From: Matt Whitlock <bip@mattwhitlock.name>
To: Gregory Maxwell <gmaxwell@gmail.com>
Date: Fri, 04 Apr 2014 13:16:27 -0400
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Cc: bitcoin-development <bitcoin-development@lists.sourceforge.net>
Subject: Re: [Bitcoin-development] Presenting a BIP for Shamir's Secret
	Sharing of Bitcoin private keys
Precedence: list

On Friday, 4 April 2014, at 10:08 am, Gregory Maxwell wrote:
> On Fri, Apr 4, 2014 at 9:36 AM, Matt Whitlock <bip@mattwhitlock.name>=
 wrote:
> > Are you proposing to switch from prime fields to a binary field? Be=
cause if you're going to "break up" a secret into little pieces, you ca=
n't assume that every piece of the secret will be strictly less than so=
me 8-bit prime modulus. And if you're going to do a base conversion, th=
en you have to do arbitrary-precision integer math anyway, so I don't s=
ee that the small field really saves you any code.
>=20
> Yes, I'm proposing using the binary extension field of GF(2^8).  Ther=
e
> 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 anythin=
g
> efficiently encoded as bytes will efficiently encode over GF(2^8).

Honestly, that sounds a lot more complicated than what I have now. I ma=
de my current implementation because I just wanted something simple tha=
t would let me divide a private key into shares for purposes of dissemi=
nation to my next of kin et al.

> > Weren't you just clamoring for implementation *simplicity* in your =
previous paragraph? :)
>=20
> 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 big=
nums are
> sufficiently consistent with the spec).

I already have a fairly polished implementation of my BIP, and it's not=
 written in a "very high-level language"; it's C++, and the parts that =
do the big-integer arithmetic are basically C. I'm using the GMP librar=
y: very straightforward, very reliable, very fast.

Do you have a use case in mind that would benefit from byte-wise operat=
ions rather than big-integer operations? I mean, I guess if you were tr=
ying to implement this BIP on a PIC microcontroller, it might be nice t=
o process the secret in smaller bites. (No pun intended.) But I get thi=
s feeling that you're only pushing me away from the present incarnation=
 of my proposal because you think it's too similar (but not quite simil=
ar enough) to a threshold ECDSA key scheme.