[Bitcoin-development] Presenting a BIP for Shamir's Secret Sharing of Bitcoin private keys

[Matt Whitlock]

On Monday, 7 April 2014, at 7:07 pm, Gregory Maxwell wrote:
> On Mon, Apr 7, 2014 at 6:46 PM, Matt Whitlock <bip at mattwhitlock.name> wrote:
> > On Monday, 7 April 2014, at 5:38 pm, Gregory Maxwell wrote:
> >> On Mon, Apr 7, 2014 at 5:33 PM, Nikita Schmidt
> >> <nikita at megiontechnologies.com> wrote:
> >> > Regarding the choice of fields, any implementation of this BIP will
> >> > need big integer arithmetic to do base-58 anyway.
> >> Nah, it doesn't. E.g.
> >> https://gitorious.org/bitcoin/libblkmaker/source/eb33f9c8e441ffef457a79d76ceed1ea20ab3059:base58.c
> > That only *decodes* Base58Check. It has no encode function, which would require biginteger division.
> 
> Yes thats only a decode but the same process (long division with
> manual carries) works just fine the other way. There is absolutely no
> need to use big integers for this.

What do you think a big-integer division by a word-sized divisor *is*? Obviously rolling your own is always an option. Are you just saying that Base58 encoding and decoding is easier than Shamir's Secret Sharing because the divisors are small?