[Bitcoin-development] Presenting a BIP for Shamir's Secret Sharing of Bitcoin private keys
Gregory Maxwell
gmaxwell at gmail.com
Fri Apr 4 17:08:05 UTC 2014
On Fri, Apr 4, 2014 at 9:36 AM, Matt Whitlock <bip at mattwhitlock.name> 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 field 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 previous 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— and are comfortable hoping that their bignums are
sufficiently consistent with the spec).
More information about the bitcoin-dev
mailing list