Received: from sog-mx-1.v43.ch3.sourceforge.com ([172.29.43.191] helo=mx.sourceforge.net) by sfs-ml-3.v29.ch3.sourceforge.com with esmtp (Exim 4.76) (envelope-from ) id 1WW4st-0008JR-Oi for bitcoin-development@lists.sourceforge.net; Fri, 04 Apr 2014 14:14:19 +0000 Received-SPF: pass (sog-mx-1.v43.ch3.sourceforge.com: domain of gmail.com designates 209.85.215.47 as permitted sender) client-ip=209.85.215.47; envelope-from=gmaxwell@gmail.com; helo=mail-la0-f47.google.com; Received: from mail-la0-f47.google.com ([209.85.215.47]) by sog-mx-1.v43.ch3.sourceforge.com with esmtps (TLSv1:RC4-SHA:128) (Exim 4.76) id 1WW4ss-0003Tj-Sq for bitcoin-development@lists.sourceforge.net; Fri, 04 Apr 2014 14:14:19 +0000 Received: by mail-la0-f47.google.com with SMTP id pn19so2504177lab.20 for ; Fri, 04 Apr 2014 07:14:12 -0700 (PDT) MIME-Version: 1.0 X-Received: by 10.152.243.35 with SMTP id wv3mr1424559lac.47.1396620852282; Fri, 04 Apr 2014 07:14:12 -0700 (PDT) Received: by 10.112.89.68 with HTTP; Fri, 4 Apr 2014 07:14:12 -0700 (PDT) In-Reply-To: References: <3837746.jqWvB0Uxrs@crushinator> Date: Fri, 4 Apr 2014 07:14:12 -0700 Message-ID: From: Gregory Maxwell To: Nikita Schmidt Content-Type: text/plain; charset=UTF-8 X-Spam-Score: -1.6 (-) X-Spam-Report: Spam Filtering performed by mx.sourceforge.net. See http://spamassassin.org/tag/ for more details. -1.5 SPF_CHECK_PASS SPF reports sender host as permitted sender for sender-domain 0.0 FREEMAIL_FROM Sender email is commonly abused enduser mail provider (gmaxwell[at]gmail.com) -0.0 SPF_PASS SPF: sender matches SPF record -0.1 DKIM_VALID_AU Message has a valid DKIM or DK signature from author's domain 0.1 DKIM_SIGNED Message has a DKIM or DK signature, not necessarily valid -0.1 DKIM_VALID Message has at least one valid DKIM or DK signature X-Headers-End: 1WW4ss-0003Tj-Sq Cc: bitcoin-development Subject: Re: [Bitcoin-development] Presenting a BIP for Shamir's Secret Sharing of Bitcoin private keys X-BeenThere: bitcoin-development@lists.sourceforge.net X-Mailman-Version: 2.1.9 Precedence: list List-Id: List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Fri, 04 Apr 2014 14:14:19 -0000 On Fri, Apr 4, 2014 at 6:51 AM, Nikita Schmidt wrote: > Fair enough. Although I would have chosen the field order (p) simply > because that's how all arithmetic already works in bitcoin. One field > for everybody. It's also very close to 2^256, although still smaller > than your maximum prime. Now of course with different bit lengths we > have to pick one consistency over others. Operation mod the group order is how secret keys must be combined in type-2 private derivation for BIP-32. It's also absolutely essential if you want to build a secret sharing scheme in which the shares are usable for threshold ECDSA. I still repeat my concern that any private key secret sharing scheme really ought to be compatible with threshold ECDSA, otherwise we're just going to have another redundant specification.