From mboxrd@z Thu Jan 1 00:00:00 1970 Received: from sog-mx-4.v43.ch3.sourceforge.com ([172.29.43.194] helo=mx.sourceforge.net) by sfs-ml-2.v29.ch3.sourceforge.com with esmtp (Exim 4.76) (envelope-from ) id 1WW7bA-0008Dp-QF for bitcoin-development@lists.sourceforge.net; Fri, 04 Apr 2014 17:08:12 +0000 Received-SPF: pass (sog-mx-4.v43.ch3.sourceforge.com: domain of gmail.com designates 209.85.217.180 as permitted sender) client-ip=209.85.217.180; envelope-from=gmaxwell@gmail.com; helo=mail-lb0-f180.google.com; Received: from mail-lb0-f180.google.com ([209.85.217.180]) by sog-mx-4.v43.ch3.sourceforge.com with esmtps (TLSv1:RC4-SHA:128) (Exim 4.76) id 1WW7b9-0003XY-Tv for bitcoin-development@lists.sourceforge.net; Fri, 04 Apr 2014 17:08:12 +0000 Received: by mail-lb0-f180.google.com with SMTP id 10so2630669lbg.25 for ; Fri, 04 Apr 2014 10:08:05 -0700 (PDT) MIME-Version: 1.0 X-Received: by 10.112.221.227 with SMTP id qh3mr1204722lbc.55.1396631285312; Fri, 04 Apr 2014 10:08:05 -0700 (PDT) Received: by 10.112.89.68 with HTTP; Fri, 4 Apr 2014 10:08:05 -0700 (PDT) In-Reply-To: <1888881.3JyvKYNUFa@crushinator> References: <12583269.b0SUbSGuCb@crushinator> <1888881.3JyvKYNUFa@crushinator> Date: Fri, 4 Apr 2014 10:08:05 -0700 Message-ID: From: Gregory Maxwell To: Matt Whitlock Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable 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: 1WW7b9-0003XY-Tv 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 17:08:13 -0000 On Fri, Apr 4, 2014 at 9:36 AM, Matt Whitlock wrote= : > Are you proposing to switch from prime fields to a binary field? Because = if you're going to "break up" a secret into little pieces, you can't assume= that every piece of the secret will be strictly less than some 8-bit prime= modulus. And if you're going to do a base conversion, then you have to do = arbitrary-precision integer math anyway, so I don't see that the small fiel= d really saves you any code. Yes, I'm proposing using the binary extension field of GF(2^8). There are many secret sharing and data integrity applications available already operating over GF(2^8) so you can go compare implementation approaches without having to try them our yourself. Obviously anything efficiently encoded as bytes will efficiently encode over GF(2^8). > Weren't you just clamoring for implementation *simplicity* in your previo= us paragraph? :) I do think there is a material difference in complexity that comes in layers rather than at a single point. It's much easier to implement a complex thing that has many individually testable parts then a single complex part. (Implementing arithmetic mod some huge P is quite a bit of work unless you're using some very high level language with integrated bignums=E2=80=94 and are comfortable hoping that their bignums a= re sufficiently consistent with the spec).