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 7008B10EA for ; Tue, 11 Sep 2018 17:51:16 +0000 (UTC) X-Greylist: whitelisted by SQLgrey-1.7.6 Received: from mail-ua1-f51.google.com (mail-ua1-f51.google.com [209.85.222.51]) by smtp1.linuxfoundation.org (Postfix) with ESMTPS id 14BD08D for ; Tue, 11 Sep 2018 17:51:15 +0000 (UTC) Received: by mail-ua1-f51.google.com with SMTP id u11-v6so21431057uan.13 for ; Tue, 11 Sep 2018 10:51:15 -0700 (PDT) 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=XHjBTvz/pqElurAqA1/RewyArqjCfKVvbueoRZFN7ms=; b=hlVgzTE2WLdRnLp80VisLeEVkJ5qZv59/WoGfvhtqPUlg+835xmfqJXluYHc4XnT/5 CrhcIrALjiM2g5vc2cZtcA/798np7mpeNXfzblr1JDpQn48G4QK+poBK04BYyRxBzkmf ExmMPuSNw1V0LSrO3ihNcg1Iss0vHuMunIWTEtPnEj/MRpOZnUXghM8UMAsBVBifviui HoLtNaz74sSy1L/cZQmeBUHB7kQTH6mvjA4SnnEbkmAj6IgCzwsFZ4gxmLycvsclw//j 8jn97NC9nFB5Eh2HXEEpVxk7qji2Fl8sbCWf/zD/mOOOxY5y5dVMCMDT74nWBpxXlIgz IFBA== X-Gm-Message-State: APzg51DIPUAZrbHOg7OGlmv4Hs1vujpQ5hF2L48zsj4OvO9rH+e/M+nQ 3y9Y2msjnwG1ZWcidLLF5VLxEqk1SZp2+qSy0rM= X-Google-Smtp-Source: ANB0VdZXxITWZltuce0diwz7+5VmgixxETf8CajrElkVGhkAgqA4PX30IlW+l9XXTpgGNGXcekgg1n3SSf9ceG2IX0Y= X-Received: by 2002:a67:3fca:: with SMTP id q71-v6mr9070199vsi.1.1536688275205; Tue, 11 Sep 2018 10:51:15 -0700 (PDT) MIME-Version: 1.0 References: <2e620d305c86f65cbff44b5fba548dc85c118f84.camel@timruffing.de> <20180812163734.GV499@boulet.lan> <20180903000518.GB18522@boulet.lan> In-Reply-To: From: Gregory Maxwell Date: Tue, 11 Sep 2018 17:51:01 +0000 Message-ID: To: Erik Aronesty Content-Type: text/plain; charset="UTF-8" X-Spam-Status: No, score=-1.9 required=5.0 tests=BAYES_00,FREEMAIL_FROM, 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 13:40:16 +0000 Cc: Bitcoin Dev 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 17:51:16 -0000 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.