Return-Path: Received: from smtp1.linuxfoundation.org (smtp1.linux-foundation.org [172.17.192.35]) by mail.linuxfoundation.org (Postfix) with ESMTPS id 09FECCD7 for ; Thu, 13 Sep 2018 18:46:52 +0000 (UTC) X-Greylist: from auto-whitelisted by SQLgrey-1.7.6 Received: from mail.wpsoftware.net (wpsoftware.net [96.53.77.134]) by smtp1.linuxfoundation.org (Postfix) with ESMTP id 96DF0716 for ; Thu, 13 Sep 2018 18:46:51 +0000 (UTC) Received: from boulet.lan (boulot.lan [192.168.0.193]) by mail.wpsoftware.net (Postfix) with ESMTPSA id 97A9B400EB; Thu, 13 Sep 2018 18:46:49 +0000 (UTC) Date: Thu, 13 Sep 2018 18:46:50 +0000 From: Andrew Poelstra To: Erik Aronesty , Bitcoin Protocol Discussion Message-ID: <20180913184649.GC18522@boulet.lan> References: <20180812163734.GV499@boulet.lan> <20180903000518.GB18522@boulet.lan> MIME-Version: 1.0 Content-Type: multipart/signed; micalg=pgp-sha256; protocol="application/pgp-signature"; boundary="aDj5WtVma0yWCzS8" Content-Disposition: inline In-Reply-To: User-Agent: Mutt/1.7.1 (2016-10-04) X-Spam-Status: No, score=-1.9 required=5.0 tests=BAYES_00 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: Fri, 14 Sep 2018 13:50:00 +0000 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: Thu, 13 Sep 2018 18:46:52 -0000 --aDj5WtVma0yWCzS8 Content-Type: text/plain; charset=utf-8 Content-Disposition: inline Content-Transfer-Encoding: quoted-printable On Tue, Sep 11, 2018 at 01:37:59PM -0400, Erik Aronesty via bitcoin-dev wro= te: > - Musig, by being M of M, is inherently prone to loss. > It has always been possible to create M-of-N threshold MuSig signatures for= any M, N with 0 < M =E2=89=A4 N. This is (a) obvious, (b) in our paper, (c) imp= lemented at https://github.com/apoelstra/secp256k1/blob/2018-04-taproot/src/modules/mus= ig/main_impl.h=20 --=20 Andrew Poelstra Research Director, Mathematics Department, Blockstream Email: apoelstra at wpsoftware.net Web: https://www.wpsoftware.net/andrew "Make it stop, my love; we were wrong to try Never saw what we could unravel in traveling light Nor how the trip debrides like a stack of slides All we saw was that time is taller than space is wide" --Joanna Newsom --aDj5WtVma0yWCzS8 Content-Type: application/pgp-signature; name="signature.asc" -----BEGIN PGP SIGNATURE----- iQEcBAEBCAAGBQJbmrCYAAoJEMWI1jzkG5fB664H/2xlvINQHEUcudpxZP7RmJ/y S6XtIL3Y2+tRPjpXEZ/JoK1HaBiEJqF5XXUR5HSVVsWAnrqf5S6Vg9Z9ujUCrMxX pQVlg2q96enXKBITWtLP3MdkUfgNDa1lwAOcHucVVlKn/5A+/OebfI1+03DUyhn8 gfo/5BDs53jthOZzv+O0Im1hEzhL8viZTRlert5C8U2/wwti/iGAWYfPQiWNP8kI i/704vLFmXRqPOOS8ug8ADKoOvnLc4Y3Sn6EIB8sabfIwi6De3Wr/+fP9oA3tAq2 h6vr9oUw6zyeu+1d8FCmwjZjlgf9bhgrZIDjba1k1K64A/B/tWUryVzbj6GARtA= =ayyq -----END PGP SIGNATURE----- --aDj5WtVma0yWCzS8--