Return-Path: Received: from smtp1.linuxfoundation.org (smtp1.linux-foundation.org [172.17.192.35]) by mail.linuxfoundation.org (Postfix) with ESMTPS id 09391D3E for ; Mon, 9 Jul 2018 16:22:01 +0000 (UTC) X-Greylist: whitelisted by SQLgrey-1.7.6 Received: from mail-vk0-f54.google.com (mail-vk0-f54.google.com [209.85.213.54]) by smtp1.linuxfoundation.org (Postfix) with ESMTPS id AC567FC for ; Mon, 9 Jul 2018 16:22:00 +0000 (UTC) Received: by mail-vk0-f54.google.com with SMTP id 125-v6so10763320vke.11 for ; Mon, 09 Jul 2018 09:22:00 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025; h=mime-version:sender:in-reply-to:references:from:date:message-id :subject:to; bh=Ccxj57NEv0EtvlmtAygOTbDBCU0SiZ1GmSgzz1a1bOk=; b=AfaAAFnvUQGQJ0lDhdekutOGQ8Nk9wfn/48hRLqckgWWdJredNcXRFo3F3uwojfPaf tXK5UIvl/JGeFl7i0WHcTUiUtnJGXWYcKf0xPlS/V79yJgRAirS5dzUYMqI3tIcW8M61 NWVe2Is1cOhf7Ng6h7dAITCXeOkcZoiJ57hOdrEIANC10NQELPiICzk69/VZ4QqnIc50 PE4mUicUuYI44YnKNuPlRYu0hRFzEiKHpkw1Bx2m0UCLaSXHBUVqpQha2aNd7hrGG0xW 4pN1ImGRhTx6sfyEs1O/n0zVb2szqYqA8ey3ixuARB5vvwR7VFfKw6pbVNrjUF+L59JB v6sw== X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:sender:in-reply-to:references:from :date:message-id:subject:to; bh=Ccxj57NEv0EtvlmtAygOTbDBCU0SiZ1GmSgzz1a1bOk=; b=dEbhIN+OyGLQ5LxIB+XjU2hKqLNSTCk9sURsEgBlwJS3xQPewChbYeletYcVhFgb2i 1vntogoTPVM35l5ywhoFT2fR2kw6nuB7ZYkl6A85DkrPe7xFA46B/yTtMzQ8cxlGhQjo NSRv+TfasPd1wh9/A3gRtqYo2pjvaEtTH17FjY3QQNDjsvt8UGibzOhFCY0XcY0fgjy2 GxaI2u54w37sngVZ+3pfG+lTokVLadyGaskq2voU0wuBhV7YVFlJJv3ATENIbWlfHvC4 UpZfaN2rxLoOf+jNMWLtk6l2rIWk7G2b3x5RGyu+fD8AVVPWR34EFMi6bGi1EvCR+8Fw vU+A== X-Gm-Message-State: APt69E0MmzafgEC1mTUhzdZNDDAaH0ktkvWTMaWkn7UyiCnFj1mF+rqo RoLoXxgj+HF60zb2Erhnz16uVf/gHb86mnGWMyI= X-Google-Smtp-Source: AAOMgpfILpU2cXs4m6gqGJ3rzGb6mGhp6mGk965DgZuaL4G7Q0rH/7iSHoZ0lrK6is69RpAVp9lQRAf4NjNvUiUDXiA= X-Received: by 2002:a1f:9cc4:: with SMTP id f187-v6mr11874306vke.87.1531153319812; Mon, 09 Jul 2018 09:21:59 -0700 (PDT) MIME-Version: 1.0 Sender: gmaxwell@gmail.com Received: by 2002:a67:51c9:0:0:0:0:0 with HTTP; Mon, 9 Jul 2018 09:21:59 -0700 (PDT) In-Reply-To: References: <08201f2292587821e6d23f6cc201d95e6e5ad2cd.camel@timruffing.de> From: Gregory Maxwell Date: Mon, 9 Jul 2018 16:21:59 +0000 X-Google-Sender-Auth: IFbcyZsN53oCln_anbmItiCZ8r0 Message-ID: To: Erik Aronesty , Bitcoin Protocol Discussion Content-Type: text/plain; charset="UTF-8" X-Spam-Status: No, score=-1.9 required=5.0 tests=BAYES_00,DKIM_SIGNED, DKIM_VALID, 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 Subject: Re: [bitcoin-dev] Multiparty signatures 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: Mon, 09 Jul 2018 16:22:01 -0000 On Mon, Jul 9, 2018 at 3:02 PM, Erik Aronesty via bitcoin-dev wrote: > and where H(g*x) can > be considered their public index for the purposes of Shamir polynomial > interpolation This is isomorphic to the insecure musig variant where keys are blinded by H(g*x) instead of a commitment to all keys. It is insecure because it vulnerable to an attacker knowing a victim pubkey P who uses wagner's algorithim to solve a random modular subset sum problem: -1H(P) = H(aP)/a + H(bP)/b + H(cP)/c + ... for some a,b,c... then claiming to be participants with keys aP, bP, cP, ..., xG (their own key) and canceling out key P, allowing the value to just be signed for with their key alone. AFAICT your suggestion is using simple multiplication in the place of a cryptographic hash. E.g. you have just suggested a schnorr signature where H() is just r*m in the field of size n. It doesn't have any new properties about how you can use it. The same linearities do and don't apply as the normal schnorr construction, but for any of the security proofs to hold we'd have to believe that multiplication in the field of n is a suitable random oracle-- which is not very plausible.