[bitcoin-dev] Removing Single Point of Failure with Seed Phrase Storage

Russell O'Connor roconnor at blockstream.com
Fri Mar 6 11:11:11 UTC 2020

On Wed, Feb 26, 2020 at 2:56 PM Jeremy via bitcoin-dev <
bitcoin-dev at lists.linuxfoundation.org> wrote:

> As a replacement for paper, something like this makes sense v.s. what you
> do with a ledger presently.
> However, shamir's shares notoriously have the issue that the key does
> exist plaintext on a device at some point.
> Non-interactive multisig has the benefit of being able to sign
> transactions without having keys in the same room/place/device ever.
> --
> @JeremyRubin <https://twitter.com/JeremyRubin>
> <https://twitter.com/JeremyRubin>

The way I see it, the main benefit of Shamir's Secret Sharing is for those
people who are already willing or wanting to be able to sign transactions
on a single device, in a single room, etc., but would prefer not to keep
their secret backup in a single room/place/device.  It is one thing to go
and gather your shares whenever you need to recover from a broken/wiped
hardware wallet versus having to go gather your shares whenever you want to
make a transaction.  (I do agree that SSS is not a suitabl for creating a
multisig from multiple participants.)

This thread inspired me tidy up and post my concept for creating secret
shares using paper computers (slide charts) and can be found at
https://github.com/roconnor-blockstream/SSS32/blob/master/SSS32.ps. It is a
design for splitting a secret encoded in the Bech32 alphabet into 2-of-n
shares (where n <= 31) using pencil, paper and lookup tables.  There are
numerous issues <https://github.com/roconnor-blockstream/SSS32/issues> and
more that need to be addressed before one could even think about using it
for actual valuable data.  Right now I'm mostly interested to find out if
paper sharing is really feasible.

A secret of 26 random Bech32 characters provides 130 bits of entropy, and a
secret of 51 random Bech32 characters provides 255 bits of entropy.
However, to enable robust recovery, the secret data ought to contain an
error correcting code.  Because each character of the secret is
independently split into shares, any single character error in one of the
shares translates into a single character error in the recovered secret
which can be corrected by the error correcting code.  See the exercise at
the end of "Verifying Bech32 Checksums with Pen and Paper" <
http://r6.ca/blog/20180106T164028Z.html> on how to attach the Bech32 error
correcting code to a raw secret string by hand.  However, protecting the
secret data is so important that one would want to design a checksum BCH
code longer than 6 characters to get strong error correcting capabilities.

I still don't know if this proposed method all a good idea or not.  I've
only experimented with encoding and recovering a 10 character "secret"
data.  Generating 2-of-n shares is quite easy as all the shares are a
function of the secret share and the first random share.  It only takes
lookup up a pair of coordinates in a table to generate one character for
each of the n shares together.  Recovering the secret data is more work;
however, if your plan is to recover a hardware wallet anyways, it is
reasonable for the hardware wallet to do the recovery from the shares
itself for you.  Generating the error correcting code by hand is a bit more
worrying, because it doesn't do you much good if your generate an incorrect
checksum.  However, by doing 1 or 2 manual passes to verify the checksum is
maybe adequate.  Also passing the secret data into the hardware wallet you
wish to use, along with its checksum, would let the hardware wallet tell
you if there was an error in the checksum.  I think creating more general
3-of-n schemes can be implemented too, but require work similar to recovery
to generate rather than the simple lookup table process.  Generating 4-of-n
and higher schemes may also be possible, but would require even more hand
computation (i.e. computing lagrange polynomials.)

Maybe this scheme is workable for the subset of people that this would
appeal to.  In anycase, my document is open source and available for those
who want to tinker with it.
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