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

Robert Ransom <rransom.8774@gmail.com> Mon, 01 December 2014 18:06 UTC

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Date: Mon, 01 Dec 2014 10:06:05 -0800
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From: Robert Ransom <rransom.8774@gmail.com>
To: Ilari Liusvaara <ilari.liusvaara@elisanet.fi>
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Subject: Re: [Cfrg] draft-black-rpgecc-00-.txt [was: Consensus and a way forward]
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On 12/1/14, Ilari Liusvaara <ilari.liusvaara@elisanet.fi> wrote:

> The reverse maps x(u,v) and y(u,v) are more annoying, seemingly containing
> two square roots and an inversion (among with few other ops).

That's because the map you are using is an isogeny, not an
isomorphism.  You don't compute a point's pre-image under an isogeny,
you get back to the original curve by applying the ‘dual isogeny’
(another rational map).  This isogeny (which I'll denote F for a
moment) is a 4-isogeny, so there is a dual isogeny G such that G(F(P))
= 4*P.


Robert Ransom

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