Re: [Cfrg] ECC mod 8^91+5 Stephen Farrell
- Re: [Cfrg] ECC mod 8^91+5 Dan Brown