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

Return-Path: <rransom.8774@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (ietfa.amsl.com [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 08BF51A875D for <cfrg@ietfa.amsl.com>; Mon, 1 Dec 2014 10:06:08 -0800 (PST)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.75
X-Spam-Level:
X-Spam-Status: No, score=-1.75 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_ENVFROM_END_DIGIT=0.25, FREEMAIL_FROM=0.001, SPF_PASS=-0.001] autolearn=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id qUCRJQ6JE5O2 for <cfrg@ietfa.amsl.com>; Mon, 1 Dec 2014 10:06:06 -0800 (PST)
Received: from mail-qa0-x22f.google.com (mail-qa0-x22f.google.com [IPv6:2607:f8b0:400d:c00::22f]) (using TLSv1 with cipher ECDHE-RSA-RC4-SHA (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 91EEF1A875C for <cfrg@irtf.org>; Mon, 1 Dec 2014 10:06:06 -0800 (PST)
Received: by mail-qa0-f47.google.com with SMTP id s7so7435716qap.20 for <cfrg@irtf.org>; Mon, 01 Dec 2014 10:06:05 -0800 (PST)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=mime-version:in-reply-to:references:date:message-id:subject:from:to :cc:content-type:content-transfer-encoding; bh=OqNJD0l1OrfNKJE/hTAaTdYcFxdTCZZ1/fXgpVu0G4g=; b=XF90LT7xJuDzHaUqI2jsUxFRhMmExn+LcBbL96nJePpmX8Q1fE6cJmBSyhOjp/UCdP L0lWyw3T0YGlK48rHCjR/fjJHXjCKoTkdg5cEiswF+7+/zUxff/hQY6fcSffRbaXQIQM 3aQqUB0SEBLPR/E+psnglNiJryXHt8iNr79IBBiJ1qYPRGn4CVfo4U9v/EIUyNbwdUix mmIY+owrDBS6ENy5+4LrBpZzCIeVLWPCQmOmjX5DwyQGDNqqqnYV+DM+dINkzJajGs50 zlPuuFgBQ6ZseHoVNH7bqgiHVF/JcjpTCVsqDrGOlgOWkhf7B2CfbT+gWlbTooIyvJKm wyFg==
MIME-Version: 1.0
X-Received: by 10.224.120.67 with SMTP id c3mr88093907qar.3.1417457165765; Mon, 01 Dec 2014 10:06:05 -0800 (PST)
Received: by 10.140.30.100 with HTTP; Mon, 1 Dec 2014 10:06:05 -0800 (PST)
In-Reply-To: <20141201175344.GA21285@LK-Perkele-VII>
References: <CA+Vbu7xvvfRWyqyE9sqU7VbjzNQZp+DwRWjaV3Lw0hjLr8ye1A@mail.gmail.com> <5476CB73.7090206@akr.io> <CAMfhd9XxkZsVPMcevWOgvvqbBK0JqLVCGBYfwWu0QFO5rsfbJQ@mail.gmail.com> <CABqy+sodVBbwNrA28AFxYMiw5rJxtUX3cbYCjtrYxK-48Ocd6A@mail.gmail.com> <CAMfhd9VF784rJ5gXiLkB6DdwS+zAi=GDgT=792jQ=+oqcK_F3Q@mail.gmail.com> <20141201175344.GA21285@LK-Perkele-VII>
Date: Mon, 1 Dec 2014 10:06:05 -0800
Message-ID: <CABqy+sqOc-EPD3khHk8c3TEKmz8PuBrhnLSGW3BE3dbjdYmu-A@mail.gmail.com>
From: Robert Ransom <rransom.8774@gmail.com>
To: Ilari Liusvaara <ilari.liusvaara@elisanet.fi>
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: quoted-printable
Archived-At: http://mailarchive.ietf.org/arch/msg/cfrg/4jKdqdHiYAyn5hxnodd5dLxH1qw
Cc: "cfrg@irtf.org" <cfrg@irtf.org>
Subject: Re: [Cfrg] draft-black-rpgecc-00-.txt [was: Consensus and a way forward]
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.15
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <http://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <http://www.irtf.org/mail-archive/web/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <http://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Mon, 01 Dec 2014 18:06:08 -0000

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