From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: from smtp1.linuxfoundation.org (smtp1.linux-foundation.org [172.17.192.35]) by mail.linuxfoundation.org (Postfix) with ESMTPS id 8EAED13DB for ; Tue, 11 Sep 2018 18:30:31 +0000 (UTC) X-Greylist: whitelisted by SQLgrey-1.7.6 Received: from mail-wm0-f52.google.com (mail-wm0-f52.google.com [74.125.82.52]) by smtp1.linuxfoundation.org (Postfix) with ESMTPS id 610023F7 for ; Tue, 11 Sep 2018 18:30:30 +0000 (UTC) Received: by mail-wm0-f52.google.com with SMTP id f21-v6so2032459wmc.5 for ; Tue, 11 Sep 2018 11:30:30 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=q32-com.20150623.gappssmtp.com; s=20150623; h=mime-version:references:in-reply-to:from:date:message-id:subject:to :cc; bh=JbX+EtC6bo+pkrh2nF0N8RsYqtuoQkBW64aLLvytchI=; b=UVa3pZVID2uOlrW1A5UARzrjlI0gv1X4dTiE3kPbavZgUa5JOCMnjTAOd+DwePuGZP 9Fu2UyulKrE3Uja5nHW5u1ltSxn6SO3KGVCEQoAVytO0nLMq3Sl4Q5dk2f0awPj2vBcB NG/m0x8/oUMQLHI9BsSc+5Zts4D1QnD0iGcJC7QangeFgTM1kPuTDOWB415Ey8I4IYpZ 3ysOZ8onNq0Nz2iNHyVkTPOdHRc3Gg6GAiCeGkutVwdl2XTVQoQw8QDzaCnx4pnJ+JbY gvtTJhUC81xz8/tHwaWet3CBqpp4G/mMFD1HIU34L1UYW7UcTen0DjiD8VZ++7OZ5Rr5 YJPg== X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:references:in-reply-to:from:date :message-id:subject:to:cc; bh=JbX+EtC6bo+pkrh2nF0N8RsYqtuoQkBW64aLLvytchI=; b=McuzxVWsX/cieaSigiK84oGd4+UV+6boEYkhRGbhMVB/iKay8UV1b50Ru8rCsjBNwK DpmC2UGGJEPzxZhL/2hEtNqcm2C9/RjdsFch309FEzxDZ8BgKbhYzblLeOxmpOT+qP/C AxXQrkL+AZ1KyS5WHiHKvgg6Xu8kCtVOrSXuGvdtgrftNUheUBsl/Ql99Kaiz9GZRS9M Cs14YUrG9VjtdVqcuF2rZ76SzYn9tuRh22GTRNQT02iqngc6m0Zl2ozZzqaRM2G/r2Ak p9qepy+7rSzJ16N+STO+HT2b+E7rPyqwqBRmQZTwd/1EHXGjZgj+hjO1S6rFdMet8Tus hYvQ== X-Gm-Message-State: APzg51A7ykfUxP8JF+d+kzlRoTOXMM+oK8p+zFh4MC3kPqOIG6A/n/cP puStd36lRuXJXU3gWLxuHc17woX0oQW/e9vRyv1lZ1g= X-Google-Smtp-Source: ANB0Vdau3mEBjQhw6JjUZoADc6TQBn51m+9rcAzS9n95vOXlVYpeYGi2inRXXuDnvM02NJOjP7FBed7+bACN9JWRxY8= X-Received: by 2002:a1c:70b:: with SMTP id 11-v6mr2185456wmh.151.1536690628637; Tue, 11 Sep 2018 11:30:28 -0700 (PDT) MIME-Version: 1.0 References: <2e620d305c86f65cbff44b5fba548dc85c118f84.camel@timruffing.de> <20180812163734.GV499@boulet.lan> <20180903000518.GB18522@boulet.lan> In-Reply-To: From: Erik Aronesty Date: Tue, 11 Sep 2018 14:30:13 -0400 Message-ID: To: Gregory Maxwell Content-Type: multipart/alternative; boundary="0000000000000cb8e105759cab03" X-Spam-Status: No, score=-1.9 required=5.0 tests=BAYES_00,DKIM_SIGNED, DKIM_VALID, FREEMAIL_FROM, HTML_MESSAGE, RCVD_IN_DNSWL_NONE autolearn=ham version=3.3.1 X-Spam-Checker-Version: SpamAssassin 3.3.1 (2010-03-16) on smtp1.linux-foundation.org X-Mailman-Approved-At: Wed, 12 Sep 2018 13:41:03 +0000 Cc: Bitcoin Protocol Discussion Subject: Re: [bitcoin-dev] Schnorr signatures BIP X-BeenThere: bitcoin-dev@lists.linuxfoundation.org X-Mailman-Version: 2.1.12 Precedence: list List-Id: Bitcoin Protocol Discussion List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Tue, 11 Sep 2018 18:30:31 -0000 --0000000000000cb8e105759cab03 Content-Type: text/plain; charset="UTF-8" > That approach has its uses but I think that in any case where delinearization can be used it's a better option. I agree, communication efficiency is a concern for some applications, and I can think of cases where delinearization is the better option as well. For users that want an "M of N" scheme that a) doesn't cost more to send funds b) allows them to lose a device and keep their coins c) allows them to establish and validate the scheme safely ... a simple, "verified signer" threshold scheme is probably the best solution. On Tue, Sep 11, 2018 at 1:51 PM Gregory Maxwell wrote: > On Tue, Sep 11, 2018 at 5:38 PM Erik Aronesty wrote: > > > > - Musig, by being M of M, is inherently prone to loss. > > M of M is a particular threshold. If you want M of M (there are > plenty of cases where M of M _must_ be used) then you get the > consequences of M of M, which presumably you want. > > This has nothing to do with musig. If you want a threshold other than > M of M then you use a threshold other than M of M. > > No one is under the impression that M of M is somehow a replacement > for other thresholds. We've spent more time talking about M of M in > some writeups in the past because it's exactly the case you need for > signature aggregation in Bitcoin and because it's a simpler case to > explain. > > > - Having the senders of the G*x pubkey shares sign their messages with > the associated private key share should be sufficient to prevent them from > using wagner's algorithm to attack the combined key. > > Yes, that is one possibility which is described in the musig paper, > but it requires users communicate an extra signature per key. So, for > example, if used with aggregate signature it would completely > eliminate the communications efficiency gains from aggregation, making > aggregation worse than pointless. It also has somewhat worse failure > properties than delinearization, because a signer that fails to > validate other's share signatures behaves behaves exactly the same as > a correct one, on honest inputs. That approach has its uses but I > think that in any case where delinearization can be used it's a better > option. > --0000000000000cb8e105759cab03 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
>=C2=A0 That approach has its uses but I think tha= t in any case where delinearization can be used it's a better option.

I agree,=20 communication efficiency is a concern for some applications, and I can thin= k of cases where=20 delinearization is the better option as well.=C2=A0=C2=A0=C2=A0
<= div>
For users that want an "M of N" scheme that

a) doesn't cost more to send funds
b) allows them to lose a device and keep their coins
c) allows = them to establish and validate the scheme safely

...=C2=A0 a simple, "verified signer" threshold scheme is prob= ably the best solution.




On Tue, Sep 11, 2018 = at 1:51 PM Gregory Maxwell <greg@xiph.o= rg> wrote:
On Tue, Sep 11, 2= 018 at 5:38 PM Erik Aronesty <erik@q32.com> wrote:
>
> - Musig, by being M of M, is inherently prone to loss.

M of M is a particular threshold.=C2=A0 =C2=A0If you want M of M (there are=
plenty of cases where M of M _must_ be used) then you get the
consequences of M of M, which presumably you want.

This has nothing to do with musig.=C2=A0 If you want a threshold other than=
M of M then you use a threshold other than M of M.

No one is under the impression that M of M is somehow a replacement
for other thresholds.=C2=A0 We've spent more time talking about M of M = in
some writeups in the past because it's exactly the case you need for signature aggregation in Bitcoin and because it's a simpler case to
explain.

> - Having the senders of the G*x pubkey shares sign their messages with= the associated private key share should be sufficient to prevent them from= using wagner's algorithm to attack the combined key.

Yes, that is one possibility which is described in the musig paper,
but it requires users communicate an extra signature per key.=C2=A0 So, for=
example, if used with aggregate signature it would completely
eliminate the communications efficiency gains from aggregation, making
aggregation worse than pointless.=C2=A0 It also has somewhat worse failure<= br> properties than delinearization, because a signer that fails to
validate other's share signatures behaves behaves exactly the same as a correct one, on honest inputs.=C2=A0 That approach has its uses but I
think that in any case where delinearization can be used it's a better<= br> option.
--0000000000000cb8e105759cab03--